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	DomainEleOp = DomainEle::UserDataOperator
	Finire element operator type.
using	EntData = EntitiesFieldData::EntData
	Data on entities.
using	OpDomainMass = FormsIntegrators< DomainEleOp >::Assembly< PETSC >::BiLinearForm< GAUSS >::OpMass< BASE_DIM, FIELD_DIM >
	OPerator to integrate mass matrix for least square approximation.
using	OpDomainSource = FormsIntegrators< DomainEleOp >::Assembly< PETSC >::LinearForm< GAUSS >::OpSource< BASE_DIM, FIELD_DIM >
	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.

DomainEleOp

using DomainEleOp = DomainEle::UserDataOperator

Finire element operator type.

Examples

mofem/atom_tests/child_and_parent.cpp.

Definition at line 29 of file higher_derivatives.cpp.

EntData

using EntData = EntitiesFieldData::EntData

Data on entities.

Definition at line 31 of file higher_derivatives.cpp.

OpDomainMass

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

OPerator to integrate mass matrix for least square approximation.

Examples

mofem/atom_tests/child_and_parent.cpp, mofem/atom_tests/dg_projection.cpp, mofem/atom_tests/hanging_node_approx.cpp, and mofem/atom_tests/higher_derivatives.cpp.

Definition at line 66 of file higher_derivatives.cpp.

OpDomainSource

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

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

Examples

mofem/atom_tests/child_and_parent.cpp, mofem/atom_tests/dg_projection.cpp, mofem/atom_tests/hanging_node_approx.cpp, and mofem/atom_tests/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

constexpr 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

mofem/atom_tests/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

mofem/atom_tests/higher_derivatives.cpp, mofem/atom_tests/prism_polynomial_approximation.cpp, and mofem/atom_tests/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

constexpr int FIELD_DIM = 1

constexpr

Examples

mofem/atom_tests/child_and_parent.cpp, mofem/atom_tests/dg_projection.cpp, mofem/atom_tests/hanging_node_approx.cpp, and mofem/atom_tests/higher_derivatives.cpp.

Definition at line 18 of file higher_derivatives.cpp.

FIELD_NAME

constexpr char FIELD_NAME[] = "U"

constexpr

Examples

mofem/atom_tests/child_and_parent.cpp, mofem/atom_tests/dg_projection.cpp, mofem/atom_tests/hanging_node_approx.cpp, and mofem/atom_tests/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

mofem/atom_tests/dg_projection.cpp, and mofem/atom_tests/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

constexpr int SPACE_DIM = 2

constexpr

Examples

mofem/atom_tests/hanging_node_approx.cpp.

Definition at line 19 of file higher_derivatives.cpp.