fem_tools.h File Reference

Loose implementation of some useful functions. More...

#include <petscsys.h>
#include <cblas.h>
#include <lapack_wrap.h>

Go to the source code of this file.

Macros
#define	LAMBDA(E, NU)
#define	MU(E, NU)
#define	DELTA(NU_P, NU_PZ, E_P, E_Z)
#define	N_MBTET0(x, y, z)
	tetrahedral shape function
#define	N_MBTET1(x, y, z)
	tetrahedral shape function
#define	N_MBTET2(x, y, z)
	tetrahedral shape function
#define	N_MBTET3(x, y, z)
	tetrahedral shape function
#define	diffN_MBTET0x   (-1.)
	derivative of tetrahedral shape function
#define	diffN_MBTET0y   (-1.)
	derivative of tetrahedral shape function
#define	diffN_MBTET0z   (-1.)
	derivative of tetrahedral shape function
#define	diffN_MBTET1x   (1.)
	derivative of tetrahedral shape function
#define	diffN_MBTET1y   (0.)
	derivative of tetrahedral shape function
#define	diffN_MBTET1z   (0.)
	derivative of tetrahedral shape function
#define	diffN_MBTET2x   (0.)
	derivative of tetrahedral shape function
#define	diffN_MBTET2y   (1.)
	derivative of tetrahedral shape function
#define	diffN_MBTET2z   (0.)
	derivative of tetrahedral shape function
#define	diffN_MBTET3x   (0.)
	derivative of tetrahedral shape function
#define	diffN_MBTET3y   (0.)
	derivative of tetrahedral shape function
#define	diffN_MBTET3z   (1.)
	derivative of tetrahedral shape function
#define	N_MBTRI0(x, y)
	triangle shape function
#define	N_MBTRI1(x, y)
	triangle shape function
#define	N_MBTRI2(x, y)
	triangle shape function
#define	diffN_MBTRI0x   (-1.)
	derivative of triangle shape function
#define	diffN_MBTRI0y   (-1.)
	derivative of triangle shape function
#define	diffN_MBTRI1x   (1.)
	derivative of triangle shape function
#define	diffN_MBTRI1y   (0.)
	derivative of triangle shape function
#define	diffN_MBTRI2x   (0.)
	derivative of triangle shape function
#define	diffN_MBTRI2y   (1.)
	derivative of triangle shape function
#define	N_MBQUAD0(x, y)
	quad shape function
#define	N_MBQUAD1(x, y)
	quad shape function
#define	N_MBQUAD2(x, y)
	quad shape function
#define	N_MBQUAD3(x, y)
	quad shape function
#define	diffN_MBQUAD0x(y)
#define	diffN_MBQUAD0y(x)
#define	diffN_MBQUAD1x(y)
#define	diffN_MBQUAD1y(x)
#define	diffN_MBQUAD2x(y)
#define	diffN_MBQUAD2y(x)
#define	diffN_MBQUAD3x(y)
#define	diffN_MBQUAD3y(x)
#define	N_MBHEX0(x, y, z)
#define	N_MBHEX1(x, y, z)
#define	N_MBHEX2(x, y, z)
#define	N_MBHEX3(x, y, z)
#define	N_MBHEX4(x, y, z)
#define	N_MBHEX5(x, y, z)
#define	N_MBHEX6(x, y, z)
#define	N_MBHEX7(x, y, z)
#define	diffN_MBHEX0x(y, z)
#define	diffN_MBHEX1x(y, z)
#define	diffN_MBHEX2x(y, z)
#define	diffN_MBHEX3x(y, z)
#define	diffN_MBHEX4x(y, z)
#define	diffN_MBHEX5x(y, z)
#define	diffN_MBHEX6x(y, z)
#define	diffN_MBHEX7x(y, z)
#define	diffN_MBHEX0y(x, z)
#define	diffN_MBHEX1y(x, z)
#define	diffN_MBHEX2y(x, z)
#define	diffN_MBHEX3y(x, z)
#define	diffN_MBHEX4y(x, z)
#define	diffN_MBHEX5y(x, z)
#define	diffN_MBHEX6y(x, z)
#define	diffN_MBHEX7y(x, z)
#define	diffN_MBHEX0z(x, y)
#define	diffN_MBHEX1z(x, y)
#define	diffN_MBHEX2z(x, y)
#define	diffN_MBHEX3z(x, y)
#define	diffN_MBHEX4z(x, y)
#define	diffN_MBHEX5z(x, y)
#define	diffN_MBHEX6z(x, y)
#define	diffN_MBHEX7z(x, y)
#define	N_MBEDGE0(x)
	edge shape function
#define	N_MBEDGE1(x)
	edge shape function
#define	diffN_MBEDGE0   (-1.)
	derivative of edge shape function
#define	diffN_MBEDGE1   (1.)
	derivative of edge shape function
#define	N_MBTRIQ0(x, y)
#define	N_MBTRIQ1(x, y)
#define	N_MBTRIQ2(x, y)
#define	N_MBTRIQ3(x, y)
#define	N_MBTRIQ4(x, y)
#define	N_MBTRIQ5(x, y)
#define	diffN_MBTRIQ0x(x, y)
#define	diffN_MBTRIQ0y(x, y)
#define	diffN_MBTRIQ1x(x, y)
#define	diffN_MBTRIQ1y(x, y)
#define	diffN_MBTRIQ2x(x, y)
#define	diffN_MBTRIQ2y(x, y)
#define	diffN_MBTRIQ3x(x, y)
#define	diffN_MBTRIQ3y(x, y)
#define	diffN_MBTRIQ4x(x, y)
#define	diffN_MBTRIQ4y(x, y)
#define	diffN_MBTRIQ5x(x, y)
#define	diffN_MBTRIQ5y(x, y)

Functions
void	print_mat (double *M, int m, int n)
	print matric M
void	print_mat_sym_upper (double *M, int m, int n)
	print upper part of the symmetric matrix
void	print_mat_complex (__CLPK_doublecomplex *M, int m, int n)
	priint complex matrix
PetscErrorCode	ShapeMBTRI (double *N, const double *X, const double *Y, const int G_DIM)
	calculate shape functions on triangle
PetscErrorCode	ShapeDiffMBTRI (double *diffN)
	calculate derivatives of shape functions
PetscErrorCode	ShapeFaceNormalMBTRI (double *diffN, const double *coords, double *normal)
PetscErrorCode	ShapeFaceBaseMBTRI (double *diffN, const double *coords, double *normal, double *s1, double *s2)
PetscErrorCode	ShapeFaceDiffNormalMBTRI (double *diffN, const double *coords, double *diff_normal)
	calculate derivative of normal in respect to nodal positions
void	ShapeJacMBTRI (double *diffN, const double *coords, double *Jac)
	calculate jacobioan
void	ShapeDiffMBTRIinvJ (double *diffN, double *invJac, double *diffNinvJac)
	calculate derivatives of shape functions in space
PetscErrorCode	ShapeMBTET (double *N, const double *G_X, const double *G_Y, const double *G_Z, int DIM)
	calculate shape functions
PetscErrorCode	ShapeDiffMBTET (double *diffN)
	calculate derivatives of shape functions
double	ShapeDetJacVolume (double *jac)
	determined of jacobian
PetscErrorCode	ShapeJacMBTET (double *diffN, const double *coords, double *jac)
	calculate jacobian
PetscErrorCode	ShapeInvJacVolume (double *jac)
double	ShapeVolumeMBTET (double *diffN, const double *coords)
	calculate TET volume
PetscErrorCode	ShapeDiffMBTETinvJ (double *diffN, double *invJac, double *diffNinvJac)
	calculate shape functions derivatives in space
PetscErrorCode	Spin (double *spinOmega, double *vecOmega)
	calculate spin matrix from vector
PetscErrorCode	make_complex_matrix (double *reA, double *imA, __CLPK_doublecomplex *xA)
	Compose complex matrix (3x3) from two real matrices.
PetscErrorCode	Normal_hierarchical (int order_approx, int *order_edge_approx, int order, int *order_edge, double *diffN, double *diffN_face, double *diffN_edge[], double *dofs, double *dofs_edge[], double *dofs_face, double *idofs, double *idofs_edge[], double *idofs_face, __CLPK_doublecomplex *xnormal, __CLPK_doublecomplex *s1, __CLPK_doublecomplex *s2, int gg)
	Complex normal.
PetscErrorCode	Base_scale (__CLPK_doublecomplex *xnormal, __CLPK_doublecomplex *xs1, __CLPK_doublecomplex *xs2)
PetscErrorCode	ShapeMBTET_inverse (double *N, double *diffN, const double *elem_coords, const double *glob_coords, double *loc_coords)
	calculate local coordinates for given global coordinates
PetscErrorCode	ShapeMBTRI_inverse (double *N, double *diffN, const double *elem_coords, const double *glob_coords, double *loc_coords)
	calculate local coordinates of triangle element for given global coordinates in 2D (Assume e.g. z=0)
PetscErrorCode	GradientOfDeformation (double *diffN, double *dofs, double *F)
	calculate gradient of deformation
PetscErrorCode	ShapeMBEDGE (double *N, const double *G_X, int DIM)
PetscErrorCode	ShapeDiffMBEDGE (double *diffN)
PetscErrorCode	ShapeMBTRIQ (double *N, const double *X, const double *Y, const int G_DIM)
PetscErrorCode	ShapeDiffMBTRIQ (double *diffN, const double *X, const double *Y, const int G_DIM)
PetscErrorCode	ShapeMBTETQ (double *N, const double x, const double y, const double z)
PetscErrorCode	ShapeDiffMBTETQ (double *diffN, const double x, const double y, const double z)
PetscErrorCode	ShapeMBTETQ_GAUSS (double *N, const double *X, const double *Y, const double *Z, const int G_DIM)
PetscErrorCode	ShapeDiffMBTETQ_GAUSS (double *diffN, const double *X, const double *Y, const double *Z, const int G_DIM)
PetscErrorCode	ShapeJacMBTETQ (const double *diffN, const double *coords, double *Jac)
PetscErrorCode	ShapeMBTETQ_detJac_at_Gauss_Points (double *detJac_at_Gauss_Points, const double *diffN, const double *coords, int G_DIM)
double	ShapeVolumeMBTETQ (const double *diffN, const double *coords, int G_DIM, double *G_TET_W)
PetscErrorCode	ShapeMBTETQ_inverse (double *N, double *diffN, const double *elem_coords, const double *glob_coords, double *loc_coords, const double eps)
void	ShapeDiffMBTETinvJ_complex (double *diffN, __CLPK_doublecomplex *invJac, __CLPK_doublecomplex *diffNinvJac, enum CBLAS_TRANSPOSE Trans)
PetscErrorCode	ShapeFaceNormalMBTRI_complex (double *diffN, __CLPK_doublecomplex *xcoords, __CLPK_doublecomplex *xnormal)
PetscErrorCode	MakeComplexTensor (double *reA, double *imA, __CLPK_doublecomplex *xA)
PetscErrorCode	InvertComplexGradient (__CLPK_doublecomplex *xF)
PetscErrorCode	DeterminantComplexGradient (__CLPK_doublecomplex *xF, __CLPK_doublecomplex *det_xF)
PetscErrorCode	Grundmann_Moeller_integration_points_1D_EDGE (int rule, double *G_TRI_X, double *G_TRI_W)
	Compute weights and integration points for edge using Grundmann_Moeller rule.
PetscErrorCode	Grundmann_Moeller_integration_points_2D_TRI (int rule, double *G_TRI_X, double *G_TRI_Y, double *G_TRI_W)
PetscErrorCode	Grundmann_Moeller_integration_points_3D_TET (int rule, double *G_TET_X, double *G_TET_Y, double *G_TET_Z, double *G_TET_W)

Variables
static const double	G_TRI_X1 [] = {3.3333333333333331e-01}
static const double	G_TRI_Y1 [] = {3.3333333333333331e-01}
static const double	G_TRI_W1 [] = {1.}
static const double	G_TRI_X3 [] = {0.5, 0., 0.5}
static const double	G_TRI_Y3 [] = {0., 0.5, 0.5}
static const double	G_TRI_W3 []
static const double	G_TRI_X4 []
static const double	G_TRI_Y4 []
static const double	G_TRI_W4 []
static const double	G_TRI_X7 []
static const double	G_TRI_Y7 []
static const double	G_TRI_W7 []
static const double	G_TRI_X13 []
static const double	G_TRI_Y13 []
static const double	G_TRI_W13 []
static const double	G_TRI_X19 []
static const double	G_TRI_Y19 []
static const double	G_TRI_W19 []
static const double	G_TRI_X28 []
static const double	G_TRI_Y28 []
static const double	G_TRI_W28 []
static const double	G_TRI_X37 []
static const double	G_TRI_Y37 []
static const double	G_TRI_W37 []
static const double	G_TRI_X286 []
static const double	G_TRI_Y286 []
static const double	G_TRI_W286 []
static const double	G_TET_X1 [] = {0.25}
static const double	G_TET_Y1 [] = {0.25}
static const double	G_TET_Z1 [] = {0.25}
static const double	G_TET_W1 [] = {1.}
static const double	G_TET_X4 []
static const double	G_TET_Y4 []
static const double	G_TET_Z4 []
static const double	G_TET_W4 [] = {0.25, 0.25, 0.25, 0.25}
static const double	G_TET_X5 []
static const double	G_TET_Y5 []
static const double	G_TET_Z5 []
static const double	G_TET_W5 []
static const double	G_TET_X10 []
static const double	G_TET_Y10 []
static const double	G_TET_Z10 []
static const double	G_TET_W10 []
static const double	G_TET_X45 []
static const double	G_TET_Y45 []
static const double	G_TET_Z45 []
static const double	G_TET_W45 []
static const double	NC_TET_X84 []
static const double	NC_TET_Y84 []
static const double	NC_TET_Z84 []
static const double	NC_TET_W84 []

Detailed Description

Loose implementation of some useful functions.

FIXME: Implementation here is very unstructured, need cleaning and pruning

Definition in file fem_tools.h.

Macro Definition Documentation

DELTA

#define DELTA	(		NU_P,
			NU_PZ,
			E_P,
			E_Z )

Value:

  (((1 + NU_P) * (1 - NU_P - 2 * NU_PZ * (NU_PZ * E_Z / E_P))) /               \
   (E_P * E_P * E_Z))

Definition at line 24 of file fem_tools.h.

#define DELTA(NU_P, NU_PZ, E_P, E_Z)                                           \
  (((1 + NU_P) * (1 - NU_P - 2 * NU_PZ * (NU_PZ * E_Z / E_P))) /               \
   (E_P * E_P * E_Z))

diffN_MBEDGE0

#define diffN_MBEDGE0   (-1.)

derivative of edge shape function

Definition at line 107 of file fem_tools.h.

diffN_MBEDGE1

#define diffN_MBEDGE1   (1.)

derivative of edge shape function

Definition at line 108 of file fem_tools.h.

diffN_MBHEX0x

#define diffN_MBHEX0x	(		y,
			z )

Value:

(diffN_MBQUAD0x(y) * (1 - z))

Definition at line 79 of file fem_tools.h.

diffN_MBHEX0y

#define diffN_MBHEX0y	(		x,
			z )

Value:

(diffN_MBQUAD0y(x) * (1 - z))

Definition at line 87 of file fem_tools.h.

diffN_MBHEX0z

#define diffN_MBHEX0z	(		x,
			y )

Value:

(-N_MBQUAD0(x, y))

Definition at line 95 of file fem_tools.h.

diffN_MBHEX1x

#define diffN_MBHEX1x	(		y,
			z )

Value:

(diffN_MBQUAD1x(y) * (1 - z))

Definition at line 80 of file fem_tools.h.

diffN_MBHEX1y

#define diffN_MBHEX1y	(		x,
			z )

Value:

(diffN_MBQUAD1y(x) * (1 - z))

Definition at line 88 of file fem_tools.h.

diffN_MBHEX1z

#define diffN_MBHEX1z	(		x,
			y )

Value:

(-N_MBQUAD1(x, y))

Definition at line 96 of file fem_tools.h.

diffN_MBHEX2x

#define diffN_MBHEX2x	(		y,
			z )

Value:

(diffN_MBQUAD2x(y) * (1 - z))

Definition at line 81 of file fem_tools.h.

diffN_MBHEX2y

#define diffN_MBHEX2y	(		x,
			z )

Value:

(diffN_MBQUAD2y(x) * (1 - z))

Definition at line 89 of file fem_tools.h.

diffN_MBHEX2z

#define diffN_MBHEX2z	(		x,
			y )

Value:

(-N_MBQUAD2(x, y))

Definition at line 97 of file fem_tools.h.

diffN_MBHEX3x

#define diffN_MBHEX3x	(		y,
			z )

Value:

(diffN_MBQUAD3x(y) * (1 - z))

Definition at line 82 of file fem_tools.h.

diffN_MBHEX3y

#define diffN_MBHEX3y	(		x,
			z )

Value:

(diffN_MBQUAD3y(x) * (1 - z))

Definition at line 90 of file fem_tools.h.

diffN_MBHEX3z

#define diffN_MBHEX3z	(		x,
			y )

Value:

(-N_MBQUAD3(x, y))

Definition at line 98 of file fem_tools.h.

diffN_MBHEX4x

#define diffN_MBHEX4x	(		y,
			z )

Value:

(diffN_MBQUAD0x(y) * (z))

Definition at line 83 of file fem_tools.h.

diffN_MBHEX4y

#define diffN_MBHEX4y	(		x,
			z )

Value:

(diffN_MBQUAD0y(x) * (z))

Definition at line 91 of file fem_tools.h.

diffN_MBHEX4z

#define diffN_MBHEX4z	(		x,
			y )

Value:

(N_MBQUAD0(x, y))

Definition at line 99 of file fem_tools.h.

diffN_MBHEX5x

#define diffN_MBHEX5x	(		y,
			z )

Value:

(diffN_MBQUAD1x(y) * (z))

Definition at line 84 of file fem_tools.h.

diffN_MBHEX5y

#define diffN_MBHEX5y	(		x,
			z )

Value:

(diffN_MBQUAD1y(x) * (z))

Definition at line 92 of file fem_tools.h.

diffN_MBHEX5z

#define diffN_MBHEX5z	(		x,
			y )

Value:

(N_MBQUAD1(x, y))

Definition at line 100 of file fem_tools.h.

diffN_MBHEX6x

#define diffN_MBHEX6x	(		y,
			z )

Value:

(diffN_MBQUAD2x(y) * (z))

Definition at line 85 of file fem_tools.h.

diffN_MBHEX6y

#define diffN_MBHEX6y	(		x,
			z )

Value:

(diffN_MBQUAD2y(x) * (z))

Definition at line 93 of file fem_tools.h.

diffN_MBHEX6z

#define diffN_MBHEX6z	(		x,
			y )

Value:

(N_MBQUAD2(x, y))

Definition at line 101 of file fem_tools.h.

diffN_MBHEX7x

#define diffN_MBHEX7x	(		y,
			z )

Value:

(diffN_MBQUAD3x(y) * (z))

Definition at line 86 of file fem_tools.h.

diffN_MBHEX7y

#define diffN_MBHEX7y	(		x,
			z )

Value:

(diffN_MBQUAD3y(x) * (z))

Definition at line 94 of file fem_tools.h.

diffN_MBHEX7z

#define diffN_MBHEX7z	(		x,
			y )

Value:

(N_MBQUAD3(x, y))

Definition at line 102 of file fem_tools.h.

diffN_MBQUAD0x

#define diffN_MBQUAD0x

(

y

)

Value:

(-(1. - y))

Examples

edge_and_bubble_shape_functions_on_quad.cpp.

Definition at line 61 of file fem_tools.h.

diffN_MBQUAD0y

#define diffN_MBQUAD0y

(

x

)

Value:

(-(1. - x))

Examples

edge_and_bubble_shape_functions_on_quad.cpp.

Definition at line 62 of file fem_tools.h.

diffN_MBQUAD1x

#define diffN_MBQUAD1x

(

y

)

Value:

((1. - y))

Examples

edge_and_bubble_shape_functions_on_quad.cpp.

Definition at line 63 of file fem_tools.h.

diffN_MBQUAD1y

#define diffN_MBQUAD1y

(

x

)

Value:

(-x)

Examples

edge_and_bubble_shape_functions_on_quad.cpp.

Definition at line 64 of file fem_tools.h.

diffN_MBQUAD2x

#define diffN_MBQUAD2x

(

y

)

Value:

(y)

Examples

edge_and_bubble_shape_functions_on_quad.cpp.

Definition at line 65 of file fem_tools.h.

diffN_MBQUAD2y

#define diffN_MBQUAD2y

(

x

)

Value:

(x)

Examples

edge_and_bubble_shape_functions_on_quad.cpp.

Definition at line 66 of file fem_tools.h.

diffN_MBQUAD3x

#define diffN_MBQUAD3x

(

y

)

Value:

(-y)

Examples

edge_and_bubble_shape_functions_on_quad.cpp.

Definition at line 67 of file fem_tools.h.

diffN_MBQUAD3y

#define diffN_MBQUAD3y

(

x

)

Value:

((1. - x))

Examples

edge_and_bubble_shape_functions_on_quad.cpp.

Definition at line 68 of file fem_tools.h.

diffN_MBTET0x

#define diffN_MBTET0x   (-1.)

derivative of tetrahedral shape function

Definition at line 32 of file fem_tools.h.

diffN_MBTET0y

#define diffN_MBTET0y   (-1.)

derivative of tetrahedral shape function

Definition at line 33 of file fem_tools.h.

diffN_MBTET0z

#define diffN_MBTET0z   (-1.)

derivative of tetrahedral shape function

Definition at line 34 of file fem_tools.h.

diffN_MBTET1x

#define diffN_MBTET1x   (1.)

derivative of tetrahedral shape function

Definition at line 35 of file fem_tools.h.

diffN_MBTET1y

#define diffN_MBTET1y   (0.)

derivative of tetrahedral shape function

Definition at line 36 of file fem_tools.h.

diffN_MBTET1z

#define diffN_MBTET1z   (0.)

derivative of tetrahedral shape function

Definition at line 37 of file fem_tools.h.

diffN_MBTET2x

#define diffN_MBTET2x   (0.)

derivative of tetrahedral shape function

Definition at line 38 of file fem_tools.h.

diffN_MBTET2y

#define diffN_MBTET2y   (1.)

derivative of tetrahedral shape function

Definition at line 39 of file fem_tools.h.

diffN_MBTET2z

#define diffN_MBTET2z   (0.)

derivative of tetrahedral shape function

Definition at line 40 of file fem_tools.h.

diffN_MBTET3x

#define diffN_MBTET3x   (0.)

derivative of tetrahedral shape function

Definition at line 41 of file fem_tools.h.

diffN_MBTET3y

#define diffN_MBTET3y   (0.)

derivative of tetrahedral shape function

Definition at line 42 of file fem_tools.h.

diffN_MBTET3z

#define diffN_MBTET3z   (1.)

derivative of tetrahedral shape function

Definition at line 43 of file fem_tools.h.

diffN_MBTRI0x

#define diffN_MBTRI0x   (-1.)

derivative of triangle shape function

Definition at line 49 of file fem_tools.h.

diffN_MBTRI0y

#define diffN_MBTRI0y   (-1.)

derivative of triangle shape function

Definition at line 50 of file fem_tools.h.

diffN_MBTRI1x

#define diffN_MBTRI1x   (1.)

derivative of triangle shape function

Definition at line 51 of file fem_tools.h.

diffN_MBTRI1y

#define diffN_MBTRI1y   (0.)

derivative of triangle shape function

Definition at line 52 of file fem_tools.h.

diffN_MBTRI2x

#define diffN_MBTRI2x   (0.)

derivative of triangle shape function

Definition at line 53 of file fem_tools.h.

diffN_MBTRI2y

#define diffN_MBTRI2y   (1.)

derivative of triangle shape function

Definition at line 54 of file fem_tools.h.

diffN_MBTRIQ0x

#define diffN_MBTRIQ0x	(		x,
			y )

Value:

(x + y - 3. * (1. - x - y))

Definition at line 117 of file fem_tools.h.

diffN_MBTRIQ0y

#define diffN_MBTRIQ0y	(		x,
			y )

Value:

(x + y - 3. * (1. - x - y))

Definition at line 118 of file fem_tools.h.

diffN_MBTRIQ1x

#define diffN_MBTRIQ1x	(		x,
			y )

Value:

(-1. + 4. * x)

Definition at line 119 of file fem_tools.h.

diffN_MBTRIQ1y

#define diffN_MBTRIQ1y	(		x,
			y )

Value:

(0.)

Definition at line 120 of file fem_tools.h.

diffN_MBTRIQ2x

#define diffN_MBTRIQ2x	(		x,
			y )

Value:

(0.)

Definition at line 121 of file fem_tools.h.

diffN_MBTRIQ2y

#define diffN_MBTRIQ2y	(		x,
			y )

Value:

(-1. + 4. * y)

Definition at line 122 of file fem_tools.h.

diffN_MBTRIQ3x

#define diffN_MBTRIQ3x	(		x,
			y )

Value:

(4. * ((1. - x - y) - x))

Definition at line 123 of file fem_tools.h.

diffN_MBTRIQ3y

#define diffN_MBTRIQ3y	(		x,
			y )

Value:

(-4. * x)

Definition at line 124 of file fem_tools.h.

diffN_MBTRIQ4x

#define diffN_MBTRIQ4x	(		x,
			y )

Value:

(4. * y)

Definition at line 125 of file fem_tools.h.

diffN_MBTRIQ4y

#define diffN_MBTRIQ4y	(		x,
			y )

Value:

(4. * x)

Definition at line 126 of file fem_tools.h.

diffN_MBTRIQ5x

#define diffN_MBTRIQ5x	(		x,
			y )

Value:

(-4. * y)

Definition at line 127 of file fem_tools.h.

diffN_MBTRIQ5y

#define diffN_MBTRIQ5y	(		x,
			y )

Value:

(4. * ((1. - x - y) - y))

Definition at line 128 of file fem_tools.h.

LAMBDA

#define LAMBDA	(		E,
			NU )

Value:

(E * NU / ((1. + NU) * (1. - 2. * NU)))

Examples

ADOLCPlasticityMaterialModels.hpp, NeoHookean.hpp, Remodeling.cpp, and ep.cpp.

Definition at line 22 of file fem_tools.h.

MU

#define MU	(		E,
			NU )

Value:

(0.5 * E / (1. + NU))

Examples

ADOLCPlasticityMaterialModels.hpp, NeoHookean.hpp, Remodeling.cpp, and ep.cpp.

Definition at line 23 of file fem_tools.h.

N_MBEDGE0

#define N_MBEDGE0

(

x

)

Value:

(1. - (x))

edge shape function

Examples

bernstein_bezier_generate_base.cpp.

Definition at line 105 of file fem_tools.h.

N_MBEDGE1

#define N_MBEDGE1

(

x

)

Value:

(x)

edge shape function

Examples

bernstein_bezier_generate_base.cpp.

Definition at line 106 of file fem_tools.h.

N_MBHEX0

#define N_MBHEX0	(		x,
			y,
			z )

Value:

(N_MBQUAD0(x, y) * (1 - z))

Examples

plot_base.cpp.

Definition at line 71 of file fem_tools.h.

N_MBHEX1

#define N_MBHEX1	(		x,
			y,
			z )

Value:

(N_MBQUAD1(x, y) * (1 - z))

Examples

plot_base.cpp.

Definition at line 72 of file fem_tools.h.

N_MBHEX2

#define N_MBHEX2	(		x,
			y,
			z )

Value:

(N_MBQUAD2(x, y) * (1 - z))

Examples

plot_base.cpp.

Definition at line 73 of file fem_tools.h.

N_MBHEX3

#define N_MBHEX3	(		x,
			y,
			z )

Value:

(N_MBQUAD3(x, y) * (1 - z))

Examples

plot_base.cpp.

Definition at line 74 of file fem_tools.h.

N_MBHEX4

#define N_MBHEX4	(		x,
			y,
			z )

Value:

(N_MBQUAD0(x, y) * (z))

Examples

plot_base.cpp.

Definition at line 75 of file fem_tools.h.

N_MBHEX5

#define N_MBHEX5	(		x,
			y,
			z )

Value:

(N_MBQUAD1(x, y) * (z))

Examples

plot_base.cpp.

Definition at line 76 of file fem_tools.h.

N_MBHEX6

#define N_MBHEX6	(		x,
			y,
			z )

Value:

(N_MBQUAD2(x, y) * (z))

Examples

plot_base.cpp.

Definition at line 77 of file fem_tools.h.

N_MBHEX7

#define N_MBHEX7	(		x,
			y,
			z )

Value:

(N_MBQUAD3(x, y) * (z))

Examples

plot_base.cpp.

Definition at line 78 of file fem_tools.h.

N_MBQUAD0

#define N_MBQUAD0	(		x,
			y )

Value:

((1. - x) * (1. - y))

quad shape function

Examples

edge_and_bubble_shape_functions_on_quad.cpp, and plot_base.cpp.

Definition at line 57 of file fem_tools.h.

N_MBQUAD1

#define N_MBQUAD1	(		x,
			y )

Value:

((x) * (1. - y))

quad shape function

Examples

edge_and_bubble_shape_functions_on_quad.cpp, and plot_base.cpp.

Definition at line 58 of file fem_tools.h.

N_MBQUAD2

#define N_MBQUAD2	(		x,
			y )

Value:

((x) * (y))

quad shape function

Examples

edge_and_bubble_shape_functions_on_quad.cpp, and plot_base.cpp.

Definition at line 59 of file fem_tools.h.

N_MBQUAD3

#define N_MBQUAD3	(		x,
			y )

Value:

((1. - x) * (y))

quad shape function

Examples

edge_and_bubble_shape_functions_on_quad.cpp, and plot_base.cpp.

Definition at line 60 of file fem_tools.h.

N_MBTET0

#define N_MBTET0	(		x,
			y,
			z )

Value:

(1. - x - y - z)

tetrahedral shape function

Definition at line 28 of file fem_tools.h.

N_MBTET1

#define N_MBTET1	(		x,
			y,
			z )

Value:

(x)

tetrahedral shape function

Definition at line 29 of file fem_tools.h.

N_MBTET2

#define N_MBTET2	(		x,
			y,
			z )

Value:

(y)

tetrahedral shape function

Definition at line 30 of file fem_tools.h.

N_MBTET3

#define N_MBTET3	(		x,
			y,
			z )

Value:

(z)

tetrahedral shape function

Definition at line 31 of file fem_tools.h.

N_MBTRI0

#define N_MBTRI0	(		x,
			y )

Value:

(1. - x - y)

triangle shape function

Definition at line 46 of file fem_tools.h.

N_MBTRI1

#define N_MBTRI1	(		x,
			y )

Value:

(x)

triangle shape function

Definition at line 47 of file fem_tools.h.

N_MBTRI2

#define N_MBTRI2	(		x,
			y )

Value:

(y)

triangle shape function

Definition at line 48 of file fem_tools.h.

N_MBTRIQ0

#define N_MBTRIQ0	(		x,
			y )

Value:

((1. - x - y) * (2 * (1. - x - y) - 1.))

Definition at line 111 of file fem_tools.h.

N_MBTRIQ1

#define N_MBTRIQ1	(		x,
			y )

Value:

(x * (2. * x - 1.))

Definition at line 112 of file fem_tools.h.

N_MBTRIQ2

#define N_MBTRIQ2	(		x,
			y )

Value:

(y * (2. * y - 1.))

Definition at line 113 of file fem_tools.h.

N_MBTRIQ3

#define N_MBTRIQ3	(		x,
			y )

Value:

(4. * (1. - x - y) * x)

Definition at line 114 of file fem_tools.h.

N_MBTRIQ4

#define N_MBTRIQ4	(		x,
			y )

Value:

(4. * x * y)

Definition at line 115 of file fem_tools.h.

N_MBTRIQ5

#define N_MBTRIQ5	(		x,
			y )

Value:

(4. * (1. - x - y) * y)

Definition at line 116 of file fem_tools.h.

Function Documentation

Base_scale()

PetscErrorCode Base_scale	(	__CLPK_doublecomplex *	xnormal,
		__CLPK_doublecomplex *	xs1,
		__CLPK_doublecomplex *	xs2 )

Definition at line 741 of file fem_tools.c.

                                                     {
  MoFEMFunctionBeginHot;
  complex double xnrm2_normal = csqrt(cpow(xnormal[0].r + I * xnormal[0].i, 2) +
                                      cpow(xnormal[1].r + I * xnormal[1].i, 2) +
                                      cpow(xnormal[2].r + I * xnormal[2].i, 2));
  int dd = 0;
  for (; dd < 3; dd++) {
    complex double s1 = (xs1[dd].r + I * xs1[dd].i) * xnrm2_normal;
    complex double s2 = (xs2[dd].r + I * xs2[dd].i) * xnrm2_normal;
    xs1[dd].r = creal(s1);
    xs1[dd].i = cimag(s1);
    xs2[dd].r = creal(s2);
    xs2[dd].i = cimag(s2);
  }
  MoFEMFunctionReturnHot(0);
}

DeterminantComplexGradient()

PetscErrorCode DeterminantComplexGradient	(	__CLPK_doublecomplex *	xF,
		__CLPK_doublecomplex *	det_xF )

Definition at line 526 of file fem_tools.c.

                                                                        {
  MoFEMFunctionBeginHot;
  __CLPK_integer IPIV[4];
  if (lapack_zgetrf(3, 3, xF, 3, IPIV) != 0) {
    SETERRQ(PETSC_COMM_SELF, 1, "lapack_zgetrf(3,3,xF,3,IPIV) != 0");
  }
  double complex det = 1;
  int i = 0, j = 0;
  for (; i < 3; i++) {
    det *= xF[3 * i + i].r + I * xF[3 * i + i].i;
    if (IPIV[i] != i + 1)
      j++;
  }
  if ((j - (j / 2) * 2) != 0)
    det = -det;
  (*det_xF).r = creal(det);
  (*det_xF).i = cimag(det);
  MoFEMFunctionReturnHot(0);
}

GradientOfDeformation()

PetscErrorCode GradientOfDeformation	(	double *	diffN,
		double *	dofs,
		double *	F )

calculate gradient of deformation

Definition at line 425 of file fem_tools.c.

                                                                             {
  MoFEMFunctionBeginHot;
  int col, row = 0;
  for (; row < 3; row++)
    for (col = 0; col < 3; col++) {
      F[3 * row + col] = cblas_ddot(4, &diffN[col], 3, &dofs[row], 3);
    }
  MoFEMFunctionReturnHot(0);
}

Grundmann_Moeller_integration_points_1D_EDGE()

PetscErrorCode Grundmann_Moeller_integration_points_1D_EDGE	(	int	rule,
		double *	G_TRI_X,
		double *	G_TRI_W )

Compute weights and integration points for edge using Grundmann_Moeller rule.

Definition at line 55 of file fem_tools.c.

                                                                             {
  MoFEMFunctionBeginHot;
 
  int dim_num = 1;
  int point;
  int point_num;
  double *w;
  double *x;
 
  //  GM_RULE_SET determines the weights and abscissas
  //  pof a Grundmann-Moeller quadrature rule for
  //  the DIM_NUM dimensional simplex,
  //  using a rule of in index RULE,
  //      which will have degree of exactness 2*RULE+1.
 
  //  printf ( "  Here we use DIM_NUM = %d\n", dim_num  );
  //  printf ( "  RULE = %d\n", rule );
  //  printf ( "  DEGREE = %d\n", 2 * rule + 1 );
 
  point_num = gm_rule_size(rule, dim_num);
 
  ierr = PetscMalloc(point_num * sizeof(double), &w);
  CHKERRQ(ierr);
  ierr = PetscMalloc(dim_num * point_num * sizeof(double), &x);
  CHKERRQ(ierr);
 
  gm_rule_set(rule, dim_num, point_num, w, x);
 
  for (point = 0; point < point_num; point++) {
    G_TRI_X[point] = x[0 + point * dim_num];
    G_TRI_W[point] = w[point];
  }
 
  ierr = PetscFree(w);
  CHKERRQ(ierr);
  ierr = PetscFree(x);
  CHKERRQ(ierr);
 
  MoFEMFunctionReturnHot(0);
}

Grundmann_Moeller_integration_points_2D_TRI()

PetscErrorCode Grundmann_Moeller_integration_points_2D_TRI	(	int	rule,
		double *	G_TRI_X,
		double *	G_TRI_Y,
		double *	G_TRI_W )

Compute weights and integration points for 2D Triangle using Grundmann_Moeller rule

Definition at line 98 of file fem_tools.c.

                                                                            {
  MoFEMFunctionBeginHot;
 
  int dim_num = 2;
  int point;
  int point_num;
  double *w;
  double *x;
 
  //  GM_RULE_SET determines the weights and abscissas
  //  pof a Grundmann-Moeller quadrature rule for
  //  the DIM_NUM dimensional simplex,
  //  using a rule of in index RULE,
  //      which will have degree of exactness 2*RULE+1.
 
  //  printf ( "  Here we use DIM_NUM = %d\n", dim_num  );
  //  printf ( "  RULE = %d\n", rule );
  //  printf ( "  DEGREE = %d\n", 2 * rule + 1 );
 
  point_num = gm_rule_size(rule, dim_num);
 
  ierr = PetscMalloc(point_num * sizeof(double), &w);
  CHKERRQ(ierr);
  ierr = PetscMalloc(dim_num * point_num * sizeof(double), &x);
  CHKERRQ(ierr);
 
  gm_rule_set(rule, dim_num, point_num, w, x);
 
  for (point = 0; point < point_num; point++) {
    G_TRI_X[point] = x[0 + point * dim_num];
    G_TRI_Y[point] = x[1 + point * dim_num];
    G_TRI_W[point] = w[point];
  }
 
  ierr = PetscFree(w);
  CHKERRQ(ierr);
  ierr = PetscFree(x);
  CHKERRQ(ierr);
 
  MoFEMFunctionReturnHot(0);
}

Grundmann_Moeller_integration_points_3D_TET()

PetscErrorCode Grundmann_Moeller_integration_points_3D_TET	(	int	rule,
		double *	G_TET_X,
		double *	G_TET_Y,
		double *	G_TET_Z,
		double *	G_TET_W )

Compute weights and integration points for 3D Tet using Grundmann_Moeller rule

Definition at line 143 of file fem_tools.c.

                                                                            {
  MoFEMFunctionBeginHot;
 
  int dim_num = 3;
  int point;
  int point_num;
  double *w;
  double *x;
 
  //    printf ( "  Here we use DIM_NUM = %d\n", dim_num  );
  //    printf ( "  RULE = %d\n", rule );
  //    printf ( "  DEGREE = %d\n", 2 * rule + 1 );
 
  point_num = gm_rule_size(rule, dim_num);
 
  ierr = PetscMalloc(point_num * sizeof(double), &w);
  CHKERRQ(ierr);
  ierr = PetscMalloc(dim_num * point_num * sizeof(double), &x);
  CHKERRQ(ierr);
 
  gm_rule_set(rule, dim_num, point_num, w, x);
  for (point = 0; point < point_num; point++) {
    G_TET_X[point] = x[0 + point * dim_num];
    G_TET_Y[point] = x[1 + point * dim_num];
    G_TET_Z[point] = x[2 + point * dim_num];
    G_TET_W[point] = w[point];
  }
 
  ierr = PetscFree(w);
  CHKERRQ(ierr);
  ierr = PetscFree(x);
  CHKERRQ(ierr);
 
  MoFEMFunctionReturnHot(0);
}

InvertComplexGradient()

PetscErrorCode InvertComplexGradient

(

__CLPK_doublecomplex *

xF

)

Definition at line 499 of file fem_tools.c.

                                                               {
  MoFEMFunctionBeginHot;
  __CLPK_integer IPIV[4];
  __CLPK_doublecomplex WORK[4];
  __CLPK_integer LWORK = 4;
  __CLPK_integer info;
  info = lapack_zgetrf(3, 3, xF, 3, IPIV);
  if (info != 0)
    SETERRQ(PETSC_COMM_SELF, 1, "info == 0");
  info = lapack_zgetri(3, xF, 3, IPIV, WORK, LWORK);
  if (info != 0)
    SETERRQ(PETSC_COMM_SELF, 1, "info == 0");
  MoFEMFunctionReturnHot(0);
}

make_complex_matrix()

PetscErrorCode make_complex_matrix	(	double *	reA,
		double *	imA,
		__CLPK_doublecomplex *	xA )

Compose complex matrix (3x3) from two real matrices.

Definition at line 557 of file fem_tools.c.

                                                             {
  MoFEMFunctionBeginHot;
  int ii = 0, jj;
  for (; ii < 3; ii++) {
    for (jj = 0; jj < 3; jj++) {
      xA[3 * ii + jj].r = reA[3 * ii + jj];
      xA[3 * ii + jj].i = imA[3 * ii + jj];
    }
  }
  MoFEMFunctionReturnHot(0);
}

MakeComplexTensor()

PetscErrorCode MakeComplexTensor	(	double *	reA,
		double *	imA,
		__CLPK_doublecomplex *	xA )

Definition at line 487 of file fem_tools.c.

                                                           {
  MoFEMFunctionBeginHot;
  int ii = 0, jj;
  for (; ii < 3; ii++) {
    for (jj = 0; jj < 3; jj++) {
      xA[3 * ii + jj].r = reA[3 * ii + jj];
      xA[3 * ii + jj].i = imA[3 * ii + jj];
    }
  }
  MoFEMFunctionReturnHot(0);
}

Normal_hierarchical()

PetscErrorCode Normal_hierarchical	(	int	order_approx,
		int *	order_edge_approx,
		int	order,
		int *	order_edge,
		double *	diffN,
		double *	diffN_face,
		double *	diffN_edge[],
		double *	dofs,
		double *	dofs_edge[],
		double *	dofs_face,
		double *	idofs,
		double *	idofs_edge[],
		double *	idofs_face,
		__CLPK_doublecomplex *	xnormal,
		__CLPK_doublecomplex *	s1,
		__CLPK_doublecomplex *	s2,
		int	gg )

Complex normal.

Definition at line 569 of file fem_tools.c.

                                                                  {
  MoFEMFunctionBeginHot;
  int nn, ee, dd;
  // node
  double complex diffX_x_node, diffX_y_node, diffX_z_node;
  double complex diffY_x_node, diffY_y_node, diffY_z_node;
  diffX_x_node = 0.;
  diffX_y_node = 0.;
  diffX_z_node = 0.;
  diffY_x_node = 0.;
  diffY_y_node = 0.;
  diffY_z_node = 0.;
  if (dofs != NULL || idofs != NULL) {
    nn = 0;
    for (; nn < 3; nn++) {
      if (dofs != NULL) {
        diffX_x_node += dofs[3 * nn + 0] * diffN[2 * nn + 0];
        diffX_y_node += dofs[3 * nn + 1] * diffN[2 * nn + 0];
        diffX_z_node += dofs[3 * nn + 2] * diffN[2 * nn + 0];
        diffY_x_node += dofs[3 * nn + 0] * diffN[2 * nn + 1];
        diffY_y_node += dofs[3 * nn + 1] * diffN[2 * nn + 1];
        diffY_z_node += dofs[3 * nn + 2] * diffN[2 * nn + 1];
      }
      if (idofs != NULL) {
        diffX_x_node += I * idofs[3 * nn + 0] * diffN[2 * nn + 0];
        diffX_y_node += I * idofs[3 * nn + 1] * diffN[2 * nn + 0];
        diffX_z_node += I * idofs[3 * nn + 2] * diffN[2 * nn + 0];
        diffY_x_node += I * idofs[3 * nn + 0] * diffN[2 * nn + 1];
        diffY_y_node += I * idofs[3 * nn + 1] * diffN[2 * nn + 1];
        diffY_z_node += I * idofs[3 * nn + 2] * diffN[2 * nn + 1];
      }
    }
  }
  double complex diffX_x, diffX_y, diffX_z;
  double complex diffY_x, diffY_y, diffY_z;
  diffX_x = diffX_x_node;
  diffX_y = diffX_y_node;
  diffX_z = diffX_z_node;
  diffY_x = diffY_x_node;
  diffY_y = diffY_y_node;
  diffY_z = diffY_z_node;
  if (dofs_face != NULL || idofs_face != NULL) {
    int nb_dofs_face = NBFACETRI_H1(order);
    int nb_dofs_approx_face = NBFACETRI_H1(order_approx);
    if (nb_dofs_face > 0) {
      if (dofs_face != NULL) {
        diffX_x += cblas_ddot(nb_dofs_face, &dofs_face[0], 3,
                              &diffN_face[gg * 2 * nb_dofs_approx_face + 0], 2);
        diffX_y += cblas_ddot(nb_dofs_face, &dofs_face[1], 3,
                              &diffN_face[gg * 2 * nb_dofs_approx_face + 0], 2);
        diffX_z += cblas_ddot(nb_dofs_face, &dofs_face[2], 3,
                              &diffN_face[gg * 2 * nb_dofs_approx_face + 0], 2);
        diffY_x += cblas_ddot(nb_dofs_face, &dofs_face[0], 3,
                              &diffN_face[gg * 2 * nb_dofs_approx_face + 1], 2);
        diffY_y += cblas_ddot(nb_dofs_face, &dofs_face[1], 3,
                              &diffN_face[gg * 2 * nb_dofs_approx_face + 1], 2);
        diffY_z += cblas_ddot(nb_dofs_face, &dofs_face[2], 3,
                              &diffN_face[gg * 2 * nb_dofs_approx_face + 1], 2);
      }
      if (idofs_face != NULL) {
        diffX_x +=
            I * cblas_ddot(nb_dofs_face, &idofs_face[0], 3,
                           &diffN_face[gg * 2 * nb_dofs_approx_face + 0], 2);
        diffX_y +=
            I * cblas_ddot(nb_dofs_face, &idofs_face[1], 3,
                           &diffN_face[gg * 2 * nb_dofs_approx_face + 0], 2);
        diffX_z +=
            I * cblas_ddot(nb_dofs_face, &idofs_face[2], 3,
                           &diffN_face[gg * 2 * nb_dofs_approx_face + 0], 2);
        diffY_x +=
            I * cblas_ddot(nb_dofs_face, &idofs_face[0], 3,
                           &diffN_face[gg * 2 * nb_dofs_approx_face + 1], 2);
        diffY_y +=
            I * cblas_ddot(nb_dofs_face, &idofs_face[1], 3,
                           &diffN_face[gg * 2 * nb_dofs_approx_face + 1], 2);
        diffY_z +=
            I * cblas_ddot(nb_dofs_face, &idofs_face[2], 3,
                           &diffN_face[gg * 2 * nb_dofs_approx_face + 1], 2);
      }
    }
  }
  ee = 0;
  if (dofs_edge != NULL || idofs_edge != NULL) {
    for (; ee < 3; ee++) {
      int nb_dofs_edge = NBEDGE_H1(order_edge[ee]);
      int nb_dofs_approx_edge = NBEDGE_H1(order_edge_approx[ee]);
      if (nb_dofs_edge > 0) {
        if (dofs_edge != NULL) {
          if (dofs_edge[ee] != NULL) {
            diffX_x += cblas_ddot(
                nb_dofs_edge, &(dofs_edge[ee])[0], 3,
                &(diffN_edge[ee])[gg * 2 * nb_dofs_approx_edge + 0], 2);
            diffX_y += cblas_ddot(
                nb_dofs_edge, &(dofs_edge[ee])[1], 3,
                &(diffN_edge[ee])[gg * 2 * nb_dofs_approx_edge + 0], 2);
            diffX_z += cblas_ddot(
                nb_dofs_edge, &(dofs_edge[ee])[2], 3,
                &(diffN_edge[ee])[gg * 2 * nb_dofs_approx_edge + 0], 2);
            diffY_x += cblas_ddot(
                nb_dofs_edge, &(dofs_edge[ee])[0], 3,
                &(diffN_edge[ee])[gg * 2 * nb_dofs_approx_edge + 1], 2);
            diffY_y += cblas_ddot(
                nb_dofs_edge, &(dofs_edge[ee])[1], 3,
                &(diffN_edge[ee])[gg * 2 * nb_dofs_approx_edge + 1], 2);
            diffY_z += cblas_ddot(
                nb_dofs_edge, &(dofs_edge[ee])[2], 3,
                &(diffN_edge[ee])[gg * 2 * nb_dofs_approx_edge + 1], 2);
          }
        }
        if (idofs_edge != NULL) {
          if (idofs_edge[ee] == NULL)
            continue;
          diffX_x +=
              I * cblas_ddot(
                      nb_dofs_edge, &(idofs_edge[ee])[0], 3,
                      &(diffN_edge[ee])[gg * 2 * nb_dofs_approx_edge + 0], 2);
          diffX_y +=
              I * cblas_ddot(
                      nb_dofs_edge, &(idofs_edge[ee])[1], 3,
                      &(diffN_edge[ee])[gg * 2 * nb_dofs_approx_edge + 0], 2);
          diffX_z +=
              I * cblas_ddot(
                      nb_dofs_edge, &(idofs_edge[ee])[2], 3,
                      &(diffN_edge[ee])[gg * 2 * nb_dofs_approx_edge + 0], 2);
          diffY_x +=
              I * cblas_ddot(
                      nb_dofs_edge, &(idofs_edge[ee])[0], 3,
                      &(diffN_edge[ee])[gg * 2 * nb_dofs_approx_edge + 1], 2);
          diffY_y +=
              I * cblas_ddot(
                      nb_dofs_edge, &(idofs_edge[ee])[1], 3,
                      &(diffN_edge[ee])[gg * 2 * nb_dofs_approx_edge + 1], 2);
          diffY_z +=
              I * cblas_ddot(
                      nb_dofs_edge, &(idofs_edge[ee])[2], 3,
                      &(diffN_edge[ee])[gg * 2 * nb_dofs_approx_edge + 1], 2);
        }
      }
    }
  }
  double complex normal[3];
  normal[0] = diffX_y * diffY_z - diffX_z * diffY_y;
  normal[1] = diffX_z * diffY_x - diffX_x * diffY_z;
  normal[2] = diffX_x * diffY_y - diffX_y * diffY_x;
  dd = 0;
  for (; dd < 3; dd++) {
    xnormal[dd].r = creal(normal[dd]);
    xnormal[dd].i = cimag(normal[dd]);
  }
  if (xs1 != NULL) {
    xs1[0].r = creal(diffX_x);
    xs1[0].i = cimag(diffX_x);
    xs1[1].r = creal(diffX_y);
    xs1[1].i = cimag(diffX_y);
    xs1[2].r = creal(diffX_z);
    xs1[2].i = cimag(diffX_z);
  }
  if (xs2 != NULL) {
    xs2[0].r = creal(diffY_x);
    xs2[0].i = cimag(diffY_x);
    xs2[1].r = creal(diffY_y);
    xs2[1].i = cimag(diffY_y);
    xs2[2].r = creal(diffY_z);
    xs2[2].i = cimag(diffY_z);
  }
  MoFEMFunctionReturnHot(0);
}

print_mat()

void print_mat	(	double *	M,
		int	m,
		int	n )

print matric M

Examples

matrix_function.cpp.

print_mat_complex()

void print_mat_complex	(	__CLPK_doublecomplex *	M,
		int	m,
		int	n )

priint complex matrix

print_mat_sym_upper()

void print_mat_sym_upper	(	double *	M,
		int	m,
		int	n )

print upper part of the symmetric matrix

ShapeDetJacVolume()

double ShapeDetJacVolume

(

double *

jac

)

determined of jacobian

Definition at line 22 of file fem_tools.c.

                                      {
  double det_jac;
  __CLPK_integer ipiv[4];
  __CLPK_integer info = lapack_dgetrf(3, 3, jac, 3, ipiv);
  if (info != 0)
    return -1;
  int i = 0, j = 0;
  det_jac = 1.;
  for (; i < 3; i++) {
    det_jac *= jac[3 * i + i];
    if (ipiv[i] != i + 1)
      j++;
  }
  if ((j - (j / 2) * 2) != 0)
    det_jac = -det_jac;
  return det_jac;
}

ShapeDiffMBEDGE()

PetscErrorCode ShapeDiffMBEDGE

(

double *

diffN

)

Definition at line 771 of file fem_tools.c.

                                              {
  MoFEMFunctionBeginHot;
  diffN[0] = diffN_MBEDGE0;
  diffN[1] = diffN_MBEDGE1;
  MoFEMFunctionReturnHot(0);
}

ShapeDiffMBTET()

PetscErrorCode ShapeDiffMBTET

(

double *

diffN

)

calculate derivatives of shape functions

Examples

EshelbianPlasticity.cpp, and forces_and_sources_testing_users_base.cpp.

Definition at line 319 of file fem_tools.c.

                                             {
  MoFEMFunctionBeginHot;
  diffN[0] = diffN_MBTET0x;
  diffN[1] = diffN_MBTET0y;
  diffN[2] = diffN_MBTET0z;
  diffN[3] = diffN_MBTET1x;
  diffN[4] = diffN_MBTET1y;
  diffN[5] = diffN_MBTET1z;
  diffN[6] = diffN_MBTET2x;
  diffN[7] = diffN_MBTET2y;
  diffN[8] = diffN_MBTET2z;
  diffN[9] = diffN_MBTET3x;
  diffN[10] = diffN_MBTET3y;
  diffN[11] = diffN_MBTET3z;
  MoFEMFunctionReturnHot(0);
}

ShapeDiffMBTETinvJ()

PetscErrorCode ShapeDiffMBTETinvJ	(	double *	diffN,
		double *	invJac,
		double *	diffNinvJac )

calculate shape functions derivatives in space

Definition at line 415 of file fem_tools.c.

                                                       {
  MoFEMFunctionBeginHot;
  int ii = 0;
  for (; ii < 4; ii++) {
    cblas_dgemv(CblasRowMajor, CblasTrans, 3, 3, 1., invJac, 3, &diffN[ii * 3],
                1, 0., &diffNinvJac[ii * 3], 1);
  }
  MoFEMFunctionReturnHot(0);
}

ShapeDiffMBTETinvJ_complex()

void ShapeDiffMBTETinvJ_complex	(	double *	diffN,
		__CLPK_doublecomplex *	invJac,
		__CLPK_doublecomplex *	diffNinvJac,
		enum CBLAS_TRANSPOSE	Trans )

Definition at line 437 of file fem_tools.c.

                                                            {
  __CLPK_doublecomplex tmp1 = {1., 0.}, tmp2 = {0., 0.};
  int ii = 0, jj;
  for (; ii < 4; ii++) {
    __CLPK_doublecomplex tmp3[3];
    for (jj = 0; jj < 3; jj++) {
      tmp3[jj].r = diffN[ii * 3 + jj];
      tmp3[jj].i = 0;
    }
    cblas_zgemv(CblasRowMajor, Trans, 3, 3, &tmp1, invJac, 3, tmp3, 1, &tmp2,
                &diffNinvJac[ii * 3], 1);
  }
}

ShapeDiffMBTETQ()

PetscErrorCode ShapeDiffMBTETQ	(	double *	diffN,
		const double	x,
		const double	y,
		const double	z )

Definition at line 873 of file fem_tools.c.

                                               {
  MoFEMFunctionBeginHot;
  diffN[0] = diffN_MBTETQ0x(x, y, z);
  diffN[1] = diffN_MBTETQ0y(x, y, z);
  diffN[2] = diffN_MBTETQ0z(x, y, z);
  diffN[3] = diffN_MBTETQ1x(x, y, z);
  diffN[4] = diffN_MBTETQ1y(x, y, z);
  diffN[5] = diffN_MBTETQ1z(x, y, z);
  diffN[6] = diffN_MBTETQ2x(x, y, z);
  diffN[7] = diffN_MBTETQ2y(x, y, z);
  diffN[8] = diffN_MBTETQ2z(x, y, z);
  diffN[9] = diffN_MBTETQ3x(x, y, z);
  diffN[10] = diffN_MBTETQ3y(x, y, z);
  diffN[11] = diffN_MBTETQ3z(x, y, z);
  diffN[12] = diffN_MBTETQ4x(x, y, z);
  diffN[13] = diffN_MBTETQ4y(x, y, z);
  diffN[14] = diffN_MBTETQ4z(x, y, z);
  diffN[15] = diffN_MBTETQ5x(x, y, z);
  diffN[16] = diffN_MBTETQ5y(x, y, z);
  diffN[17] = diffN_MBTETQ5z(x, y, z);
  diffN[18] = diffN_MBTETQ6x(x, y, z);
  diffN[19] = diffN_MBTETQ6y(x, y, z);
  diffN[20] = diffN_MBTETQ6z(x, y, z);
  diffN[21] = diffN_MBTETQ7x(x, y, z);
  diffN[22] = diffN_MBTETQ7y(x, y, z);
  diffN[23] = diffN_MBTETQ7z(x, y, z);
  diffN[24] = diffN_MBTETQ8x(x, y, z);
  diffN[25] = diffN_MBTETQ8y(x, y, z);
  diffN[26] = diffN_MBTETQ8z(x, y, z);
  diffN[27] = diffN_MBTETQ9x(x, y, z);
  diffN[28] = diffN_MBTETQ9y(x, y, z);
  diffN[29] = diffN_MBTETQ9z(x, y, z);
  MoFEMFunctionReturnHot(0);
}

ShapeDiffMBTETQ_GAUSS()

PetscErrorCode ShapeDiffMBTETQ_GAUSS	(	double *	diffN,
		const double *	X,
		const double *	Y,
		const double *	Z,
		const int	G_DIM )

Definition at line 927 of file fem_tools.c.

                                                      {
  MoFEMFunctionBeginHot;
  int ii = 0;
  for (; ii < G_DIM; ii++) {
    double x = X[ii], y = Y[ii], z = Z[ii];
    diffN[30 * ii + 0] = diffN_MBTETQ0x(x, y, z);
    diffN[30 * ii + 1] = diffN_MBTETQ0y(x, y, z);
    diffN[30 * ii + 2] = diffN_MBTETQ0z(x, y, z);
    diffN[30 * ii + 3] = diffN_MBTETQ1x(x, y, z);
    diffN[30 * ii + 4] = diffN_MBTETQ1y(x, y, z);
    diffN[30 * ii + 5] = diffN_MBTETQ1z(x, y, z);
    diffN[30 * ii + 6] = diffN_MBTETQ2x(x, y, z);
    diffN[30 * ii + 7] = diffN_MBTETQ2y(x, y, z);
    diffN[30 * ii + 8] = diffN_MBTETQ2z(x, y, z);
    diffN[30 * ii + 9] = diffN_MBTETQ3x(x, y, z);
    diffN[30 * ii + 10] = diffN_MBTETQ3y(x, y, z);
    diffN[30 * ii + 11] = diffN_MBTETQ3z(x, y, z);
    diffN[30 * ii + 12] = diffN_MBTETQ4x(x, y, z);
    diffN[30 * ii + 13] = diffN_MBTETQ4y(x, y, z);
    diffN[30 * ii + 14] = diffN_MBTETQ4z(x, y, z);
    diffN[30 * ii + 15] = diffN_MBTETQ5x(x, y, z);
    diffN[30 * ii + 16] = diffN_MBTETQ5y(x, y, z);
    diffN[30 * ii + 17] = diffN_MBTETQ5z(x, y, z);
    diffN[30 * ii + 18] = diffN_MBTETQ6x(x, y, z);
    diffN[30 * ii + 19] = diffN_MBTETQ6y(x, y, z);
    diffN[30 * ii + 20] = diffN_MBTETQ6z(x, y, z);
    diffN[30 * ii + 21] = diffN_MBTETQ7x(x, y, z);
    diffN[30 * ii + 22] = diffN_MBTETQ7y(x, y, z);
    diffN[30 * ii + 23] = diffN_MBTETQ7z(x, y, z);
    diffN[30 * ii + 24] = diffN_MBTETQ8x(x, y, z);
    diffN[30 * ii + 25] = diffN_MBTETQ8y(x, y, z);
    diffN[30 * ii + 26] = diffN_MBTETQ8z(x, y, z);
    diffN[30 * ii + 27] = diffN_MBTETQ9x(x, y, z);
    diffN[30 * ii + 28] = diffN_MBTETQ9y(x, y, z);
    diffN[30 * ii + 29] = diffN_MBTETQ9z(x, y, z);
  }
  MoFEMFunctionReturnHot(0);
}

ShapeDiffMBTRI()

PetscErrorCode ShapeDiffMBTRI

(

double *

diffN

)

calculate derivatives of shape functions

Definition at line 194 of file fem_tools.c.

                                             {
  MoFEMFunctionBeginHot;
  diffN[0] = diffN_MBTRI0x;
  diffN[1] = diffN_MBTRI0y;
  diffN[2] = diffN_MBTRI1x;
  diffN[3] = diffN_MBTRI1y;
  diffN[4] = diffN_MBTRI2x;
  diffN[5] = diffN_MBTRI2y;
  MoFEMFunctionReturnHot(0);
}

ShapeDiffMBTRIinvJ()

void ShapeDiffMBTRIinvJ	(	double *	diffN,
		double *	invJac,
		double *	diffNinvJac )

calculate derivatives of shape functions in space

ShapeDiffMBTRIQ()

PetscErrorCode ShapeDiffMBTRIQ	(	double *	diffN,
		const double *	X,
		const double *	Y,
		const int	G_DIM )

Definition at line 795 of file fem_tools.c.

                                                {
  MoFEMFunctionBeginHot;
  int ii = 0;
  for (; ii < G_DIM; ii++) {
    double x = X[ii], y = Y[ii];
    diffN[12 * ii + 0] = diffN_MBTRIQ0x(x, y);
    diffN[12 * ii + 1] = diffN_MBTRIQ0y(x, y);
    diffN[12 * ii + 2] = diffN_MBTRIQ1x(x, y);
    diffN[12 * ii + 3] = diffN_MBTRIQ1y(x, y);
    diffN[12 * ii + 4] = diffN_MBTRIQ2x(x, y);
    diffN[12 * ii + 5] = diffN_MBTRIQ2y(x, y);
    diffN[12 * ii + 6] = diffN_MBTRIQ3x(x, y);
    diffN[12 * ii + 7] = diffN_MBTRIQ3y(x, y);
    diffN[12 * ii + 8] = diffN_MBTRIQ4x(x, y);
    diffN[12 * ii + 9] = diffN_MBTRIQ4y(x, y);
    diffN[12 * ii + 10] = diffN_MBTRIQ5x(x, y);
    diffN[12 * ii + 11] = diffN_MBTRIQ5y(x, y);
  }
  MoFEMFunctionReturnHot(0);
}

ShapeFaceBaseMBTRI()

PetscErrorCode ShapeFaceBaseMBTRI	(	double *	diffN,
		const double *	coords,
		double *	normal,
		double *	s1,
		double *	s2 )

Definition at line 204 of file fem_tools.c.

                                                                          {
  MoFEMFunctionBeginHot;
 
  double diffX_ksi[3];
  double diffX_eta[3];
  int ii = 0;
  for (; ii < 3; ii++) {
    diffX_ksi[ii] = cblas_ddot(3, &coords[ii], 3, &diffN[0], 2);
    diffX_eta[ii] = cblas_ddot(3, &coords[ii], 3, &diffN[1], 2);
  }
  if (s1 != NULL) {
    cblas_dcopy(3, diffX_ksi, 1, s1, 1);
  }
  if (s2 != NULL) {
    cblas_dcopy(3, diffX_eta, 1, s2, 1);
  }
  double Spin_diffX_ksi[9];
  ierr = Spin(Spin_diffX_ksi, diffX_ksi);
  CHKERRQ(ierr);
  cblas_dgemv(CblasRowMajor, CblasNoTrans, 3, 3, 1., Spin_diffX_ksi, 3,
              diffX_eta, 1, 0., normal, 1);
  MoFEMFunctionReturnHot(0);
}

ShapeFaceDiffNormalMBTRI()

PetscErrorCode ShapeFaceDiffNormalMBTRI	(	double *	diffN,
		const double *	coords,
		double *	diff_normal )

calculate derivative of normal in respect to nodal positions

Definition at line 237 of file fem_tools.c.

                                                             {
  MoFEMFunctionBeginHot;
  // N = Spin(dX/dksi)*dX/deta = -Spin(dX/deta)*dX/dksi
 
  double diffX_ksi[3];
  double diffX_eta[3];
  int ii = 0;
  for (; ii < 3; ii++) {
    diffX_ksi[ii] = cblas_ddot(3, &coords[ii], 3, &diffN[0], 2);
    diffX_eta[ii] = cblas_ddot(3, &coords[ii], 3, &diffN[1], 2);
  }
  double Spin_diffX_ksi[9];
  ierr = Spin(Spin_diffX_ksi, diffX_ksi);
  CHKERRQ(ierr);
  double Spin_diffX_eta[9];
  ierr = Spin(Spin_diffX_eta, diffX_eta);
  CHKERRQ(ierr);
  double B_ksi[3 * 9];
  bzero(B_ksi, 3 * 9 * sizeof(double));
  double B_eta[3 * 9];
  bzero(B_eta, 3 * 9 * sizeof(double));
  // B_ksi[] = [
  // diffN[2*0+0],  0,  0,  diffN[2*1+0],   0,  0,  diffN[2*2+0],   0,
  // 0
  // 0,     diffN[2*0+0],   0,  0,  diffN[2*1+0],   0,  0,  diffN[2*2+0],
  // 0
  // 0,     0,  diffM[2*0+0],   0,  0,  diffN[2*1+0],   0,  0,
  // diffN[2*2+0]
  //]
  // B_eta[] = [
  // diffN[2*0+1],  0,  0,  diffN[2*1+1],   0,  0,  diffN[2*2+1],   0,
  // 0
  // 0,     diffN[2*0+1],   0,  0,  diffN[2*1+1],   0,  0,  diffN[2*2+1],
  // 0
  // 0,     0,  diffM[2*0+1],   0,  0,  diffN[2*1+1],   0,  0,
  // diffN[2*2+1]
  //]
  ii = 0;
  for (; ii < 3; ii++) {
    cblas_dcopy(3, &diffN[0], 2, &B_ksi[ii * 9 + ii], 3);
    cblas_dcopy(3, &diffN[1], 2, &B_eta[ii * 9 + ii], 3);
  }
  cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, 3, 9, 3, +1.,
              Spin_diffX_ksi, 3, B_eta, 9, 0., diff_normal, 9);
  cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, 3, 9, 3, -1.,
              Spin_diffX_eta, 3, B_ksi, 9, 1., diff_normal, 9);
  MoFEMFunctionReturnHot(0);
}

ShapeFaceNormalMBTRI()

PetscErrorCode ShapeFaceNormalMBTRI	(	double *	diffN,
		const double *	coords,
		double *	normal )

calculate face normal

Parameters

diffN	derivatives of shape functions
coords	is position of the nodes
normal	vector

Definition at line 229 of file fem_tools.c.

                                                    {
  MoFEMFunctionBeginHot;
  ierr = ShapeFaceBaseMBTRI(diffN, coords, normal, NULL, NULL);
  CHKERRQ(ierr);
  MoFEMFunctionReturnHot(0);
}

ShapeFaceNormalMBTRI_complex()

PetscErrorCode ShapeFaceNormalMBTRI_complex	(	double *	diffN,
		__CLPK_doublecomplex *	xcoords,
		__CLPK_doublecomplex *	xnormal )

Definition at line 452 of file fem_tools.c.

                                                                           {
  MoFEMFunctionBeginHot;
  double complex diffX_x, diffX_y, diffX_z;
  double complex diffY_x, diffY_y, diffY_z;
  diffX_x = diffX_y = diffX_z = 0.;
  diffY_x = diffY_y = diffY_z = 0.;
  int ii;
  for (ii = 0; ii < 3; ii++) {
    diffX_x +=
        (xcoords[3 * ii + 0].r + I * xcoords[3 * ii + 0].i) * diffN[2 * ii + 0];
    diffX_y +=
        (xcoords[3 * ii + 1].r + I * xcoords[3 * ii + 1].i) * diffN[2 * ii + 0];
    diffX_z +=
        (xcoords[3 * ii + 2].r + I * xcoords[3 * ii + 2].i) * diffN[2 * ii + 0];
    diffY_x +=
        (xcoords[3 * ii + 0].r + I * xcoords[3 * ii + 0].i) * diffN[2 * ii + 1];
    diffY_y +=
        (xcoords[3 * ii + 1].r + I * xcoords[3 * ii + 1].i) * diffN[2 * ii + 1];
    diffY_z +=
        (xcoords[3 * ii + 2].r + I * xcoords[3 * ii + 2].i) * diffN[2 * ii + 1];
  }
  double complex tmp;
  tmp = diffX_y * diffY_z - diffX_z * diffY_y;
  xnormal[0].r = creal(tmp);
  xnormal[0].i = cimag(tmp);
  tmp = diffX_z * diffY_x - diffX_x * diffY_z;
  xnormal[1].r = creal(tmp);
  xnormal[1].i = cimag(tmp);
  tmp = diffX_x * diffY_y - diffX_y * diffY_x;
  xnormal[2].r = creal(tmp);
  xnormal[2].i = cimag(tmp);
  MoFEMFunctionReturnHot(0);
}

ShapeInvJacVolume()

PetscErrorCode ShapeInvJacVolume

(

double *

jac

)

Definition at line 39 of file fem_tools.c.

                                              {
  MoFEMFunctionBeginHot;
  __CLPK_integer ipiv[4];
  __CLPK_doublereal work[3];
  __CLPK_integer lwork = 3;
  __CLPK_integer info;
  info = lapack_dgetrf(3, 3, jac, 3, ipiv);
  if (info != 0)
    SETERRQ1(PETSC_COMM_SELF, 1, "info = %d", info);
  info = lapack_dgetri(3, jac, 3, ipiv, work, lwork);
  if (info != 0)
    SETERRQ1(PETSC_COMM_SELF, 1, "info = %d", info);
  MoFEMFunctionReturnHot(0);
}

ShapeJacMBTET()

PetscErrorCode ShapeJacMBTET	(	double *	diffN,
		const double *	coords,
		double *	jac )

calculate jacobian

Definition at line 288 of file fem_tools.c.

                                                                               {
  MoFEMFunctionBeginHot;
  int ii, jj, kk;
  bzero(jac, sizeof(double) * 9);
  for (ii = 0; ii < 4; ii++)     // shape func.
    for (jj = 0; jj < 3; jj++)   // space
      for (kk = 0; kk < 3; kk++) // derivative of shape func.
        jac[jj * 3 + kk] += diffN[ii * 3 + kk] * coords[ii * 3 + jj];
  MoFEMFunctionReturnHot(0);
}

ShapeJacMBTETQ()

PetscErrorCode ShapeJacMBTETQ	(	const double *	diffN,
		const double *	coords,
		double *	Jac )

Definition at line 967 of file fem_tools.c.

                                           {
  MoFEMFunctionBeginHot;
  int ii, jj, kk;
  bzero(Jac, sizeof(double) * 9);
  for (ii = 0; ii < 10; ii++)    // shape func.
    for (jj = 0; jj < 3; jj++)   // space
      for (kk = 0; kk < 3; kk++) // derivative of shape func.
        Jac[jj * 3 + kk] += diffN[ii * 3 + kk] * coords[ii * 3 + jj];
  MoFEMFunctionReturnHot(0);
}

ShapeJacMBTRI()

void ShapeJacMBTRI	(	double *	diffN,
		const double *	coords,
		double *	Jac )

calculate jacobioan

ShapeMBEDGE()

PetscErrorCode ShapeMBEDGE	(	double *	N,
		const double *	G_X,
		int	DIM )

Definition at line 761 of file fem_tools.c.

                                                                  {
  MoFEMFunctionBeginHot;
  int ii = 0;
  for (; ii < DIM; ii++) {
    double x = G_X[ii];
    N[2 * ii + 0] = N_MBEDGE0(x);
    N[2 * ii + 1] = N_MBEDGE1(x);
  }
  MoFEMFunctionReturnHot(0);
}

ShapeMBTET()

PetscErrorCode ShapeMBTET	(	double *	N,
		const double *	G_X,
		const double *	G_Y,
		const double *	G_Z,
		int	DIM )

calculate shape functions

Examples

EshelbianPlasticity.cpp, and forces_and_sources_testing_users_base.cpp.

Definition at line 306 of file fem_tools.c.

                                                      {
  MoFEMFunctionBeginHot;
  int ii = 0;
  for (; ii < DIM; ii++) {
    double x = G_X[ii], y = G_Y[ii], z = G_Z[ii];
    N[4 * ii + 0] = N_MBTET0(x, y, z);
    N[4 * ii + 1] = N_MBTET1(x, y, z);
    N[4 * ii + 2] = N_MBTET2(x, y, z);
    N[4 * ii + 3] = N_MBTET3(x, y, z);
  }
  MoFEMFunctionReturnHot(0);
}

ShapeMBTET_inverse()

PetscErrorCode ShapeMBTET_inverse	(	double *	N,
		double *	diffN,
		const double *	elem_coords,
		const double *	glob_coords,
		double *	loc_coords )

calculate local coordinates for given global coordinates

new version for multiple points need to be implemented

Definition at line 335 of file fem_tools.c.

                                                      {
  MoFEMFunctionBeginHot;
  double A[3 * 3];
  int IPIV[3];
  // COL MAJOR
  // X
  A[0 + 3 * 0] =
      cblas_ddot(4, &diffN[0 * 3 + 0], 3, &elem_coords[0 * 3 + 0], 3);
  A[0 + 3 * 1] =
      cblas_ddot(4, &diffN[0 * 3 + 1], 3, &elem_coords[0 * 3 + 0], 3);
  A[0 + 3 * 2] =
      cblas_ddot(4, &diffN[0 * 3 + 2], 3, &elem_coords[0 * 3 + 0], 3);
  loc_coords[0] =
      glob_coords[0] - cblas_ddot(4, &N[0], 1, &elem_coords[0 * 3 + 0], 3);
  // printf("A\n[ %3.2f %3.2f %3.2f ] %3.2f \n",A[0*3],A[1*3],A[2*3],R[0]);
  // Y
  A[1 + 3 * 0] =
      cblas_ddot(4, &diffN[0 * 3 + 0], 3, &elem_coords[0 * 3 + 1], 3);
  A[1 + 3 * 1] =
      cblas_ddot(4, &diffN[0 * 3 + 1], 3, &elem_coords[0 * 3 + 1], 3);
  A[1 + 3 * 2] =
      cblas_ddot(4, &diffN[0 * 3 + 2], 3, &elem_coords[0 * 3 + 1], 3);
  loc_coords[1] =
      glob_coords[1] - cblas_ddot(4, &N[0], 1, &elem_coords[0 * 3 + 1], 3);
  // printf("[ %3.2f %3.2f %3.2f ] %3.2f \n",A[1+3*0],A[1+3*1],A[1+3*2],R[1]);
  // Z
  A[2 + 3 * 0] =
      cblas_ddot(4, &diffN[0 * 3 + 0], 3, &elem_coords[0 * 3 + 2], 3);
  A[2 + 3 * 1] =
      cblas_ddot(4, &diffN[0 * 3 + 1], 3, &elem_coords[0 * 3 + 2], 3);
  A[2 + 3 * 2] =
      cblas_ddot(4, &diffN[0 * 3 + 2], 3, &elem_coords[0 * 3 + 2], 3);
  loc_coords[2] =
      glob_coords[2] - cblas_ddot(4, &N[0], 1, &elem_coords[0 * 3 + 2], 3);
  // printf("[ %3.2f %3.2f %3.2f ] %3.2f \n",A[2+3*0],A[2+3*1],A[2+3*2],R[1]);
  int info =
      lapack_dgesv(3, 1, &A[0], 3, (__CLPK_integer *)IPIV, loc_coords, 3);
  if (info != 0)
    SETERRQ1(PETSC_COMM_SELF, 1, "info == %d", info);
  MoFEMFunctionReturnHot(0);
}

ShapeMBTETQ()

PetscErrorCode ShapeMBTETQ	(	double *	N,
		const double	x,
		const double	y,
		const double	z )

Definition at line 858 of file fem_tools.c.

                                           {
  MoFEMFunctionBeginHot;
  N[0] = N_MBTETQ0(x, y, z);
  N[1] = N_MBTETQ1(x, y, z);
  N[2] = N_MBTETQ2(x, y, z);
  N[3] = N_MBTETQ3(x, y, z);
  N[4] = N_MBTETQ4(x, y, z);
  N[5] = N_MBTETQ5(x, y, z);
  N[6] = N_MBTETQ6(x, y, z);
  N[7] = N_MBTETQ7(x, y, z);
  N[8] = N_MBTETQ8(x, y, z);
  N[9] = N_MBTETQ9(x, y, z);
  MoFEMFunctionReturnHot(0);
}

ShapeMBTETQ_detJac_at_Gauss_Points()

PetscErrorCode ShapeMBTETQ_detJac_at_Gauss_Points	(	double *	detJac_at_Gauss_Points,
		const double *	diffN,
		const double *	coords,
		int	G_DIM )

Definition at line 979 of file fem_tools.c.

                                              {
  MoFEMFunctionBeginHot;
 
  double Jac[9];
  int ii = 0;
  for (; ii < G_DIM; ii++) {
    ierr = ShapeJacMBTETQ(&diffN[30 * ii], coords, Jac);
    CHKERRQ(ierr);
    detJac_at_Gauss_Points[ii] = ShapeDetJacVolume(Jac);
  }
  MoFEMFunctionReturnHot(0);
}

ShapeMBTETQ_GAUSS()

PetscErrorCode ShapeMBTETQ_GAUSS	(	double *	N,
		const double *	X,
		const double *	Y,
		const double *	Z,
		const int	G_DIM )

Definition at line 908 of file fem_tools.c.

                                                                   {
  MoFEMFunctionBeginHot;
  int ii = 0;
  for (; ii < G_DIM; ii++) {
    double x = X[ii], y = Y[ii], z = Z[ii];
    N[10 * ii + 0] = N_MBTETQ0(x, y, z);
    N[10 * ii + 1] = N_MBTETQ1(x, y, z);
    N[10 * ii + 2] = N_MBTETQ2(x, y, z);
    N[10 * ii + 3] = N_MBTETQ3(x, y, z);
    N[10 * ii + 4] = N_MBTETQ4(x, y, z);
    N[10 * ii + 5] = N_MBTETQ5(x, y, z);
    N[10 * ii + 6] = N_MBTETQ6(x, y, z);
    N[10 * ii + 7] = N_MBTETQ7(x, y, z);
    N[10 * ii + 8] = N_MBTETQ8(x, y, z);
    N[10 * ii + 9] = N_MBTETQ9(x, y, z);
  }
  MoFEMFunctionReturnHot(0);
}

ShapeMBTETQ_inverse()

PetscErrorCode ShapeMBTETQ_inverse	(	double *	N,
		double *	diffN,
		const double *	elem_coords,
		const double *	glob_coords,
		double *	loc_coords,
		const double	eps )

Definition at line 1007 of file fem_tools.c.

                                                                         {
  MoFEMFunctionBeginHot;
  double A[3 * 3];
  double R[3];
  int IPIV[3];
  float NORM_dR = 1000.;
  float NORM_R0;
  ShapeMBTETQ(N, 0.1, 0.1, 0.1);
  ShapeDiffMBTETQ(diffN, 0.1, 0.1, 0.1);
  R[0] = glob_coords[0] - cblas_ddot(10, &N[0], 1, &elem_coords[0], 3);
  R[1] = glob_coords[1] - cblas_ddot(10, &N[0], 1, &elem_coords[1], 3);
  R[2] = glob_coords[2] - cblas_ddot(10, &N[0], 1, &elem_coords[2], 3);
  NORM_R0 = cblas_dnrm2(3, &R[0], 1);
  while ((NORM_dR / NORM_R0) > eps) {
    // COL MAJOR
    // X
    A[0 + 3 * 0] = cblas_ddot(10, &diffN[0 * 3 + 0], 3, &elem_coords[0], 3);
    A[0 + 3 * 1] = cblas_ddot(10, &diffN[0 * 3 + 1], 3, &elem_coords[0], 3);
    A[0 + 3 * 2] = cblas_ddot(10, &diffN[0 * 3 + 2], 3, &elem_coords[0], 3);
    R[0] = glob_coords[0] - cblas_ddot(10, &N[0], 1, &elem_coords[0], 3);
    // Y
    A[1 + 3 * 0] = cblas_ddot(10, &diffN[0 * 3 + 0], 3, &elem_coords[1], 3);
    A[1 + 3 * 1] = cblas_ddot(10, &diffN[0 * 3 + 1], 3, &elem_coords[1], 3);
    A[1 + 3 * 2] = cblas_ddot(10, &diffN[0 * 3 + 2], 3, &elem_coords[1], 3);
    R[1] = glob_coords[1] - cblas_ddot(10, &N[0], 1, &elem_coords[1], 3);
    // Z
    A[2 + 3 * 0] =
        cblas_ddot(10, &diffN[0 * 3 + 0], 3, &elem_coords[0 * 3 + 2], 3);
    A[2 + 3 * 1] =
        cblas_ddot(10, &diffN[0 * 3 + 1], 3, &elem_coords[0 * 3 + 2], 3);
    A[2 + 3 * 2] =
        cblas_ddot(10, &diffN[0 * 3 + 2], 3, &elem_coords[0 * 3 + 2], 3);
    R[2] = glob_coords[2] - cblas_ddot(10, &N[0], 1, &elem_coords[2], 3);
    int info = lapack_dgesv(3, 1, &A[0], 3, (__CLPK_integer *)IPIV, R, 3);
    assert(info == 0);
    NOT_USED(info);
    cblas_daxpy(3, 1., R, 1, loc_coords, 1);
    NORM_dR = cblas_dnrm2(3, &R[0], 1);
    ShapeMBTETQ(N, loc_coords[0], loc_coords[1], loc_coords[2]);
    ShapeDiffMBTETQ(diffN, loc_coords[0], loc_coords[1], loc_coords[2]);
  }
  MoFEMFunctionReturnHot(0);
}

ShapeMBTRI()

PetscErrorCode ShapeMBTRI	(	double *	N,
		const double *	X,
		const double *	Y,
		const int	G_DIM )

calculate shape functions on triangle

Parameters

N	shape function array
X	array of Gauss X coordinates
Y	array of Gauss Y coordinates
G_DIM	number of Gauss points

Examples

EshelbianPlasticity.cpp.

Definition at line 182 of file fem_tools.c.

                                           {
  MoFEMFunctionBeginHot;
  int ii = 0;
  for (; ii < G_DIM; ii++) {
    double x = X[ii], y = Y[ii];
    N[3 * ii + 0] = N_MBTRI0(x, y);
    N[3 * ii + 1] = N_MBTRI1(x, y);
    N[3 * ii + 2] = N_MBTRI2(x, y);
  }
  MoFEMFunctionReturnHot(0);
}

ShapeMBTRI_inverse()

PetscErrorCode ShapeMBTRI_inverse	(	double *	N,
		double *	diffN,
		const double *	elem_coords,
		const double *	glob_coords,
		double *	loc_coords )

calculate local coordinates of triangle element for given global coordinates in 2D (Assume e.g. z=0)

\[ \left[\begin{array}{cc} \frac{\partial N_{1}}{\partial\xi}x_{N_{1}}+\frac{\partial N_{2}}{\partial\xi}x_{N_{2}}+\frac{\partial N_{3}}{\partial\xi}x_{N_{3}} & \frac{\partial N_{1}}{\partial\eta}x_{N_{1}}+\frac{\partial N_{2}}{\partial\eta}x_{N_{2}}+\frac{\partial N_{3}}{\partial\eta}x_{N_{3}}\\ \frac{\partial N_{1}}{\partial\xi}y_{N_{1}}+\frac{\partial N_{2}}{\partial\xi}y_{N_{2}}+\frac{\partial N_{3}}{\partial\xi}y_{N_{3}} & \frac{\partial N_{1}}{\partial\eta}y_{N_{1}}+\frac{\partial N_{2}}{\partial\eta}y_{N_{2}}+\frac{\partial N_{3}}{\partial\eta}y_{N_{3}} \end{array}\right]\left\{ \begin{array}{c} \xi\\ \eta \end{array}\right\} =\left\{ \begin{array}{c} x_{gp}-\left(N_{1}x_{N_{1}}+N_{2}x_{N_{2}}+N_{3}x_{N_{3}}\right)\\ y_{gp}-\left(N_{1}y_{N_{1}}+N_{2}y_{N_{2}}+N_{3}y_{N_{3}}\right) \end{array}\right\} \]

/

Parameters

N	shape function array /
diffN	array of shape function derivative w.r.t to local coordinates /
elem_coords	global coordinates of element /
glob_coords	global coordinates of required point /
loc_coords	local coordinates of required point

Definition at line 380 of file fem_tools.c.

                                                      {
  MoFEMFunctionBeginHot;
  double A[2 * 2];
 
  // 1st and 2nd element of matrix A
  A[0] = cblas_ddot(3, &diffN[0], 2, &elem_coords[0], 2); // dot product
  A[1] = cblas_ddot(3, &diffN[1], 2, &elem_coords[0], 2);
  loc_coords[0] = glob_coords[0] - cblas_ddot(3, &N[0], 1, &elem_coords[0], 2);
 
  // 3rd and 4th element of matrix A
  A[2] = cblas_ddot(3, &diffN[0], 2, &elem_coords[1], 2);
  A[3] = cblas_ddot(3, &diffN[1], 2, &elem_coords[1], 2);
  loc_coords[1] = glob_coords[1] - cblas_ddot(3, &N[0], 1, &elem_coords[1], 2);
 
  // calculate directly the solution (as the size of matrix is only 2x2)
  double invA[2 * 2], detA;
  detA = A[0] * A[3] - A[1] * A[2];
  detA = 1.0 / detA;
  invA[0] = A[3] * detA;
  invA[1] = -1.0 * A[1] * detA;
  invA[2] = -1.0 * A[2] * detA;
  invA[3] = A[0] * detA;
 
  double loc_coords_new[2];
  loc_coords_new[0] = invA[0] * loc_coords[0] + invA[1] * loc_coords[1];
  loc_coords_new[1] = invA[2] * loc_coords[0] + invA[3] * loc_coords[1];
 
  loc_coords[0] = loc_coords_new[0];
  loc_coords[1] = loc_coords_new[1];
  MoFEMFunctionReturnHot(0);
}

ShapeMBTRIQ()

PetscErrorCode ShapeMBTRIQ	(	double *	N,
		const double *	X,
		const double *	Y,
		const int	G_DIM )

Definition at line 780 of file fem_tools.c.

                                            {
  MoFEMFunctionBeginHot;
  int ii = 0;
  for (; ii < G_DIM; ii++) {
    double x = X[ii], y = Y[ii];
    N[6 * ii + 0] = N_MBTRIQ0(x, y);
    N[6 * ii + 1] = N_MBTRIQ1(x, y);
    N[6 * ii + 2] = N_MBTRIQ2(x, y);
    N[6 * ii + 3] = N_MBTRIQ3(x, y);
    N[6 * ii + 4] = N_MBTRIQ4(x, y);
    N[6 * ii + 5] = N_MBTRIQ5(x, y);
  }
  MoFEMFunctionReturnHot(0);
}

ShapeVolumeMBTET()

double ShapeVolumeMBTET	(	double *	diffN,
		const double *	coords )

calculate TET volume

Definition at line 298 of file fem_tools.c.

                                                             {
  double Jac[9];
  ShapeJacMBTET(diffN, coords, Jac);
  double detJac = ShapeDetJacVolume(Jac);
  // printf("detJac = +%6.4e\n",detJac);
  // print_mat(Jac,3,3);
  return detJac * G_TET_W1[0] / 6.;
}

ShapeVolumeMBTETQ()

double ShapeVolumeMBTETQ	(	const double *	diffN,
		const double *	coords,
		int	G_DIM,
		double *	G_TET_W )

Definition at line 993 of file fem_tools.c.

                                          {
 
  int ii = 0;
  double vol = 0;
  double detJac_at_Gauss_Points[G_DIM];
  ierr = ShapeMBTETQ_detJac_at_Gauss_Points(detJac_at_Gauss_Points, diffN,
                                            coords, G_DIM);
  CHKERRQ(ierr);
  for (; ii < G_DIM; ii++) {
    vol += G_TET_W[ii] * (detJac_at_Gauss_Points[ii]) / 6;
  }
  return vol;
}

Spin()

PetscErrorCode Spin	(	double *	spinOmega,
		double *	vecOmega )

calculate spin matrix from vector

Definition at line 546 of file fem_tools.c.

                                                         {
  MoFEMFunctionBeginHot;
  bzero(spinOmega, 9 * sizeof(double));
  spinOmega[0 * 3 + 1] = -vecOmega[2];
  spinOmega[0 * 3 + 2] = +vecOmega[1];
  spinOmega[1 * 3 + 0] = +vecOmega[2];
  spinOmega[1 * 3 + 2] = -vecOmega[0];
  spinOmega[2 * 3 + 0] = -vecOmega[1];
  spinOmega[2 * 3 + 1] = +vecOmega[0];
  MoFEMFunctionReturnHot(0);
}

Variable Documentation

G_TET_W1

const double G_TET_W1[] = {1.}

static

Definition at line 1115 of file fem_tools.h.

{1.};

G_TET_W10

const double G_TET_W10[]

static

Initial value:

= {0.2177650698804054, 0.2177650698804054,
                                   0.2177650698804054, 0.2177650698804054,
                                   0.0214899534130631, 0.0214899534130631,
                                   0.0214899534130631, 0.0214899534130631,
                                   0.0214899534130631, 0.0214899534130631}

Definition at line 1150 of file fem_tools.h.

                                  {0.2177650698804054, 0.2177650698804054,
                                   0.2177650698804054, 0.2177650698804054,
                                   0.0214899534130631, 0.0214899534130631,
                                   0.0214899534130631, 0.0214899534130631,
                                   0.0214899534130631, 0.0214899534130631};

G_TET_W4

const double G_TET_W4[] = {0.25, 0.25, 0.25, 0.25}

static

Definition at line 1122 of file fem_tools.h.

{0.25, 0.25, 0.25, 0.25};

G_TET_W45

const double G_TET_W45[]

static

Initial value:

= {
    -0.2359620398477557, 0.0244878963560562, 0.0244878963560562,
    0.0244878963560562,  0.0244878963560562, 0.0039485206398261,
    0.0039485206398261,  0.0039485206398261, 0.0039485206398261,
    0.0263055529507371,  0.0263055529507371, 0.0263055529507371,
    0.0263055529507371,  0.0263055529507371, 0.0263055529507371,
    0.0829803830550589,  0.0829803830550589, 0.0829803830550589,
    0.0829803830550589,  0.0829803830550589, 0.0829803830550589,
    0.0254426245481023,  0.0254426245481023, 0.0254426245481023,
    0.0254426245481023,  0.0254426245481023, 0.0254426245481023,
    0.0254426245481023,  0.0254426245481023, 0.0254426245481023,
    0.0254426245481023,  0.0254426245481023, 0.0254426245481023,
    0.0134324384376852,  0.0134324384376852, 0.0134324384376852,
    0.0134324384376852,  0.0134324384376852, 0.0134324384376852,
    0.0134324384376852,  0.0134324384376852, 0.0134324384376852,
    0.0134324384376852,  0.0134324384376852, 0.0134324384376852}

Definition at line 1204 of file fem_tools.h.

                                  {
    -0.2359620398477557, 0.0244878963560562, 0.0244878963560562,
    0.0244878963560562,  0.0244878963560562, 0.0039485206398261,
    0.0039485206398261,  0.0039485206398261, 0.0039485206398261,
    0.0263055529507371,  0.0263055529507371, 0.0263055529507371,
    0.0263055529507371,  0.0263055529507371, 0.0263055529507371,
    0.0829803830550589,  0.0829803830550589, 0.0829803830550589,
    0.0829803830550589,  0.0829803830550589, 0.0829803830550589,
    0.0254426245481023,  0.0254426245481023, 0.0254426245481023,
    0.0254426245481023,  0.0254426245481023, 0.0254426245481023,
    0.0254426245481023,  0.0254426245481023, 0.0254426245481023,
    0.0254426245481023,  0.0254426245481023, 0.0254426245481023,
    0.0134324384376852,  0.0134324384376852, 0.0134324384376852,
    0.0134324384376852,  0.0134324384376852, 0.0134324384376852,
    0.0134324384376852,  0.0134324384376852, 0.0134324384376852,
    0.0134324384376852,  0.0134324384376852, 0.0134324384376852};

G_TET_W5

const double G_TET_W5[]

static

Initial value:

= {-0.80000000000000000, 0.45000000000000000,
                                  0.45000000000000000, 0.45000000000000000,
                                  0.45000000000000000}

Definition at line 1132 of file fem_tools.h.

                                 {-0.80000000000000000, 0.45000000000000000,
                                  0.45000000000000000, 0.45000000000000000,
                                  0.45000000000000000};

G_TET_X1

const double G_TET_X1[] = {0.25}

static

Definition at line 1112 of file fem_tools.h.

{0.25};

G_TET_X10

const double G_TET_X10[]

static

Initial value:

= {0.5684305841968444, 0.1438564719343852,
                                   0.1438564719343852, 0.1438564719343852,
                                   0.0000000000000000, 0.5000000000000000,
                                   0.5000000000000000, 0.5000000000000000,
                                   0.0000000000000000, 0.0000000000000000}

Definition at line 1135 of file fem_tools.h.

                                  {0.5684305841968444, 0.1438564719343852,
                                   0.1438564719343852, 0.1438564719343852,
                                   0.0000000000000000, 0.5000000000000000,
                                   0.5000000000000000, 0.5000000000000000,
                                   0.0000000000000000, 0.0000000000000000};

G_TET_X4

const double G_TET_X4[]

static

Initial value:

= {0.1757281246520584, 0.2445310270213291,
                                  0.5556470949048655, 0.0240937534217468}

Definition at line 1116 of file fem_tools.h.

                                 {0.1757281246520584, 0.2445310270213291,
                                  0.5556470949048655, 0.0240937534217468};

G_TET_X45

const double G_TET_X45[]

static

Initial value:

= {
    0.2500000000000000, 0.6175871903000830, 0.1274709365666390,
    0.1274709365666390, 0.1274709365666390, 0.9037635088221031,
    0.0320788303926323, 0.0320788303926323, 0.0320788303926323,
    0.4502229043567190, 0.0497770956432810, 0.0497770956432810,
    0.0497770956432810, 0.4502229043567190, 0.4502229043567190,
    0.3162695526014501, 0.1837304473985499, 0.1837304473985499,
    0.1837304473985499, 0.3162695526014501, 0.3162695526014501,
    0.0229177878448171, 0.2319010893971509, 0.2319010893971509,
    0.5132800333608811, 0.2319010893971509, 0.2319010893971509,
    0.2319010893971509, 0.0229177878448171, 0.5132800333608811,
    0.2319010893971509, 0.0229177878448171, 0.5132800333608811,
    0.7303134278075384, 0.0379700484718286, 0.0379700484718286,
    0.1937464752488044, 0.0379700484718286, 0.0379700484718286,
    0.0379700484718286, 0.7303134278075384, 0.1937464752488044,
    0.0379700484718286, 0.7303134278075384, 0.1937464752488044}

Definition at line 1156 of file fem_tools.h.

                                  {
    0.2500000000000000, 0.6175871903000830, 0.1274709365666390,
    0.1274709365666390, 0.1274709365666390, 0.9037635088221031,
    0.0320788303926323, 0.0320788303926323, 0.0320788303926323,
    0.4502229043567190, 0.0497770956432810, 0.0497770956432810,
    0.0497770956432810, 0.4502229043567190, 0.4502229043567190,
    0.3162695526014501, 0.1837304473985499, 0.1837304473985499,
    0.1837304473985499, 0.3162695526014501, 0.3162695526014501,
    0.0229177878448171, 0.2319010893971509, 0.2319010893971509,
    0.5132800333608811, 0.2319010893971509, 0.2319010893971509,
    0.2319010893971509, 0.0229177878448171, 0.5132800333608811,
    0.2319010893971509, 0.0229177878448171, 0.5132800333608811,
    0.7303134278075384, 0.0379700484718286, 0.0379700484718286,
    0.1937464752488044, 0.0379700484718286, 0.0379700484718286,
    0.0379700484718286, 0.7303134278075384, 0.1937464752488044,
    0.0379700484718286, 0.7303134278075384, 0.1937464752488044};

G_TET_X5

const double G_TET_X5[]

static

Initial value:

= {0.25000000000000000, 0.50000000000000000,
                                  0.16666666666666667, 0.16666666666666667,
                                  0.16666666666666667}

Definition at line 1123 of file fem_tools.h.

                                 {0.25000000000000000, 0.50000000000000000,
                                  0.16666666666666667, 0.16666666666666667,
                                  0.16666666666666667};

G_TET_Y1

const double G_TET_Y1[] = {0.25}

static

Definition at line 1113 of file fem_tools.h.

{0.25};

G_TET_Y10

const double G_TET_Y10[]

static

Initial value:

= {0.1438564719343852, 0.1438564719343852,
                                   0.1438564719343852, 0.5684305841968444,
                                   0.5000000000000000, 0.0000000000000000,
                                   0.5000000000000000, 0.0000000000000000,
                                   0.5000000000000000, 0.0000000000000000}

Definition at line 1140 of file fem_tools.h.

                                  {0.1438564719343852, 0.1438564719343852,
                                   0.1438564719343852, 0.5684305841968444,
                                   0.5000000000000000, 0.0000000000000000,
                                   0.5000000000000000, 0.0000000000000000,
                                   0.5000000000000000, 0.0000000000000000};

G_TET_Y4

const double G_TET_Y4[]

static

Initial value:

= {0.5656137776620919, 0.0501800797762026,
                                  0.1487681308666864, 0.2354380116950194}

Definition at line 1118 of file fem_tools.h.

                                 {0.5656137776620919, 0.0501800797762026,
                                  0.1487681308666864, 0.2354380116950194};

G_TET_Y45

const double G_TET_Y45[]

static

Initial value:

= {
    0.2500000000000000, 0.1274709365666390, 0.1274709365666390,
    0.1274709365666390, 0.6175871903000830, 0.0320788303926323,
    0.0320788303926323, 0.0320788303926323, 0.9037635088221031,
    0.0497770956432810, 0.4502229043567190, 0.0497770956432810,
    0.4502229043567190, 0.0497770956432810, 0.4502229043567190,
    0.1837304473985499, 0.3162695526014501, 0.1837304473985499,
    0.3162695526014501, 0.1837304473985499, 0.3162695526014501,
    0.2319010893971509, 0.0229177878448171, 0.2319010893971509,
    0.2319010893971509, 0.5132800333608811, 0.2319010893971509,
    0.0229177878448171, 0.5132800333608811, 0.2319010893971509,
    0.5132800333608811, 0.2319010893971509, 0.0229177878448171,
    0.0379700484718286, 0.7303134278075384, 0.0379700484718286,
    0.0379700484718286, 0.1937464752488044, 0.0379700484718286,
    0.7303134278075384, 0.1937464752488044, 0.0379700484718286,
    0.1937464752488044, 0.0379700484718286, 0.7303134278075384}

Definition at line 1172 of file fem_tools.h.

                                  {
    0.2500000000000000, 0.1274709365666390, 0.1274709365666390,
    0.1274709365666390, 0.6175871903000830, 0.0320788303926323,
    0.0320788303926323, 0.0320788303926323, 0.9037635088221031,
    0.0497770956432810, 0.4502229043567190, 0.0497770956432810,
    0.4502229043567190, 0.0497770956432810, 0.4502229043567190,
    0.1837304473985499, 0.3162695526014501, 0.1837304473985499,
    0.3162695526014501, 0.1837304473985499, 0.3162695526014501,
    0.2319010893971509, 0.0229177878448171, 0.2319010893971509,
    0.2319010893971509, 0.5132800333608811, 0.2319010893971509,
    0.0229177878448171, 0.5132800333608811, 0.2319010893971509,
    0.5132800333608811, 0.2319010893971509, 0.0229177878448171,
    0.0379700484718286, 0.7303134278075384, 0.0379700484718286,
    0.0379700484718286, 0.1937464752488044, 0.0379700484718286,
    0.7303134278075384, 0.1937464752488044, 0.0379700484718286,
    0.1937464752488044, 0.0379700484718286, 0.7303134278075384};

G_TET_Y5

const double G_TET_Y5[]

static

Initial value:

= {0.25000000000000000, 0.16666666666666667,
                                  0.50000000000000000, 0.16666666666666667,
                                  0.16666666666666667}

Definition at line 1126 of file fem_tools.h.

                                 {0.25000000000000000, 0.16666666666666667,
                                  0.50000000000000000, 0.16666666666666667,
                                  0.16666666666666667};

G_TET_Z1

const double G_TET_Z1[] = {0.25}

static

Definition at line 1114 of file fem_tools.h.

{0.25};

G_TET_Z10

const double G_TET_Z10[]

static

Initial value:

= {0.1438564719343852, 0.1438564719343852,
                                   0.5684305841968444, 0.1438564719343852,
                                   0.5000000000000000, 0.5000000000000000,
                                   0.0000000000000000, 0.0000000000000000,
                                   0.0000000000000000, 0.5000000000000000}

Definition at line 1145 of file fem_tools.h.

                                  {0.1438564719343852, 0.1438564719343852,
                                   0.5684305841968444, 0.1438564719343852,
                                   0.5000000000000000, 0.5000000000000000,
                                   0.0000000000000000, 0.0000000000000000,
                                   0.0000000000000000, 0.5000000000000000};

G_TET_Z4

const double G_TET_Z4[]

static

Initial value:

= {0.2180665126782654, 0.5635595064952189,
                                  0.0350112499848832, 0.1833627308416330}

Definition at line 1120 of file fem_tools.h.

                                 {0.2180665126782654, 0.5635595064952189,
                                  0.0350112499848832, 0.1833627308416330};

G_TET_Z45

const double G_TET_Z45[]

static

Initial value:

= {
    0.2500000000000000, 0.1274709365666390, 0.1274709365666390,
    0.6175871903000830, 0.1274709365666390, 0.0320788303926323,
    0.0320788303926323, 0.9037635088221031, 0.0320788303926323,
    0.0497770956432810, 0.0497770956432810, 0.4502229043567190,
    0.4502229043567190, 0.4502229043567190, 0.0497770956432810,
    0.1837304473985499, 0.1837304473985499, 0.3162695526014501,
    0.3162695526014501, 0.3162695526014501, 0.1837304473985499,
    0.2319010893971509, 0.2319010893971509, 0.0229177878448171,
    0.2319010893971509, 0.2319010893971509, 0.5132800333608811,
    0.5132800333608811, 0.2319010893971509, 0.0229177878448171,
    0.0229177878448171, 0.5132800333608811, 0.2319010893971509,
    0.0379700484718286, 0.0379700484718286, 0.7303134278075384,
    0.0379700484718286, 0.0379700484718286, 0.1937464752488044,
    0.1937464752488044, 0.0379700484718286, 0.7303134278075384,
    0.7303134278075384, 0.1937464752488044, 0.0379700484718286}

Definition at line 1188 of file fem_tools.h.

                                  {
    0.2500000000000000, 0.1274709365666390, 0.1274709365666390,
    0.6175871903000830, 0.1274709365666390, 0.0320788303926323,
    0.0320788303926323, 0.9037635088221031, 0.0320788303926323,
    0.0497770956432810, 0.0497770956432810, 0.4502229043567190,
    0.4502229043567190, 0.4502229043567190, 0.0497770956432810,
    0.1837304473985499, 0.1837304473985499, 0.3162695526014501,
    0.3162695526014501, 0.3162695526014501, 0.1837304473985499,
    0.2319010893971509, 0.2319010893971509, 0.0229177878448171,
    0.2319010893971509, 0.2319010893971509, 0.5132800333608811,
    0.5132800333608811, 0.2319010893971509, 0.0229177878448171,
    0.0229177878448171, 0.5132800333608811, 0.2319010893971509,
    0.0379700484718286, 0.0379700484718286, 0.7303134278075384,
    0.0379700484718286, 0.0379700484718286, 0.1937464752488044,
    0.1937464752488044, 0.0379700484718286, 0.7303134278075384,
    0.7303134278075384, 0.1937464752488044, 0.0379700484718286};

G_TET_Z5

const double G_TET_Z5[]

static

Initial value:

= {0.25000000000000000, 0.16666666666666667,
                                  0.16666666666666667, 0.50000000000000000,
                                  0.16666666666666667}

Definition at line 1129 of file fem_tools.h.

                                 {0.25000000000000000, 0.16666666666666667,
                                  0.16666666666666667, 0.50000000000000000,
                                  0.16666666666666667};

G_TRI_W1

const double G_TRI_W1[] = {1.}

static

Definition at line 314 of file fem_tools.h.

{1.};

G_TRI_W13

const double G_TRI_W13[]

static

Initial value:

= {
    -0.149570044467670, 0.175615257433204, 0.175615257433204, 0.175615257433204,
    0.053347235608839,  0.053347235608839, 0.053347235608839, 0.077113760890257,
    0.077113760890257,  0.077113760890257, 0.077113760890257, 0.077113760890257,
    0.077113760890257}

Definition at line 347 of file fem_tools.h.

                                  {
    -0.149570044467670, 0.175615257433204, 0.175615257433204, 0.175615257433204,
    0.053347235608839,  0.053347235608839, 0.053347235608839, 0.077113760890257,
    0.077113760890257,  0.077113760890257, 0.077113760890257, 0.077113760890257,
    0.077113760890257};

G_TRI_W19

const double G_TRI_W19[]

static

Initial value:

= {
    9.71357962827961025E-002, 3.13347002271398278E-002,
    3.13347002271398278E-002, 3.13347002271398278E-002,
    7.78275410047754301E-002, 7.78275410047754301E-002,
    7.78275410047754301E-002, 7.96477389272090969E-002,
    7.96477389272090969E-002, 7.96477389272090969E-002,
    2.55776756586981006E-002, 2.55776756586981006E-002,
    2.55776756586981006E-002, 4.32835393772893970E-002,
    4.32835393772893970E-002, 4.32835393772893970E-002,
    4.32835393772893970E-002, 4.32835393772893970E-002,
    4.32835393772893970E-002}

Definition at line 365 of file fem_tools.h.

                                  {
    9.71357962827961025E-002, 3.13347002271398278E-002,
    3.13347002271398278E-002, 3.13347002271398278E-002,
    7.78275410047754301E-002, 7.78275410047754301E-002,
    7.78275410047754301E-002, 7.96477389272090969E-002,
    7.96477389272090969E-002, 7.96477389272090969E-002,
    2.55776756586981006E-002, 2.55776756586981006E-002,
    2.55776756586981006E-002, 4.32835393772893970E-002,
    4.32835393772893970E-002, 4.32835393772893970E-002,
    4.32835393772893970E-002, 4.32835393772893970E-002,
    4.32835393772893970E-002};

G_TRI_W28

const double G_TRI_W28[]

static

Initial value:

= {
    0.08797730116222190,  0.008744311553736190, 0.008744311553736190,
    0.008744311553736190, 0.03808157199393533,  0.03808157199393533,
    0.03808157199393533,  0.01885544805613125,  0.01885544805613125,
    0.01885544805613125,  0.07215969754474100,  0.07215969754474100,
    0.07215969754474100,  0.06932913870553720,  0.06932913870553720,
    0.06932913870553720,  0.04105631542928860,  0.04105631542928860,
    0.04105631542928860,  0.04105631542928860,  0.04105631542928860,
    0.04105631542928860,  0.007362383783300573, 0.007362383783300573,
    0.007362383783300573, 0.007362383783300573, 0.007362383783300573,
    0.007362383783300573}

Definition at line 396 of file fem_tools.h.

                                  {
    0.08797730116222190,  0.008744311553736190, 0.008744311553736190,
    0.008744311553736190, 0.03808157199393533,  0.03808157199393533,
    0.03808157199393533,  0.01885544805613125,  0.01885544805613125,
    0.01885544805613125,  0.07215969754474100,  0.07215969754474100,
    0.07215969754474100,  0.06932913870553720,  0.06932913870553720,
    0.06932913870553720,  0.04105631542928860,  0.04105631542928860,
    0.04105631542928860,  0.04105631542928860,  0.04105631542928860,
    0.04105631542928860,  0.007362383783300573, 0.007362383783300573,
    0.007362383783300573, 0.007362383783300573, 0.007362383783300573,
    0.007362383783300573};

G_TRI_W286

const double G_TRI_W286[]

static

Initial value:

= {
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      -0.6133639040302452,
    -0.6133639040302452,    -0.6133639040302452,    -0.6133639040302452,
    -0.6133639040302452,    -0.6133639040302452,    -0.6133639040302452,
    -0.6133639040302452,    -0.6133639040302452,    -0.6133639040302452,
    -0.6133639040302452,    -0.6133639040302452,    -0.6133639040302452,
    -0.6133639040302452,    -0.6133639040302452,    -0.6133639040302452,
    -0.6133639040302452,    -0.6133639040302452,    -0.6133639040302452,
    -0.6133639040302452,    -0.6133639040302452,    0.05511571669513555,
    0.05511571669513555,    0.05511571669513555,    0.05511571669513555,
    0.05511571669513555,    0.05511571669513555,    0.05511571669513555,
    0.05511571669513555,    0.05511571669513555,    0.05511571669513555,
    0.05511571669513555,    0.05511571669513555,    0.05511571669513555,
    0.05511571669513555,    0.05511571669513555,    -0.001979122382447095,
    -0.001979122382447095,  -0.001979122382447095,  -0.001979122382447095,
    -0.001979122382447095,  -0.001979122382447095,  -0.001979122382447095,
    -0.001979122382447095,  -0.001979122382447095,  -0.001979122382447095,
    2.02054621415273e-05,   2.02054621415273e-05,   2.02054621415273e-05,
    2.02054621415273e-05,   2.02054621415273e-05,   2.02054621415273e-05,
    -2.874940020535803e-08, -2.874940020535803e-08, -2.874940020535803e-08,
    8.829438425435718e-13}

Definition at line 1013 of file fem_tools.h.

                                   {
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    2.912193380035668,      2.912193380035668,      2.912193380035668,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     -9.914451197589852,     -9.914451197589852,
    -9.914451197589852,     13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      13.33158527957992,      13.33158527957992,
    13.33158527957992,      -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     -9.027792408986382,     -9.027792408986382,
    -9.027792408986382,     3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      3.258672079964582,
    3.258672079964582,      3.258672079964582,      -0.6133639040302452,
    -0.6133639040302452,    -0.6133639040302452,    -0.6133639040302452,
    -0.6133639040302452,    -0.6133639040302452,    -0.6133639040302452,
    -0.6133639040302452,    -0.6133639040302452,    -0.6133639040302452,
    -0.6133639040302452,    -0.6133639040302452,    -0.6133639040302452,
    -0.6133639040302452,    -0.6133639040302452,    -0.6133639040302452,
    -0.6133639040302452,    -0.6133639040302452,    -0.6133639040302452,
    -0.6133639040302452,    -0.6133639040302452,    0.05511571669513555,
    0.05511571669513555,    0.05511571669513555,    0.05511571669513555,
    0.05511571669513555,    0.05511571669513555,    0.05511571669513555,
    0.05511571669513555,    0.05511571669513555,    0.05511571669513555,
    0.05511571669513555,    0.05511571669513555,    0.05511571669513555,
    0.05511571669513555,    0.05511571669513555,    -0.001979122382447095,
    -0.001979122382447095,  -0.001979122382447095,  -0.001979122382447095,
    -0.001979122382447095,  -0.001979122382447095,  -0.001979122382447095,
    -0.001979122382447095,  -0.001979122382447095,  -0.001979122382447095,
    2.02054621415273e-05,   2.02054621415273e-05,   2.02054621415273e-05,
    2.02054621415273e-05,   2.02054621415273e-05,   2.02054621415273e-05,
    -2.874940020535803e-08, -2.874940020535803e-08, -2.874940020535803e-08,
    8.829438425435718e-13};

G_TRI_W3

const double G_TRI_W3[]

static

Initial value:

= {
    3.3333333333333331e-01, 3.3333333333333331e-01, 3.3333333333333331e-01}

Definition at line 317 of file fem_tools.h.

                                 {
    3.3333333333333331e-01, 3.3333333333333331e-01, 3.3333333333333331e-01};

G_TRI_W37

const double G_TRI_W37[]

static

Initial value:

= {
    0.051739766065744, 0.008007799555565, 0.008007799555565, 0.008007799555565,
    0.046868898981822, 0.046868898981822, 0.046868898981822, 0.046590940183976,
    0.046590940183976, 0.046590940183976, 0.031016943313796, 0.031016943313796,
    0.031016943313796, 0.010791612736631, 0.010791612736631, 0.010791612736631,
    0.032195534242432, 0.032195534242432, 0.032195534242432, 0.015445834210702,
    0.015445834210702, 0.015445834210702, 0.015445834210702, 0.015445834210702,
    0.015445834210702, 0.017822989923179, 0.017822989923179, 0.017822989923179,
    0.017822989923179, 0.017822989923179, 0.017822989923179, 0.037038683681385,
    0.037038683681385, 0.037038683681385, 0.037038683681385, 0.037038683681385,
    0.037038683681385}

Definition at line 430 of file fem_tools.h.

                                  {
    0.051739766065744, 0.008007799555565, 0.008007799555565, 0.008007799555565,
    0.046868898981822, 0.046868898981822, 0.046868898981822, 0.046590940183976,
    0.046590940183976, 0.046590940183976, 0.031016943313796, 0.031016943313796,
    0.031016943313796, 0.010791612736631, 0.010791612736631, 0.010791612736631,
    0.032195534242432, 0.032195534242432, 0.032195534242432, 0.015445834210702,
    0.015445834210702, 0.015445834210702, 0.015445834210702, 0.015445834210702,
    0.015445834210702, 0.017822989923179, 0.017822989923179, 0.017822989923179,
    0.017822989923179, 0.017822989923179, 0.017822989923179, 0.037038683681385,
    0.037038683681385, 0.037038683681385, 0.037038683681385, 0.037038683681385,
    0.037038683681385};

G_TRI_W4

const double G_TRI_W4[]

static

Initial value:

= {
    1.8195861825602258066e-01, 3.1804138174397683647e-01,
    1.8195861825602258066e-01, 3.1804138174397683647e-01}

Definition at line 325 of file fem_tools.h.

                                 {
    1.8195861825602258066e-01, 3.1804138174397683647e-01,
    1.8195861825602258066e-01, 3.1804138174397683647e-01};

G_TRI_W7

const double G_TRI_W7[]

static

Initial value:

= {
    0.375000000000000, 0.104166666666667, 0.104166666666667, 0.104166666666667,
    0.104166666666667, 0.104166666666667, 0.104166666666667}

Definition at line 334 of file fem_tools.h.

                                 {
    0.375000000000000, 0.104166666666667, 0.104166666666667, 0.104166666666667,
    0.104166666666667, 0.104166666666667, 0.104166666666667};

G_TRI_X1

const double G_TRI_X1[] = {3.3333333333333331e-01}

static

Definition at line 312 of file fem_tools.h.

{3.3333333333333331e-01};

G_TRI_X13

const double G_TRI_X13[]

static

Initial value:

= {
    0.333333333333333, 0.479308067841923, 0.260345966079038, 0.260345966079038,
    0.869739794195568, 0.065130102902216, 0.065130102902216, 0.638444188569809,
    0.638444188569809, 0.312865496004875, 0.312865496004875, 0.048690315425316,
    0.048690315425316}

Definition at line 337 of file fem_tools.h.

                                  {
    0.333333333333333, 0.479308067841923, 0.260345966079038, 0.260345966079038,
    0.869739794195568, 0.065130102902216, 0.065130102902216, 0.638444188569809,
    0.638444188569809, 0.312865496004875, 0.312865496004875, 0.048690315425316,
    0.048690315425316};

G_TRI_X19

const double G_TRI_X19[]

static

Initial value:

= {
    0.333333333333333, 0.797426985353087, 0.101286507323456, 0.101286507323456,
    0.059715871789770, 0.470142064105115, 0.470142064105115, 0.535795346449899,
    0.232102326775050, 0.232102326775050, 0.941038278231121, 0.029480860884440,
    0.029480860884440, 0.738416812340510, 0.738416812340510, 0.232102326775050,
    0.232102326775050, 0.029480860884440, 0.029480860884440}

Definition at line 353 of file fem_tools.h.

                                  {
    0.333333333333333, 0.797426985353087, 0.101286507323456, 0.101286507323456,
    0.059715871789770, 0.470142064105115, 0.470142064105115, 0.535795346449899,
    0.232102326775050, 0.232102326775050, 0.941038278231121, 0.029480860884440,
    0.029480860884440, 0.738416812340510, 0.738416812340510, 0.232102326775050,
    0.232102326775050, 0.029480860884440, 0.029480860884440};

G_TRI_X28

const double G_TRI_X28[]

static

Initial value:

= {
    0.333333333333333,  0.948021718143423,  0.025989140928288,
    0.025989140928288,  0.811424994704155,  0.094287502647923,
    0.094287502647923,  0.010726449965571,  0.494636775017215,
    0.494636775017215,  0.585313234770972,  0.207343382614514,
    0.207343382614514,  0.122184388599019,  0.438907805700491,
    0.438907805700491,  0.677937654882590,  0.677937654882590,
    0.044841677589131,  0.044841677589131,  0.277220667528279,
    0.277220667528279,  0.858870281282636,  0.858870281282636,
    0.0000000000000000, 0.0000000000000000, 0.141129718717364,
    0.141129718717364}

Definition at line 377 of file fem_tools.h.

                                  {
    0.333333333333333,  0.948021718143423,  0.025989140928288,
    0.025989140928288,  0.811424994704155,  0.094287502647923,
    0.094287502647923,  0.010726449965571,  0.494636775017215,
    0.494636775017215,  0.585313234770972,  0.207343382614514,
    0.207343382614514,  0.122184388599019,  0.438907805700491,
    0.438907805700491,  0.677937654882590,  0.677937654882590,
    0.044841677589131,  0.044841677589131,  0.277220667528279,
    0.277220667528279,  0.858870281282636,  0.858870281282636,
    0.0000000000000000, 0.0000000000000000, 0.141129718717364,
    0.141129718717364};

G_TRI_X286

const double G_TRI_X286[]

static

Definition at line 441 of file fem_tools.h.

                                   {0.04347826086956522,
                                    0.1304347826086956,
                                    0.2173913043478261,
                                    0.3043478260869565,
                                    0.391304347826087,
                                    0.4782608695652174,
                                    0.5652173913043478,
                                    0.6521739130434783,
                                    0.7391304347826086,
                                    0.8260869565217391,
                                    0.9130434782608695,
                                    0.04347826086956522,
                                    0.1304347826086956,
                                    0.2173913043478261,
                                    0.3043478260869565,
                                    0.391304347826087,
                                    0.4782608695652174,
                                    0.5652173913043478,
                                    0.6521739130434783,
                                    0.7391304347826086,
                                    0.8260869565217391,
                                    0.04347826086956522,
                                    0.1304347826086956,
                                    0.2173913043478261,
                                    0.3043478260869565,
                                    0.391304347826087,
                                    0.4782608695652174,
                                    0.5652173913043478,
                                    0.6521739130434783,
                                    0.7391304347826086,
                                    0.04347826086956522,
                                    0.1304347826086956,
                                    0.2173913043478261,
                                    0.3043478260869565,
                                    0.391304347826087,
                                    0.4782608695652174,
                                    0.5652173913043478,
                                    0.6521739130434783,
                                    0.04347826086956522,
                                    0.1304347826086956,
                                    0.2173913043478261,
                                    0.3043478260869565,
                                    0.391304347826087,
                                    0.4782608695652174,
                                    0.5652173913043478,
                                    0.04347826086956522,
                                    0.1304347826086956,
                                    0.2173913043478261,
                                    0.3043478260869565,
                                    0.391304347826087,
                                    0.4782608695652174,
                                    0.04347826086956522,
                                    0.1304347826086956,
                                    0.2173913043478261,
                                    0.3043478260869565,
                                    0.391304347826087,
                                    0.04347826086956522,
                                    0.1304347826086956,
                                    0.2173913043478261,
                                    0.3043478260869565,
                                    0.04347826086956522,
                                    0.1304347826086956,
                                    0.2173913043478261,
                                    0.04347826086956522,
                                    0.1304347826086956,
                                    0.04347826086956522,
                                    0.04761904761904762,
                                    0.1428571428571428,
                                    0.2380952380952381,
                                    0.3333333333333333,
                                    0.4285714285714285,
                                    0.5238095238095238,
                                    0.6190476190476191,
                                    0.7142857142857143,
                                    0.8095238095238095,
                                    0.9047619047619048,
                                    0.04761904761904762,
                                    0.1428571428571428,
                                    0.2380952380952381,
                                    0.3333333333333333,
                                    0.4285714285714285,
                                    0.5238095238095238,
                                    0.6190476190476191,
                                    0.7142857142857143,
                                    0.8095238095238095,
                                    0.04761904761904762,
                                    0.1428571428571428,
                                    0.2380952380952381,
                                    0.3333333333333333,
                                    0.4285714285714285,
                                    0.5238095238095238,
                                    0.6190476190476191,
                                    0.7142857142857143,
                                    0.04761904761904762,
                                    0.1428571428571428,
                                    0.2380952380952381,
                                    0.3333333333333333,
                                    0.4285714285714285,
                                    0.5238095238095238,
                                    0.6190476190476191,
                                    0.04761904761904762,
                                    0.1428571428571428,
                                    0.2380952380952381,
                                    0.3333333333333333,
                                    0.4285714285714285,
                                    0.5238095238095238,
                                    0.04761904761904762,
                                    0.1428571428571428,
                                    0.2380952380952381,
                                    0.3333333333333333,
                                    0.4285714285714285,
                                    0.04761904761904762,
                                    0.1428571428571428,
                                    0.2380952380952381,
                                    0.3333333333333333,
                                    0.04761904761904762,
                                    0.1428571428571428,
                                    0.2380952380952381,
                                    0.04761904761904762,
                                    0.1428571428571428,
                                    0.04761904761904762,
                                    0.05263157894736842,
                                    0.1578947368421053,
                                    0.2631578947368421,
                                    0.3684210526315789,
                                    0.4736842105263158,
                                    0.5789473684210527,
                                    0.6842105263157895,
                                    0.7894736842105263,
                                    0.8947368421052632,
                                    0.05263157894736842,
                                    0.1578947368421053,
                                    0.2631578947368421,
                                    0.3684210526315789,
                                    0.4736842105263158,
                                    0.5789473684210527,
                                    0.6842105263157895,
                                    0.7894736842105263,
                                    0.05263157894736842,
                                    0.1578947368421053,
                                    0.2631578947368421,
                                    0.3684210526315789,
                                    0.4736842105263158,
                                    0.5789473684210527,
                                    0.6842105263157895,
                                    0.05263157894736842,
                                    0.1578947368421053,
                                    0.2631578947368421,
                                    0.3684210526315789,
                                    0.4736842105263158,
                                    0.5789473684210527,
                                    0.05263157894736842,
                                    0.1578947368421053,
                                    0.2631578947368421,
                                    0.3684210526315789,
                                    0.4736842105263158,
                                    0.05263157894736842,
                                    0.1578947368421053,
                                    0.2631578947368421,
                                    0.3684210526315789,
                                    0.05263157894736842,
                                    0.1578947368421053,
                                    0.2631578947368421,
                                    0.05263157894736842,
                                    0.1578947368421053,
                                    0.05263157894736842,
                                    0.05882352941176471,
                                    0.1764705882352941,
                                    0.2941176470588235,
                                    0.4117647058823529,
                                    0.5294117647058824,
                                    0.6470588235294118,
                                    0.7647058823529411,
                                    0.8823529411764706,
                                    0.05882352941176471,
                                    0.1764705882352941,
                                    0.2941176470588235,
                                    0.4117647058823529,
                                    0.5294117647058824,
                                    0.6470588235294118,
                                    0.7647058823529411,
                                    0.05882352941176471,
                                    0.1764705882352941,
                                    0.2941176470588235,
                                    0.4117647058823529,
                                    0.5294117647058824,
                                    0.6470588235294118,
                                    0.05882352941176471,
                                    0.1764705882352941,
                                    0.2941176470588235,
                                    0.4117647058823529,
                                    0.5294117647058824,
                                    0.05882352941176471,
                                    0.1764705882352941,
                                    0.2941176470588235,
                                    0.4117647058823529,
                                    0.05882352941176471,
                                    0.1764705882352941,
                                    0.2941176470588235,
                                    0.05882352941176471,
                                    0.1764705882352941,
                                    0.05882352941176471,
                                    0.06666666666666667,
                                    0.2,
                                    0.3333333333333333,
                                    0.4666666666666667,
                                    0.6,
                                    0.7333333333333333,
                                    0.8666666666666667,
                                    0.06666666666666667,
                                    0.2,
                                    0.3333333333333333,
                                    0.4666666666666667,
                                    0.6,
                                    0.7333333333333333,
                                    0.06666666666666667,
                                    0.2,
                                    0.3333333333333333,
                                    0.4666666666666667,
                                    0.6,
                                    0.06666666666666667,
                                    0.2,
                                    0.3333333333333333,
                                    0.4666666666666667,
                                    0.06666666666666667,
                                    0.2,
                                    0.3333333333333333,
                                    0.06666666666666667,
                                    0.2,
                                    0.06666666666666667,
                                    0.07692307692307693,
                                    0.2307692307692308,
                                    0.3846153846153846,
                                    0.5384615384615384,
                                    0.6923076923076923,
                                    0.8461538461538461,
                                    0.07692307692307693,
                                    0.2307692307692308,
                                    0.3846153846153846,
                                    0.5384615384615384,
                                    0.6923076923076923,
                                    0.07692307692307693,
                                    0.2307692307692308,
                                    0.3846153846153846,
                                    0.5384615384615384,
                                    0.07692307692307693,
                                    0.2307692307692308,
                                    0.3846153846153846,
                                    0.07692307692307693,
                                    0.2307692307692308,
                                    0.07692307692307693,
                                    0.09090909090909091,
                                    0.2727272727272727,
                                    0.4545454545454545,
                                    0.6363636363636364,
                                    0.8181818181818182,
                                    0.09090909090909091,
                                    0.2727272727272727,
                                    0.4545454545454545,
                                    0.6363636363636364,
                                    0.09090909090909091,
                                    0.2727272727272727,
                                    0.4545454545454545,
                                    0.09090909090909091,
                                    0.2727272727272727,
                                    0.09090909090909091,
                                    0.1111111111111111,
                                    0.3333333333333333,
                                    0.5555555555555556,
                                    0.7777777777777778,
                                    0.1111111111111111,
                                    0.3333333333333333,
                                    0.5555555555555556,
                                    0.1111111111111111,
                                    0.3333333333333333,
                                    0.1111111111111111,
                                    0.1428571428571428,
                                    0.4285714285714285,
                                    0.7142857142857143,
                                    0.1428571428571428,
                                    0.4285714285714285,
                                    0.1428571428571428,
                                    0.2,
                                    0.6,
                                    0.2,
                                    0.3333333333333333};

G_TRI_X3

const double G_TRI_X3[] = {0.5, 0., 0.5}

static

Definition at line 315 of file fem_tools.h.

{0.5, 0., 0.5};

G_TRI_X37

const double G_TRI_X37[]

static

Initial value:

= {
    0.333333333333333, 0.950275662924106, 0.024862168537947, 0.024862168537947,
    0.171614914923835, 0.414192542538082, 0.414192542538082, 0.539412243677190,
    0.230293878161405, 0.230293878161405, 0.772160036676533, 0.113919981661734,
    0.113919981661734, 0.009085399949835, 0.495457300025082, 0.495457300025082,
    0.062277290305887, 0.468861354847056, 0.468861354847056, 0.022076289653624,
    0.022076289653624, 0.851306504174348, 0.851306504174348, 0.126617206172027,
    0.126617206172027, 0.018620522802521, 0.018620522802521, 0.689441970728591,
    0.689441970728591, 0.291937506468888, 0.291937506468888, 0.096506481292159,
    0.096506481292159, 0.635867859433873, 0.635867859433873, 0.267625659273968,
    0.267625659273968}

Definition at line 408 of file fem_tools.h.

                                  {
    0.333333333333333, 0.950275662924106, 0.024862168537947, 0.024862168537947,
    0.171614914923835, 0.414192542538082, 0.414192542538082, 0.539412243677190,
    0.230293878161405, 0.230293878161405, 0.772160036676533, 0.113919981661734,
    0.113919981661734, 0.009085399949835, 0.495457300025082, 0.495457300025082,
    0.062277290305887, 0.468861354847056, 0.468861354847056, 0.022076289653624,
    0.022076289653624, 0.851306504174348, 0.851306504174348, 0.126617206172027,
    0.126617206172027, 0.018620522802521, 0.018620522802521, 0.689441970728591,
    0.689441970728591, 0.291937506468888, 0.291937506468888, 0.096506481292159,
    0.096506481292159, 0.635867859433873, 0.635867859433873, 0.267625659273968,
    0.267625659273968};

G_TRI_X4

const double G_TRI_X4[]

static

Initial value:

= {
    7.503111022260811058e-02, 1.785587282636164064e-01,
    2.800199154990741235e-01, 6.663902460147014262e-01}

Definition at line 319 of file fem_tools.h.

                                 {
    7.503111022260811058e-02, 1.785587282636164064e-01,
    2.800199154990741235e-01, 6.663902460147014262e-01};

G_TRI_X7

const double G_TRI_X7[]

static

Initial value:

= {
    0.333333333333333, 0.736712498968435, 0.736712498968435, 0.237932366472434,
    0.237932366472434, 0.025355134551932, 0.025355134551932}

Definition at line 328 of file fem_tools.h.

                                 {
    0.333333333333333, 0.736712498968435, 0.736712498968435, 0.237932366472434,
    0.237932366472434, 0.025355134551932, 0.025355134551932};

G_TRI_Y1

const double G_TRI_Y1[] = {3.3333333333333331e-01}

static

Definition at line 313 of file fem_tools.h.

{3.3333333333333331e-01};

G_TRI_Y13

const double G_TRI_Y13[]

static

Initial value:

= {
    0.333333333333333, 0.260345966079038, 0.479308067841923, 0.260345966079038,
    0.065130102902216, 0.869739794195568, 0.065130102902216, 0.312865496004875,
    0.048690315425316, 0.638444188569809, 0.048690315425316, 0.638444188569809,
    0.312865496004875}

Definition at line 342 of file fem_tools.h.

                                  {
    0.333333333333333, 0.260345966079038, 0.479308067841923, 0.260345966079038,
    0.065130102902216, 0.869739794195568, 0.065130102902216, 0.312865496004875,
    0.048690315425316, 0.638444188569809, 0.048690315425316, 0.638444188569809,
    0.312865496004875};

G_TRI_Y19

const double G_TRI_Y19[]

static

Initial value:

= {
    0.333333333333333, 0.101286507323456, 0.797426985353087, 0.101286507323456,
    0.470142064105115, 0.059715871789770, 0.470142064105115, 0.232102326775050,
    0.535795346449899, 0.232102326775050, 0.029480860884440, 0.941038278231121,
    0.029480860884440, 0.232102326775050, 0.029480860884440, 0.738416812340510,
    0.029480860884440, 0.738416812340510, 0.232102326775050}

Definition at line 359 of file fem_tools.h.

                                  {
    0.333333333333333, 0.101286507323456, 0.797426985353087, 0.101286507323456,
    0.470142064105115, 0.059715871789770, 0.470142064105115, 0.232102326775050,
    0.535795346449899, 0.232102326775050, 0.029480860884440, 0.941038278231121,
    0.029480860884440, 0.232102326775050, 0.029480860884440, 0.738416812340510,
    0.029480860884440, 0.738416812340510, 0.232102326775050};

G_TRI_Y28

const double G_TRI_Y28[]

static

Initial value:

= {
    0.333333333333333, 0.025989140928288, 0.948021718143423, 0.025989140928288,
    0.094287502647923, 0.811424994704155, 0.094287502647923, 0.494636775017215,
    0.010726449965571, 0.494636775017215, 0.207343382614514, 0.585313234770972,
    0.207343382614514, 0.438907805700491, 0.122184388599019, 0.438907805700491,
    0.044841677589131, 0.277220667528279, 0.677937654882590, 0.277220667528279,
    0.677937654882590, 0.044841677589131, 0.000000000000000, 0.141129718717364,
    0.858870281282636, 0.141129718717364, 0.858870281282636, 0.000000000000000}

Definition at line 388 of file fem_tools.h.

                                  {
    0.333333333333333, 0.025989140928288, 0.948021718143423, 0.025989140928288,
    0.094287502647923, 0.811424994704155, 0.094287502647923, 0.494636775017215,
    0.010726449965571, 0.494636775017215, 0.207343382614514, 0.585313234770972,
    0.207343382614514, 0.438907805700491, 0.122184388599019, 0.438907805700491,
    0.044841677589131, 0.277220667528279, 0.677937654882590, 0.277220667528279,
    0.677937654882590, 0.044841677589131, 0.000000000000000, 0.141129718717364,
    0.858870281282636, 0.141129718717364, 0.858870281282636, 0.000000000000000};

G_TRI_Y286

const double G_TRI_Y286[]

static

Definition at line 727 of file fem_tools.h.

                                   {0.04347826086956522,
                                    0.04347826086956522,
                                    0.04347826086956522,
                                    0.04347826086956522,
                                    0.04347826086956522,
                                    0.04347826086956522,
                                    0.04347826086956522,
                                    0.04347826086956522,
                                    0.04347826086956522,
                                    0.04347826086956522,
                                    0.04347826086956522,
                                    0.1304347826086956,
                                    0.1304347826086956,
                                    0.1304347826086956,
                                    0.1304347826086956,
                                    0.1304347826086956,
                                    0.1304347826086956,
                                    0.1304347826086956,
                                    0.1304347826086956,
                                    0.1304347826086956,
                                    0.1304347826086956,
                                    0.2173913043478261,
                                    0.2173913043478261,
                                    0.2173913043478261,
                                    0.2173913043478261,
                                    0.2173913043478261,
                                    0.2173913043478261,
                                    0.2173913043478261,
                                    0.2173913043478261,
                                    0.2173913043478261,
                                    0.3043478260869565,
                                    0.3043478260869565,
                                    0.3043478260869565,
                                    0.3043478260869565,
                                    0.3043478260869565,
                                    0.3043478260869565,
                                    0.3043478260869565,
                                    0.3043478260869565,
                                    0.391304347826087,
                                    0.391304347826087,
                                    0.391304347826087,
                                    0.391304347826087,
                                    0.391304347826087,
                                    0.391304347826087,
                                    0.391304347826087,
                                    0.4782608695652174,
                                    0.4782608695652174,
                                    0.4782608695652174,
                                    0.4782608695652174,
                                    0.4782608695652174,
                                    0.4782608695652174,
                                    0.5652173913043478,
                                    0.5652173913043478,
                                    0.5652173913043478,
                                    0.5652173913043478,
                                    0.5652173913043478,
                                    0.6521739130434783,
                                    0.6521739130434783,
                                    0.6521739130434783,
                                    0.6521739130434783,
                                    0.7391304347826086,
                                    0.7391304347826086,
                                    0.7391304347826086,
                                    0.8260869565217391,
                                    0.8260869565217391,
                                    0.9130434782608695,
                                    0.04761904761904762,
                                    0.04761904761904762,
                                    0.04761904761904762,
                                    0.04761904761904762,
                                    0.04761904761904762,
                                    0.04761904761904762,
                                    0.04761904761904762,
                                    0.04761904761904762,
                                    0.04761904761904762,
                                    0.04761904761904762,
                                    0.1428571428571428,
                                    0.1428571428571428,
                                    0.1428571428571428,
                                    0.1428571428571428,
                                    0.1428571428571428,
                                    0.1428571428571428,
                                    0.1428571428571428,
                                    0.1428571428571428,
                                    0.1428571428571428,
                                    0.2380952380952381,
                                    0.2380952380952381,
                                    0.2380952380952381,
                                    0.2380952380952381,
                                    0.2380952380952381,
                                    0.2380952380952381,
                                    0.2380952380952381,
                                    0.2380952380952381,
                                    0.3333333333333333,
                                    0.3333333333333333,
                                    0.3333333333333333,
                                    0.3333333333333333,
                                    0.3333333333333333,
                                    0.3333333333333333,
                                    0.3333333333333333,
                                    0.4285714285714285,
                                    0.4285714285714285,
                                    0.4285714285714285,
                                    0.4285714285714285,
                                    0.4285714285714285,
                                    0.4285714285714285,
                                    0.5238095238095238,
                                    0.5238095238095238,
                                    0.5238095238095238,
                                    0.5238095238095238,
                                    0.5238095238095238,
                                    0.6190476190476191,
                                    0.6190476190476191,
                                    0.6190476190476191,
                                    0.6190476190476191,
                                    0.7142857142857143,
                                    0.7142857142857143,
                                    0.7142857142857143,
                                    0.8095238095238095,
                                    0.8095238095238095,
                                    0.9047619047619048,
                                    0.05263157894736842,
                                    0.05263157894736842,
                                    0.05263157894736842,
                                    0.05263157894736842,
                                    0.05263157894736842,
                                    0.05263157894736842,
                                    0.05263157894736842,
                                    0.05263157894736842,
                                    0.05263157894736842,
                                    0.1578947368421053,
                                    0.1578947368421053,
                                    0.1578947368421053,
                                    0.1578947368421053,
                                    0.1578947368421053,
                                    0.1578947368421053,
                                    0.1578947368421053,
                                    0.1578947368421053,
                                    0.2631578947368421,
                                    0.2631578947368421,
                                    0.2631578947368421,
                                    0.2631578947368421,
                                    0.2631578947368421,
                                    0.2631578947368421,
                                    0.2631578947368421,
                                    0.3684210526315789,
                                    0.3684210526315789,
                                    0.3684210526315789,
                                    0.3684210526315789,
                                    0.3684210526315789,
                                    0.3684210526315789,
                                    0.4736842105263158,
                                    0.4736842105263158,
                                    0.4736842105263158,
                                    0.4736842105263158,
                                    0.4736842105263158,
                                    0.5789473684210527,
                                    0.5789473684210527,
                                    0.5789473684210527,
                                    0.5789473684210527,
                                    0.6842105263157895,
                                    0.6842105263157895,
                                    0.6842105263157895,
                                    0.7894736842105263,
                                    0.7894736842105263,
                                    0.8947368421052632,
                                    0.05882352941176471,
                                    0.05882352941176471,
                                    0.05882352941176471,
                                    0.05882352941176471,
                                    0.05882352941176471,
                                    0.05882352941176471,
                                    0.05882352941176471,
                                    0.05882352941176471,
                                    0.1764705882352941,
                                    0.1764705882352941,
                                    0.1764705882352941,
                                    0.1764705882352941,
                                    0.1764705882352941,
                                    0.1764705882352941,
                                    0.1764705882352941,
                                    0.2941176470588235,
                                    0.2941176470588235,
                                    0.2941176470588235,
                                    0.2941176470588235,
                                    0.2941176470588235,
                                    0.2941176470588235,
                                    0.4117647058823529,
                                    0.4117647058823529,
                                    0.4117647058823529,
                                    0.4117647058823529,
                                    0.4117647058823529,
                                    0.5294117647058824,
                                    0.5294117647058824,
                                    0.5294117647058824,
                                    0.5294117647058824,
                                    0.6470588235294118,
                                    0.6470588235294118,
                                    0.6470588235294118,
                                    0.7647058823529411,
                                    0.7647058823529411,
                                    0.8823529411764706,
                                    0.06666666666666667,
                                    0.06666666666666667,
                                    0.06666666666666667,
                                    0.06666666666666667,
                                    0.06666666666666667,
                                    0.06666666666666667,
                                    0.06666666666666667,
                                    0.2,
                                    0.2,
                                    0.2,
                                    0.2,
                                    0.2,
                                    0.2,
                                    0.3333333333333333,
                                    0.3333333333333333,
                                    0.3333333333333333,
                                    0.3333333333333333,
                                    0.3333333333333333,
                                    0.4666666666666667,
                                    0.4666666666666667,
                                    0.4666666666666667,
                                    0.4666666666666667,
                                    0.6,
                                    0.6,
                                    0.6,
                                    0.7333333333333333,
                                    0.7333333333333333,
                                    0.8666666666666667,
                                    0.07692307692307693,
                                    0.07692307692307693,
                                    0.07692307692307693,
                                    0.07692307692307693,
                                    0.07692307692307693,
                                    0.07692307692307693,
                                    0.2307692307692308,
                                    0.2307692307692308,
                                    0.2307692307692308,
                                    0.2307692307692308,
                                    0.2307692307692308,
                                    0.3846153846153846,
                                    0.3846153846153846,
                                    0.3846153846153846,
                                    0.3846153846153846,
                                    0.5384615384615384,
                                    0.5384615384615384,
                                    0.5384615384615384,
                                    0.6923076923076923,
                                    0.6923076923076923,
                                    0.8461538461538461,
                                    0.09090909090909091,
                                    0.09090909090909091,
                                    0.09090909090909091,
                                    0.09090909090909091,
                                    0.09090909090909091,
                                    0.2727272727272727,
                                    0.2727272727272727,
                                    0.2727272727272727,
                                    0.2727272727272727,
                                    0.4545454545454545,
                                    0.4545454545454545,
                                    0.4545454545454545,
                                    0.6363636363636364,
                                    0.6363636363636364,
                                    0.8181818181818182,
                                    0.1111111111111111,
                                    0.1111111111111111,
                                    0.1111111111111111,
                                    0.1111111111111111,
                                    0.3333333333333333,
                                    0.3333333333333333,
                                    0.3333333333333333,
                                    0.5555555555555556,
                                    0.5555555555555556,
                                    0.7777777777777778,
                                    0.1428571428571428,
                                    0.1428571428571428,
                                    0.1428571428571428,
                                    0.4285714285714285,
                                    0.4285714285714285,
                                    0.7142857142857143,
                                    0.2,
                                    0.2,
                                    0.6,
                                    0.3333333333333333};

G_TRI_Y3

const double G_TRI_Y3[] = {0., 0.5, 0.5}

static

Definition at line 316 of file fem_tools.h.

{0., 0.5, 0.5};

G_TRI_Y37

const double G_TRI_Y37[]

static

Initial value:

= {
    0.333333333333333, 0.024862168537947, 0.950275662924106, 0.024862168537947,
    0.414192542538082, 0.171614914923835, 0.414192542538082, 0.230293878161405,
    0.539412243677190, 0.230293878161405, 0.113919981661734, 0.772160036676533,
    0.113919981661734, 0.495457300025082, 0.009085399949835, 0.495457300025082,
    0.468861354847056, 0.062277290305887, 0.468861354847056, 0.851306504174348,
    0.126617206172027, 0.022076289653624, 0.126617206172027, 0.022076289653624,
    0.851306504174348, 0.689441970728591, 0.291937506468888, 0.018620522802521,
    0.291937506468888, 0.018620522802521, 0.689441970728591, 0.635867859433873,
    0.267625659273968, 0.096506481292159, 0.267625659273968, 0.096506481292159,
    0.635867859433873}

Definition at line 419 of file fem_tools.h.

                                  {
    0.333333333333333, 0.024862168537947, 0.950275662924106, 0.024862168537947,
    0.414192542538082, 0.171614914923835, 0.414192542538082, 0.230293878161405,
    0.539412243677190, 0.230293878161405, 0.113919981661734, 0.772160036676533,
    0.113919981661734, 0.495457300025082, 0.009085399949835, 0.495457300025082,
    0.468861354847056, 0.062277290305887, 0.468861354847056, 0.851306504174348,
    0.126617206172027, 0.022076289653624, 0.126617206172027, 0.022076289653624,
    0.851306504174348, 0.689441970728591, 0.291937506468888, 0.018620522802521,
    0.291937506468888, 0.018620522802521, 0.689441970728591, 0.635867859433873,
    0.267625659273968, 0.096506481292159, 0.267625659273968, 0.096506481292159,
    0.635867859433873};

G_TRI_Y4

const double G_TRI_Y4[]

static

Initial value:

= {
    2.800199154990741235e-01, 6.663902460147014262e-01,
    7.503111022260811058e-02, 1.785587282636164064e-01}

Definition at line 322 of file fem_tools.h.

                                 {
    2.800199154990741235e-01, 6.663902460147014262e-01,
    7.503111022260811058e-02, 1.785587282636164064e-01};

G_TRI_Y7

const double G_TRI_Y7[]

static

Initial value:

= {
    0.333333333333333, 0.237932366472434, 0.025355134551932, 0.736712498968435,
    0.025355134551932, 0.736712498968435, 0.237932366472434}

Definition at line 331 of file fem_tools.h.

                                 {
    0.333333333333333, 0.237932366472434, 0.025355134551932, 0.736712498968435,
    0.025355134551932, 0.736712498968435, 0.237932366472434};

NC_TET_W84

const double NC_TET_W84[]

static

Initial value:

= {
    0.2843915343915344,  0.2843915343915344,  0.2843915343915344,
    0.2843915343915344,  -0.3882275132275133, -0.3882275132275133,
    -0.3882275132275133, -0.3882275132275133, -0.3882275132275133,
    -0.3882275132275133, -0.3882275132275133, -0.3882275132275133,
    -0.3882275132275133, -0.3882275132275133, -0.3882275132275133,
    -0.3882275132275133, 0.8776455026455027,  0.8776455026455027,
    0.8776455026455027,  0.8776455026455027,  0.8776455026455027,
    0.8776455026455027,  0.8776455026455027,  0.8776455026455027,
    0.8776455026455027,  0.8776455026455027,  0.8776455026455027,
    0.8776455026455027,  0.1236772486772487,  0.1236772486772487,
    0.1236772486772487,  0.1236772486772487,  0.1236772486772487,
    0.1236772486772487,  0.1236772486772487,  0.1236772486772487,
    0.1236772486772487,  0.1236772486772487,  0.1236772486772487,
    0.1236772486772487,  -0.8584656084656085, -0.8584656084656085,
    -0.8584656084656085, -0.8584656084656085, -0.8584656084656085,
    -0.8584656084656085, -0.2632275132275133, -0.2632275132275133,
    -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
    -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
    -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
    -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
    -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
    -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
    -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
    -0.2632275132275133, 0.0145502645502645,  0.0145502645502645,
    0.0145502645502645,  0.0145502645502645,  1.0165343915343916,
    1.0165343915343916,  1.0165343915343916,  1.0165343915343916,
    -0.0251322751322751, -0.0251322751322751, -0.0251322751322751,
    -0.0251322751322751, -0.0251322751322751, -0.0251322751322751}

Definition at line 1307 of file fem_tools.h.

                                   {
    0.2843915343915344,  0.2843915343915344,  0.2843915343915344,
    0.2843915343915344,  -0.3882275132275133, -0.3882275132275133,
    -0.3882275132275133, -0.3882275132275133, -0.3882275132275133,
    -0.3882275132275133, -0.3882275132275133, -0.3882275132275133,
    -0.3882275132275133, -0.3882275132275133, -0.3882275132275133,
    -0.3882275132275133, 0.8776455026455027,  0.8776455026455027,
    0.8776455026455027,  0.8776455026455027,  0.8776455026455027,
    0.8776455026455027,  0.8776455026455027,  0.8776455026455027,
    0.8776455026455027,  0.8776455026455027,  0.8776455026455027,
    0.8776455026455027,  0.1236772486772487,  0.1236772486772487,
    0.1236772486772487,  0.1236772486772487,  0.1236772486772487,
    0.1236772486772487,  0.1236772486772487,  0.1236772486772487,
    0.1236772486772487,  0.1236772486772487,  0.1236772486772487,
    0.1236772486772487,  -0.8584656084656085, -0.8584656084656085,
    -0.8584656084656085, -0.8584656084656085, -0.8584656084656085,
    -0.8584656084656085, -0.2632275132275133, -0.2632275132275133,
    -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
    -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
    -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
    -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
    -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
    -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
    -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
    -0.2632275132275133, 0.0145502645502645,  0.0145502645502645,
    0.0145502645502645,  0.0145502645502645,  1.0165343915343916,
    1.0165343915343916,  1.0165343915343916,  1.0165343915343916,
    -0.0251322751322751, -0.0251322751322751, -0.0251322751322751,
    -0.0251322751322751, -0.0251322751322751, -0.0251322751322751};

NC_TET_X84

const double NC_TET_X84[]

static

Initial value:

= {
    0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.7000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.6000000000000000, 0.6000000000000000,
    0.6000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.2000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.5000000000000000, 0.5000000000000000,
    0.5000000000000000, 0.3000000000000000, 0.3000000000000000,
    0.3000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.2000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.5000000000000000, 0.5000000000000000,
    0.5000000000000000, 0.4000000000000000, 0.4000000000000000,
    0.4000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.4000000000000000, 0.4000000000000000,
    0.4000000000000000, 0.4000000000000000, 0.4000000000000000,
    0.4000000000000000, 0.3000000000000000, 0.3000000000000000,
    0.3000000000000000, 0.3000000000000000, 0.3000000000000000,
    0.3000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.2000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.2000000000000000, 0.4000000000000000, 0.3000000000000000,
    0.3000000000000000, 0.3000000000000000, 0.1000000000000000,
    0.3000000000000000, 0.3000000000000000, 0.3000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.2000000000000000}

Definition at line 1220 of file fem_tools.h.

                                   {
    0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.7000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.6000000000000000, 0.6000000000000000,
    0.6000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.2000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.5000000000000000, 0.5000000000000000,
    0.5000000000000000, 0.3000000000000000, 0.3000000000000000,
    0.3000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.2000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.5000000000000000, 0.5000000000000000,
    0.5000000000000000, 0.4000000000000000, 0.4000000000000000,
    0.4000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.4000000000000000, 0.4000000000000000,
    0.4000000000000000, 0.4000000000000000, 0.4000000000000000,
    0.4000000000000000, 0.3000000000000000, 0.3000000000000000,
    0.3000000000000000, 0.3000000000000000, 0.3000000000000000,
    0.3000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.2000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.2000000000000000, 0.4000000000000000, 0.3000000000000000,
    0.3000000000000000, 0.3000000000000000, 0.1000000000000000,
    0.3000000000000000, 0.3000000000000000, 0.3000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.2000000000000000};

NC_TET_Y84

const double NC_TET_Y84[]

static

Initial value:

= {
    0.1000000000000000, 0.1000000000000000, 0.7000000000000000,
    0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.6000000000000000, 0.6000000000000000, 0.2000000000000000,
    0.2000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.2000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.6000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.5000000000000000, 0.5000000000000000, 0.3000000000000000,
    0.3000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.3000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.5000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.1000000000000000, 0.1000000000000000, 0.5000000000000000,
    0.5000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.5000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.1000000000000000, 0.4000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.4000000000000000, 0.4000000000000000,
    0.1000000000000000, 0.3000000000000000, 0.3000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.4000000000000000, 0.4000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.4000000000000000, 0.4000000000000000,
    0.3000000000000000, 0.3000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.4000000000000000, 0.4000000000000000,
    0.3000000000000000, 0.3000000000000000, 0.2000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.4000000000000000, 0.2000000000000000, 0.3000000000000000,
    0.3000000000000000, 0.1000000000000000, 0.3000000000000000,
    0.3000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.3000000000000000, 0.3000000000000000, 0.2000000000000000}

Definition at line 1249 of file fem_tools.h.

                                   {
    0.1000000000000000, 0.1000000000000000, 0.7000000000000000,
    0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.6000000000000000, 0.6000000000000000, 0.2000000000000000,
    0.2000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.2000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.6000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.5000000000000000, 0.5000000000000000, 0.3000000000000000,
    0.3000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.3000000000000000, 0.1000000000000000, 0.1000000000000000,
    0.5000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.1000000000000000, 0.1000000000000000, 0.5000000000000000,
    0.5000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.5000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.1000000000000000, 0.4000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.4000000000000000, 0.4000000000000000,
    0.1000000000000000, 0.3000000000000000, 0.3000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.4000000000000000, 0.4000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.4000000000000000, 0.4000000000000000,
    0.3000000000000000, 0.3000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.4000000000000000, 0.4000000000000000,
    0.3000000000000000, 0.3000000000000000, 0.2000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.4000000000000000, 0.2000000000000000, 0.3000000000000000,
    0.3000000000000000, 0.1000000000000000, 0.3000000000000000,
    0.3000000000000000, 0.2000000000000000, 0.2000000000000000,
    0.3000000000000000, 0.3000000000000000, 0.2000000000000000};

NC_TET_Z84

const double NC_TET_Z84[]

static

Initial value:

= {
    0.1000000000000000, 0.7000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.6000000000000000, 0.2000000000000000,
    0.1000000000000000, 0.2000000000000000, 0.1000000000000000,
    0.6000000000000000, 0.1000000000000000, 0.2000000000000000,
    0.1000000000000000, 0.1000000000000000, 0.6000000000000000,
    0.1000000000000000, 0.5000000000000000, 0.3000000000000000,
    0.1000000000000000, 0.3000000000000000, 0.1000000000000000,
    0.5000000000000000, 0.1000000000000000, 0.3000000000000000,
    0.1000000000000000, 0.1000000000000000, 0.5000000000000000,
    0.1000000000000000, 0.1000000000000000, 0.5000000000000000,
    0.2000000000000000, 0.5000000000000000, 0.2000000000000000,
    0.1000000000000000, 0.2000000000000000, 0.5000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.1000000000000000,
    0.2000000000000000, 0.1000000000000000, 0.4000000000000000,
    0.1000000000000000, 0.4000000000000000, 0.1000000000000000,
    0.4000000000000000, 0.2000000000000000, 0.1000000000000000,
    0.3000000000000000, 0.1000000000000000, 0.3000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.1000000000000000,
    0.4000000000000000, 0.1000000000000000, 0.4000000000000000,
    0.2000000000000000, 0.3000000000000000, 0.1000000000000000,
    0.4000000000000000, 0.1000000000000000, 0.4000000000000000,
    0.3000000000000000, 0.3000000000000000, 0.2000000000000000,
    0.4000000000000000, 0.2000000000000000, 0.4000000000000000,
    0.3000000000000000, 0.2000000000000000, 0.4000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.3000000000000000,
    0.1000000000000000, 0.3000000000000000, 0.3000000000000000,
    0.2000000000000000, 0.3000000000000000, 0.2000000000000000,
    0.3000000000000000, 0.2000000000000000, 0.3000000000000000}

Definition at line 1278 of file fem_tools.h.

                                   {
    0.1000000000000000, 0.7000000000000000, 0.1000000000000000,
    0.1000000000000000, 0.6000000000000000, 0.2000000000000000,
    0.1000000000000000, 0.2000000000000000, 0.1000000000000000,
    0.6000000000000000, 0.1000000000000000, 0.2000000000000000,
    0.1000000000000000, 0.1000000000000000, 0.6000000000000000,
    0.1000000000000000, 0.5000000000000000, 0.3000000000000000,
    0.1000000000000000, 0.3000000000000000, 0.1000000000000000,
    0.5000000000000000, 0.1000000000000000, 0.3000000000000000,
    0.1000000000000000, 0.1000000000000000, 0.5000000000000000,
    0.1000000000000000, 0.1000000000000000, 0.5000000000000000,
    0.2000000000000000, 0.5000000000000000, 0.2000000000000000,
    0.1000000000000000, 0.2000000000000000, 0.5000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.1000000000000000,
    0.2000000000000000, 0.1000000000000000, 0.4000000000000000,
    0.1000000000000000, 0.4000000000000000, 0.1000000000000000,
    0.4000000000000000, 0.2000000000000000, 0.1000000000000000,
    0.3000000000000000, 0.1000000000000000, 0.3000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.1000000000000000,
    0.4000000000000000, 0.1000000000000000, 0.4000000000000000,
    0.2000000000000000, 0.3000000000000000, 0.1000000000000000,
    0.4000000000000000, 0.1000000000000000, 0.4000000000000000,
    0.3000000000000000, 0.3000000000000000, 0.2000000000000000,
    0.4000000000000000, 0.2000000000000000, 0.4000000000000000,
    0.3000000000000000, 0.2000000000000000, 0.4000000000000000,
    0.2000000000000000, 0.2000000000000000, 0.3000000000000000,
    0.1000000000000000, 0.3000000000000000, 0.3000000000000000,
    0.2000000000000000, 0.3000000000000000, 0.2000000000000000,
    0.3000000000000000, 0.2000000000000000, 0.3000000000000000};