h1_hdiv_hcurl_l2.h

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/** \file h1_hdiv_hcurl_l2.h
\brief Functions to approximate hierarchical spaces
 
\FIXME: Name Shape Functions is used, in that context is more appropriate
to use base functions. Need to be changed.
 
*/
 
#ifndef __H1_HDIV_HCURL_L2_H__
#define __H1_HDIV_HCURL_L2_H__
 
#ifndef DEPRECATED
#define DEPRECATED
#endif
 
#ifdef __cplusplus
extern "C" {
#endif
 
// L2
 
// Number of dofs for L2 space
 
/**
 * @brief Number of base functions on tetrahedron for L2 space
 */
#define NBVOLUMETET_L2(P) ((P + 1) * (P + 2) * (P + 3) / 6)
 
/**
 * @brief Number of base functions on hexahedron for L2 space
 */
#define NBVOLUMEHEX_L2_GENERAL(P, Q, R) ((P + 1) * (Q + 1) * (R + 1))
 
/**
 * @brief Number of base functions on hexahedron for L2 space
 */
#define NBVOLUMEHEX_L2(P) (NBVOLUMEHEX_L2_GENERAL(P, P, P))
 
/**
 * @brief Number of base functions on triangle for L2 space
 */
#define NBFACETRI_L2(P) ((P + 1) * (P + 2) / 2)
 
/**
 * @brief Number of base functions on edge from L2 space
 *
 */
#define NBEDGE_L2(P) ((P) + 1)
 
// H1
 
/**
 * @brief Number of base function on edge for H1 space
 */
#define NBEDGE_H1(P) (((P) > 1) ? (P - 1) : 0)
 
/**
 * @brief Number of base function on triangle for H1 space
 */
#define NBFACETRI_H1(P) (((P) > 2) ? ((P - 2) * (P - 1) / 2) : 0)
 
/**
 * @brief Number of base functions on quad for H1 space
 */
#define NBFACEQUAD_H1(P) (((P) > 1) ? ((P - 1) * (P - 1)) : 0)
 
/**
 * @brief Number of base functions on quad for L2 space
 */
#define NBFACEQUAD_L2(P) (((P) >= 0) ? (P + 1) * (P + 1) : 0)
 
/**
 * @brief Number of base functions on tetrahedron for H1 space
 */
#define NBVOLUMETET_H1(P) (((P) > 3) ? ((P - 3) * (P - 2) * (P - 1) / 6) : 0)
 
/**
 * @brief Number of base functions on prism for H1 space
 */
#define NBVOLUMEPRISM_H1(P) ((P > 3) ? ((P - 2) * (P - 2) * (P - 2)) : 0)
 
/**
 * @brief  Number of base functions on hex for H1 space
 *
 */
#define NBVOLUMEHEX_H1_GENERAL(P, Q, R)                                        \
  ((((P) > 1) && ((Q) > 1) && ((R) > 1)) ? (((P)-1) * ((Q)-1) * ((R)-1)) : 0)
 
/**
 * @brief  Number of base functions on hex for H1 space
 *
 */
#define NBVOLUMEHEX_H1(P) (NBVOLUMEHEX_H1_GENERAL(P, P, P))
 
// H curl
 
#define NBEDGE_AINSWORTH_HCURL(P) (((P) > 0) ? (P + 1) : 0)
#define NBFACETRI_AINSWORTH_EDGE_HCURL(P) (((P) > 1) ? P - 1 : 0)
#define NBFACETRI_AINSWORTH_FACE_HCURL(P) (((P) > 2) ? (P - 1) * (P - 2) : 0)
#define NBFACETRI_AINSWORTH_HCURL(P) ((P > 1) ? ((P)-1) * (P + 1) : 0)
#define NBVOLUMETET_AINSWORTH_FACE_HCURL(P)                                    \
  (((P) > 2) ? (2 * (P - 1) * (P - 2)) : 0)
#define NBVOLUMETET_AINSWORTH_TET_HCURL(P)                                     \
  (((P) > 3) ? ((P - 3) * (P - 2) * (P - 1) / 2) : 0)
#define NBVOLUMETET_AINSWORTH_HCURL(P)                                         \
  (((P) > 2) ? (P - 2) * (P - 1) * (P + 1) / 2 : 0)
 
#define NBEDGE_DEMKOWICZ_HCURL(P) (((P) > 0) ? (P) : 0)
#define NBFACETRI_DEMKOWICZ_HCURL(P) (((P) > 1) ? (P) * ((P)-1) : 0)
#define NBVOLUMETET_DEMKOWICZ_HCURL(P)                                         \
  (((P) > 2) ? ((P) * ((P)-1) * ((P)-2) / 2) : 0)
 
/**
 * @brief Number of base functions on quad for Hcurl space
 */
#define NBFACEQUAD_DEMKOWICZ_FAMILY_HCURL(P, Q)                                \
  (((P) > 0 && (Q) > 1) ? P * (Q - 1) : 0)
#define NBFACEQUAD_DEMKOWICZ_HCURL(P)                                          \
  (2 * NBFACEQUAD_DEMKOWICZ_FAMILY_HCURL(P, P))
 
#define NBVOLUMEHEX_DEMKOWICZ_FAMILY_HCURL(P, Q, R)                            \
  ((P > 0) && (Q > 1) && (R > 1) ? ((P) * (Q - 1) * (R - 1)) : 0)
 
#define NBVOLUMEHEX_DEMKOWICZ_HCURL(P)                                         \
  (3 * NBVOLUMEHEX_DEMKOWICZ_FAMILY_HCURL(P, P, P))
 
// H div
 
#define NBEDGE_HDIV(P) (0)
#define NBFACETRI_AINSWORTH_EDGE_HDIV(P) (((P) > 0) ? (P) : 0)
#define NBFACETRI_AINSWORTH_FACE_HDIV(P) (((P) > 2) ? (P - 1) * (P - 2) / 2 : 0)
#define NBFACETRI_AINSWORTH_HDIV(P) (((P) > 0) ? (P + 1) * (P + 2) / 2 : 0)
#define NBVOLUMETET_AINSWORTH_EDGE_HDIV(P) (((P) > 1) ? (P - 1) : 0)
#define NBVOLUMETET_AINSWORTH_FACE_HDIV(P) (((P) > 2) ? (P - 1) * (P - 2) : 0)
#define NBVOLUMETET_AINSWORTH_VOLUME_HDIV(P)                                   \
  (((P) > 3) ? (P - 3) * (P - 2) * (P - 1) / 2 : 0)
#define NBVOLUMETET_AINSWORTH_HDIV(P)                                          \
  (((P) > 1) ? (P - 1) * (P + 1) * (P + 2) / 2 : 0)
#define NBFACETRI_DEMKOWICZ_HDIV(P) ((P > 0) ? (P) * (P + 1) / 2 : 0)
#define NBVOLUMETET_DEMKOWICZ_HDIV(P)                                          \
  (((P) > 1) ? (P) * (P - 1) * (P + 1) / 2 : 0)
 
#define NBFACEQUAD_DEMKOWICZ_QUAD_HDIV_GENERAL(P, Q)                           \
  (((P) > 0 && (Q) > 0) ? ((P) * (Q)) : 0)
#define NBFACEQUAD_DEMKOWICZ_HDIV(P)                                           \
  (NBFACEQUAD_DEMKOWICZ_QUAD_HDIV_GENERAL(P, P))
#define NBVOLUMEHEX_DEMKOWICZ_FAMILY_HDIV(P, Q, R)                             \
  ((((P) > 0) && ((Q) > 0) && ((R) > 0)) ? ((P - 1) * Q * R) : 0)
#define NBVOLUMEHEX_DEMKOWICZ_HDIV(P)                                          \
  (3 * NBVOLUMEHEX_DEMKOWICZ_FAMILY_HDIV(P, P, P))
 
/**
 * @brief Get base functions on triangle for L2 space
 *
 * @param p polynomial order
 * @param N barycentric coordinates (shape functions) at integration points
 * @param diffN derivatives of barycentric coordinates, i.e. derivatives of
 * shape functions
 * @param L2N values of L2 base at integration points
 * @param diff_L2N dirvatives of base functions at integration points
 * @param GDIM number of integration points
 * @param base_polynomials polynomial base used to construct L2 base on
 * element
 * @return PetscErrorCode
 */
PetscErrorCode L2_Ainsworth_ShapeFunctions_MBTRI(
    int p, double *N, double *diffN, double *L2N, double *diff_L2N, int GDIM,
    PetscErrorCode (*base_polynomials)(int p, double s, double *diff_s,
                                       double *L, double *diffL,
                                       const int dim));
/**
 * @brief Get base functions on tetrahedron for L2 space
 *
 * @param p polynomial order
 * @param N barycentric coordinates (shape functions) at integration points
 * @param diffN derivatives of barycentric coordinates, i.e. derivatives of
 * shape functions
 * @param L2N values of L2 base at integration points
 * @param diff_L2N dirvatives of base functions at integration points
 * @param GDIM number of integration points
 * @param base_polynomials polynomial base used to construct L2 base on element
 * @return PetscErrorCode
 */
PetscErrorCode L2_Ainsworth_ShapeFunctions_MBTET(
    int p, double *N, double *diffN, double *L2N, double *diff_L2N, int GDIM,
    PetscErrorCode (*base_polynomials)(int p, double s, double *diff_s,
                                       double *L, double *diffL,
                                       const int dim));
 
/**
 * \brief H1_EdgeShapeFunctions_MBTRI
 *
 * \param sense of edges, it is array of integers dim 3 (3-edges of triangle)
 * \param p of edges
 */
PetscErrorCode H1_EdgeShapeFunctions_MBTRI(
    int *sense, int *p, double *N, double *diffN, double *edgeN[3],
    double *diff_edgeN[3], int GDIM,
    PetscErrorCode (*base_polynomials)(int p, double s, double *diff_s,
                                       double *L, double *diffL,
                                       const int dim));
PetscErrorCode H1_FaceShapeFunctions_MBTRI(
    const int *face_nodes, int p, double *N, double *diffN, double *faceN,
    double *diff_faceN, int GDIM,
    PetscErrorCode (*base_polynomials)(int p, double s, double *diff_s,
                                       double *L, double *diffL,
                                       const int dim));
PetscErrorCode H1_EdgeShapeFunctions_MBTET(
    int *sense, int *p, double *N, double *diffN, double *edgeN[],
    double *diff_edgeN[], int GDIM,
    PetscErrorCode (*base_polynomials)(int p, double s, double *diff_s,
                                       double *L, double *diffL,
                                       const int dim));
PetscErrorCode H1_FaceShapeFunctions_MBTET(
    int *faces_nodes, int *p, double *N, double *diffN, double *faceN[],
    double *diff_faceN[], int GDIM,
    PetscErrorCode (*base_polynomials)(int p, double s, double *diff_s,
                                       double *L, double *diffL,
                                       const int dim));
PetscErrorCode H1_VolumeShapeFunctions_MBTET(
    int p, double *N, double *diffN, double *volumeN, double *diff_volumeN,
    int GDIM,
    PetscErrorCode (*base_polynomials)(int p, double s, double *diff_s,
                                       double *L, double *diffL,
                                       const int dim));
PetscErrorCode H1_EdgeShapeDiffMBTETinvJ(int *base_p, int *p,
                                         double *edge_diffN[], double *invJac,
                                         double *edge_diffNinvJac[], int GDIM);
PetscErrorCode H1_FaceShapeDiffMBTETinvJ(int *base_p, int *p,
                                         double *face_diffN[], double *invJac,
                                         double *face_diffNinvJac[], int GDIM);
PetscErrorCode H1_VolumeShapeDiffMBTETinvJ(int base_p, int p,
                                           double *volume_diffN, double *invJac,
                                           double *volume_diffNinvJac,
                                           int GDIM);
 
PetscErrorCode H1_EdgeGradientOfDeformation_hierarchical(int p, double *diffN,
                                                         double *dofs,
                                                         double *F);
PetscErrorCode H1_FaceGradientOfDeformation_hierarchical(int p, double *diffN,
                                                         double *dofs,
                                                         double *F);
PetscErrorCode H1_VolumeGradientOfDeformation_hierarchical(int p, double *diffN,
                                                           double *dofs,
                                                           double *F);
 
PetscErrorCode H1_QuadShapeFunctions_MBPRISM(
    int *faces_nodes, int *p, double *N, double *diffN, double *faceN[],
    double *diff_faceN[], int GDIM,
    PetscErrorCode (*base_polynomials)(int p, double s, double *diff_s,
                                       double *L, double *diffL,
                                       const int dim));
PetscErrorCode H1_VolumeShapeFunctions_MBPRISM(
    int p, double *N, double *diffN, double *volumeN, double *diff_volumeN,
    int GDIM,
    PetscErrorCode (*base_polynomials)(int p, double s, double *diff_s,
                                       double *L, double *diffL,
                                       const int dim));
PetscErrorCode H1_QuadShapeFunctions_MBQUAD(
    int *faces_nodes, int p, double *N, double *diffN, double *faceN,
    double *diff_faceN, int GDIM,
    PetscErrorCode (*base_polynomials)(int p, double s, double *diff_s,
                                       double *L, double *diffL,
                                       const int dim));
PetscErrorCode H1_EdgeShapeFunctions_MBQUAD(
    int *sense, int *p, double *N, double *diffN, double *edgeN[4],
    double *diff_edgeN[4], int GDIM,
    PetscErrorCode (*base_polynomials)(int p, double s, double *diff_s,
                                       double *L, double *diffL,
                                       const int dim));
 
// Hdiv and Hcurl are implemented and declared in other files
 
#ifdef __cplusplus
}
#endif
 
#endif // __H1_HDIV_HCURL_L2_H__