higher_derivatives.cpp File Reference

#include <MoFEM.hpp>

Go to the source code of this file.

Classes
struct	ElementsAndOps< DIM >
struct	ElementsAndOps< 2 >
struct	AtomTest
struct	AtomTest::CommonData
	Collected data use d by operator to evaluate errors for the test. More...
struct	AtomTest::OpError< FIELD_DIM >
	Operator to evaluate errors. More...

Typedefs
using	DomainEle = ElementsAndOps<SPACE_DIM>::DomainEle
	Finite elenent type.
using	OpDomainMass
	OPerator to integrate mass matrix for least square approximation.
using	OpDomainSource
	Operator to integrate the right hand side matrix for the problem.

Functions
int	main (int argc, char *argv[])
	[Check results]

Variables
static char	help [] = "...\n\n"
constexpr char	FIELD_NAME [] = "U"
constexpr int	BASE_DIM = 1
constexpr int	FIELD_DIM = 1
constexpr int	SPACE_DIM = 2
auto	fun
	Function to approximate.
auto	diff_fun
	Function derivative.
auto	diff2_fun
	Function second derivative.

Typedef Documentation

DomainEle

using DomainEle = ElementsAndOps<SPACE_DIM>::DomainEle

Finite elenent type.

Definition at line 28 of file higher_derivatives.cpp.

OpDomainMass

using OpDomainMass

Initial value:

 FormsIntegrators<DomainEleOp>::Assembly<
    PETSC>::BiLinearForm<GAUSS>::OpMass<BASE_DIM, FIELD_DIM>

OPerator to integrate mass matrix for least square approximation.

Examples

child_and_parent.cpp, dg_projection.cpp, hanging_node_approx.cpp, and higher_derivatives.cpp.

Definition at line 66 of file higher_derivatives.cpp.

OpDomainSource

using OpDomainSource

Initial value:

 FormsIntegrators<DomainEleOp>::Assembly<
    PETSC>::LinearForm<GAUSS>::OpSource<BASE_DIM, FIELD_DIM>

Operator to integrate the right hand side matrix for the problem.

Examples

child_and_parent.cpp, dg_projection.cpp, hanging_node_approx.cpp, and higher_derivatives.cpp.

Definition at line 73 of file higher_derivatives.cpp.

Function Documentation

main()

int main	(	int	argc,
		char *	argv[] )

[Check results]

[Register MoFEM discrete manager in PETSc]

[Register MoFEM discrete manager in PETSc

[Create MoAB]

< mesh database

< mesh database interface

[Create MoAB]

[Create MoFEM]

< finite element database

< finite element database insterface

[Create MoFEM]

[AtomTest]

[AtomTest]

Definition at line 397 of file higher_derivatives.cpp.

                                 {
 
  // Initialisation of MoFEM/PETSc and MOAB data structures
  MoFEM::Core::Initialize(&argc, &argv, NULL, help);
 
  try {
 
    //! [Register MoFEM discrete manager in PETSc]
    DMType dm_name = "DMMOFEM";
    CHKERR DMRegister_MoFEM(dm_name);
    //! [Register MoFEM discrete manager in PETSc
 
    //! [Create MoAB]
    moab::Core mb_instance;              ///< mesh database
    moab::Interface &moab = mb_instance; ///< mesh database interface
    //! [Create MoAB]
 
    //! [Create MoFEM]
    MoFEM::Core core(moab);           ///< finite element database
    MoFEM::Interface &m_field = core; ///< finite element database insterface
    //! [Create MoFEM]
 
    //! [AtomTest]
    AtomTest ex(m_field);
    CHKERR ex.runProblem();
    //! [AtomTest]
  }
  CATCH_ERRORS;
 
  CHKERR MoFEM::Core::Finalize();
}

Variable Documentation

BASE_DIM

int BASE_DIM = 1

constexpr

Definition at line 17 of file higher_derivatives.cpp.

diff2_fun

auto diff2_fun

Initial value:

= [](const double x, const double y, const double z) {
  return FTensor::Tensor2<double, SPACE_DIM, SPACE_DIM>{
      2 + 6 * x + 12 * pow(x, 2), 1.,
 
      1., 2 + 6 * y + 12 * pow(y, 2)};
}

Function second derivative.

Examples

higher_derivatives.cpp.

Definition at line 55 of file higher_derivatives.cpp.

                                                                    {
  return FTensor::Tensor2<double, SPACE_DIM, SPACE_DIM>{
      2 + 6 * x + 12 * pow(x, 2), 1.,
 
      1., 2 + 6 * y + 12 * pow(y, 2)};
};

diff_fun

auto diff_fun

Initial value:

= [](const double x, const double y, const double z) {
  return FTensor::Tensor1<double, SPACE_DIM>{
      2 * x + y + 3 * pow(x, 2) + 4 * pow(x, 3),
      2 * y + x + 3 * pow(y, 2) + 4 * pow(y, 3)};
}

Function derivative.

Examples

higher_derivatives.cpp, prism_polynomial_approximation.cpp, and quad_polynomial_approximation.cpp.

Definition at line 45 of file higher_derivatives.cpp.

                                                                   {
  return FTensor::Tensor1<double, SPACE_DIM>{
      2 * x + y + 3 * pow(x, 2) + 4 * pow(x, 3),
      2 * y + x + 3 * pow(y, 2) + 4 * pow(y, 3)};
};

FIELD_DIM

int FIELD_DIM = 1

constexpr

Examples

child_and_parent.cpp, dg_projection.cpp, hanging_node_approx.cpp, and higher_derivatives.cpp.

Definition at line 18 of file higher_derivatives.cpp.

FIELD_NAME

char FIELD_NAME[] = "U"

constexpr

Examples

child_and_parent.cpp, dg_projection.cpp, hanging_node_approx.cpp, and higher_derivatives.cpp.

Definition at line 16 of file higher_derivatives.cpp.

fun

auto fun

Initial value:

= [](const double x, const double y, const double z) {
  return x * x + y * y + x * y + pow(x, 3) + pow(y, 3) + pow(x, 4) + pow(y, 4);
}

Function to approximate.

Examples

dg_projection.cpp, and higher_derivatives.cpp.

Definition at line 37 of file higher_derivatives.cpp.

                                                              {
  return x * x + y * y + x * y + pow(x, 3) + pow(y, 3) + pow(x, 4) + pow(y, 4);
};

help

char help[] = "...\n\n"

static

Definition at line 14 of file higher_derivatives.cpp.

SPACE_DIM

int SPACE_DIM = 2

constexpr

Examples

hanging_node_approx.cpp.

Definition at line 19 of file higher_derivatives.cpp.