Example solution of a Poisson equation on a hexahedral mesh using nodal (Hgrad) elements. The system is assembled but not solved. More...

#include "TrilinosCouplings_config.h"
#include "TrilinosCouplings_Pamgen_Utils.hpp"
#include "Intrepid_FunctionSpaceTools.hpp"
#include "Intrepid_CellTools.hpp"
#include "Intrepid_ArrayTools.hpp"
#include "Intrepid_HGRAD_HEX_C1_FEM.hpp"
#include "Intrepid_RealSpaceTools.hpp"
#include "Intrepid_DefaultCubatureFactory.hpp"
#include "Intrepid_Utils.hpp"
#include "Tpetra_Map.hpp"
#include "Tpetra_Core.hpp"
#include "Tpetra_Export.hpp"
#include "Tpetra_Import.hpp"
#include "Tpetra_CrsGraph.hpp"
#include "Tpetra_CrsMatrix.hpp"
#include "Tpetra_DistObject.hpp"
#include "Tpetra_Vector.hpp"
#include "Tpetra_MultiVector.hpp"
#include "MatrixMarket_Tpetra.hpp"
#include "Tpetra_Operator.hpp"
#include "Teuchos_oblackholestream.hpp"
#include "Teuchos_RCP.hpp"
#include "Teuchos_BLAS.hpp"
#include "Teuchos_XMLParameterListHelpers.hpp"
#include "Teuchos_ArrayView.hpp"
#include "Teuchos_ArrayRCP.hpp"
#include "Teuchos_TimeMonitor.hpp"
#include "Shards_CellTopology.hpp"
#include "create_inline_mesh.h"
#include "pamgen_im_exodusII_l.h"
#include "pamgen_im_ne_nemesisI_l.h"
#include "pamgen_extras.h"
#include "RTC_FunctionRTC.hh"
#include "BelosLinearProblem.hpp"
#include "BelosPseudoBlockCGSolMgr.hpp"
#include "BelosConfigDefs.hpp"
#include "BelosTpetraAdapter.hpp"
#include "Sacado_No_Kokkos.hpp"

Include dependency graph for example_Poisson_NoFE_Tpetra.cpp:

Typedefs
typedef Sacado::Fad::SFad< double, 3 >	Fad3
typedef Intrepid::RealSpaceTools< double >	IntrepidRSTools
typedef Intrepid::CellTools< double >	IntrepidCTools
typedef Tpetra::Map ::global_ordinal_type	GlobalOrdinal
typedef Tpetra::Map	Map
typedef Tpetra::Export	export_type
typedef Tpetra::Import	import_type
typedef Teuchos::ArrayView< Ordinal >::size_type	size_type
typedef Tpetra::CrsMatrix< ST >	sparse_matrix_type
typedef Tpetra::CrsGraph	sparse_graph_type
typedef Tpetra::MultiVector< ST >	MV
typedef Tpetra::Vector< ST >	vector_type
typedef Tpetra::Operator< ST >	OP
typedef Belos::MultiVecTraits< ST, MV >	MVT
typedef Belos::OperatorTraits< ST, MV, OP >	OPT

Functions
template<typename Scalar>
const Scalar	exactSolution (const Scalar &x, const Scalar &y, const Scalar &z)
	User-defined exact solution.
template<typename Scalar>
void	materialTensor (Scalar material[][3], const Scalar &x, const Scalar &y, const Scalar &z)
	User-defined material tensor.
template<typename Scalar>
void	exactSolutionGrad (Scalar gradExact[3], const Scalar &x, const Scalar &y, const Scalar &z)
	Computes gradient of the exact solution. Requires user-defined exact solution.
template<typename Scalar>
const Scalar	sourceTerm (Scalar &x, Scalar &y, Scalar &z)
	Computes source term: f = -div(A.grad u). Requires user-defined exact solution and material tensor.
template<class ArrayOut, class ArrayIn>
void	evaluateMaterialTensor (ArrayOut &worksetMaterialValues, const ArrayIn &evaluationPoints)
	Computation of the material tensor at array of points in physical space.
template<class ArrayOut, class ArrayIn>
void	evaluateSourceTerm (ArrayOut &sourceTermValues, const ArrayIn &evaluationPoints)
	Computation of the source term at array of points in physical space.
template<class ArrayOut, class ArrayIn>
void	evaluateExactSolution (ArrayOut &exactSolutionValues, const ArrayIn &evaluationPoints)
	Computation of the exact solution at array of points in physical space.
template<class ArrayOut, class ArrayIn>
void	evaluateExactSolutionGrad (ArrayOut &exactSolutionGradValues, const ArrayIn &evaluationPoints)
	Computation of the gradient of the exact solution at array of points in physical space.
int	main (int argc, char *argv[])

Detailed Description

Example solution of a Poisson equation on a hexahedral mesh using nodal (Hgrad) elements. The system is assembled but not solved.

This example uses the following Trilinos packages:

Pamgen to generate a Hexahedral mesh.
Sacado to form the source term from user-specified manufactured solution.
Intrepid to build the discretization matrix and right-hand side.
Tpetra to handle the global matrix and vector.

 Poisson system:

        div A grad u = f in Omega
                   u = g on Gamma

  where
         A is a symmetric, positive definite material tensor
         f is a given source term

 Corresponding discrete linear system for nodal coefficients(x):

             Kx = b

        K - HGrad stiffness matrix
        b - right hand side vector

Author: Created by P. Bochev, D. Ridzal, K. Peterson, D. Hensinger, C. Siefert. Converted to Tpetra by I. Kalashnikova (ikala.nosp@m.sh@s.nosp@m.andia.nosp@m..gov)

Remarks: Usage:
./TrilinosCouplings_examples_scaling_example_Poisson.exe; Example driver requires input file named Poisson.xml with Pamgen formatted mesh description and settings for Isorropia (a version is included in the Trilinos repository with this driver).; The exact solution (u) and material tensor (A) are set in the functions "exactSolution" and "materialTensor" and may be modified by the user.

Function Documentation

◆ evaluateExactSolution()

template<class ArrayOut, class ArrayIn>

void evaluateExactSolution	(	ArrayOut &	exactSolutionValues,
		const ArrayIn &	evaluationPoints )

Computation of the exact solution at array of points in physical space.

Parameters

exactSolutionValues	[out] Rank-2 (C,P) array with the values of the exact solution
evaluationPoints	[in] Rank-3 (C,P,D) array with the evaluation points in physical frame

References exactSolution().

◆ evaluateExactSolutionGrad()

template<class ArrayOut, class ArrayIn>

void evaluateExactSolutionGrad	(	ArrayOut &	exactSolutionGradValues,
		const ArrayIn &	evaluationPoints )

Computation of the gradient of the exact solution at array of points in physical space.

Parameters

exactSolutionGradValues	[out] Rank-3 (C,P,D) array with the values of the gradient of the exact solution
evaluationPoints	[in] Rank-3 (C,P,D) array with the evaluation points in physical frame

References exactSolutionGrad().

◆ evaluateMaterialTensor()

template<class ArrayOut, class ArrayIn>

void evaluateMaterialTensor	(	ArrayOut &	worksetMaterialValues,
		const ArrayIn &	evaluationPoints )

Computation of the material tensor at array of points in physical space.

Parameters

worksetMaterialValues	[out] Rank-2, 3 or 4 array with dimensions (C,P), (C,P,D) or (C,P,D,D) with the values of the material tensor
evaluationPoints	[in] Rank-3 (C,P,D) array with the evaluation points in physical frame

References materialTensor().

◆ evaluateSourceTerm()

template<class ArrayOut, class ArrayIn>

void evaluateSourceTerm	(	ArrayOut &	sourceTermValues,
		const ArrayIn &	evaluationPoints )

Computation of the source term at array of points in physical space.

Parameters

sourceTermValues	[out] Rank-2 (C,P) array with the values of the source term
evaluationPoints	[in] Rank-3 (C,P,D) array with the evaluation points in physical frame

References sourceTerm().

◆ exactSolution()

template<typename Scalar>

const Scalar exactSolution	(	const Scalar &	x,
		const Scalar &	y,
		const Scalar &	z )

User-defined exact solution.

Parameters

x	[in] x-coordinate of the evaluation point
y	[in] y-coordinate of the evaluation point
z	[in] z-coordinate of the evaluation point

Returns: Value of the exact solution at (x,y,z)

Referenced by evaluateExactSolution(), exactSolutionGrad(), and sourceTerm().

◆ exactSolutionGrad()

template<typename Scalar>

void exactSolutionGrad	(	Scalar	gradExact[3],
		const Scalar &	x,
		const Scalar &	y,
		const Scalar &	z )

Computes gradient of the exact solution. Requires user-defined exact solution.

Parameters

gradExact	[out] gradient of the exact solution evaluated at (x,y,z)
x	[in] x-coordinate of the evaluation point
y	[in] y-coordinate of the evaluation point
z	[in] z-coordinate of the evaluation point

References exactSolution().

Referenced by evaluateExactSolutionGrad(), and sourceTerm().

◆ materialTensor()

template<typename Scalar>

void materialTensor	(	Scalar	material[][3],
		const Scalar &	x,
		const Scalar &	y,
		const Scalar &	z )

User-defined material tensor.

Parameters

material	[out] 3 x 3 material tensor evaluated at (x,y,z)
x	[in] x-coordinate of the evaluation point
y	[in] y-coordinate of the evaluation point
z	[in] z-coordinate of the evaluation point

Warning: Symmetric and positive definite tensor is required for every (x,y,z).

Referenced by evaluateMaterialTensor(), and sourceTerm().

◆ sourceTerm()

template<typename Scalar>

const Scalar sourceTerm	(	Scalar &	x,
		Scalar &	y,
		Scalar &	z )

Computes source term: f = -div(A.grad u). Requires user-defined exact solution and material tensor.

Parameters

x	[in] x-coordinate of the evaluation point
y	[in] y-coordinate of the evaluation point
z	[in] z-coordinate of the evaluation point

Returns: Source term corresponding to the user-defined exact solution evaluated at (x,y,z)

References exactSolution(), exactSolutionGrad(), and materialTensor().

Typedefs

Functions

Detailed Description

Function Documentation

◆ evaluateExactSolution()

◆ evaluateExactSolutionGrad()

◆ evaluateMaterialTensor()

◆ evaluateSourceTerm()

◆ exactSolution()

◆ exactSolutionGrad()

◆ materialTensor()

◆ sourceTerm()