example_Poisson.cpp File Reference

Example solution of a Poisson equation on a hexahedral mesh using nodal (Hgrad) elements. 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 "Epetra_Time.h"
#include "Epetra_Map.h"
#include "Epetra_SerialComm.h"
#include "Epetra_FECrsMatrix.h"
#include "Epetra_FEVector.h"
#include "Epetra_Import.h"
#include "Teuchos_oblackholestream.hpp"
#include "Teuchos_RCP.hpp"
#include "Teuchos_BLAS.hpp"
#include "Teuchos_GlobalMPISession.hpp"
#include "Teuchos_XMLParameterListHelpers.hpp"
#include "Shards_CellTopology.hpp"
#include "EpetraExt_RowMatrixOut.h"
#include "EpetraExt_MultiVectorOut.h"
#include "create_inline_mesh.h"
#include "pamgen_im_exodusII_l.h"
#include "pamgen_im_ne_nemesisI_l.h"
#include "pamgen_extras.h"
#include "AztecOO.h"
#include "ml_MultiLevelPreconditioner.h"
#include "ml_epetra_utils.h"
#include "Sacado_No_Kokkos.hpp"

Include dependency graph for example_Poisson.cpp:

Typedefs
typedef Sacado::Fad::SFad< double, 3 >	Fad3
typedef Intrepid::FunctionSpaceTools	IntrepidFSTools
typedef Intrepid::RealSpaceTools< double >	IntrepidRSTools
typedef Intrepid::CellTools< double >	IntrepidCTools

Functions
int	TestMultiLevelPreconditionerLaplace (char ProblemType[], Teuchos::ParameterList &MLList, Epetra_CrsMatrix &A, const Epetra_MultiVector &xexact, Epetra_MultiVector &b, Epetra_MultiVector &uh, double &TotalErrorResidual, double &TotalErrorExactSol)
	ML Preconditioner.
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.

Example solution of a Poisson equation on a quad mesh using nodal (Hgrad) elements.

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.
• Epetra to handle the global matrix and vector.
• Isorropia to partition the matrix. (Optional)
• ML to solve the linear system.

 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.

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.

This example uses the following Trilinos packages:

• Pamgen to generate a Quad mesh.
• Sacado to form the source term from user-specified manufactured solution.
• Intrepid to build the discretization matrix and right-hand side.
• Epetra to handle the global matrix and vector.
• Isorropia to partition the matrix. (Optional)
• ML to solve the linear system.

 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.

Remarks

Usage:

./TrilinosCouplings_examples_scaling_example_Poisson.exe 

Example driver requires input file named Poisson2D.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.

This example uses the following Trilinos packages:

• Pamgen to generate a Quad 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.
• Isorropia to partition the matrix. (Optional)
• MueLu to solve the linear system.

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.

Remarks

Usage:

./TrilinosCouplings_examples_scaling_example_Poisson.exe 

Example driver requires input file named Poisson2D.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.

This example uses the following Trilinos packages:

• Pamgen to generate a Quad 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.
• Isorropia to partition the matrix. (Optional)
• ML to solve the linear system.

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.

Remarks

Usage:

./TrilinosCouplings_examples_scaling_example_Poisson.exe 

Example driver requires input file named Poisson2D.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.

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.
• Epetra to handle the global matrix and vector.
• Isorropia to partition the matrix. (Optional)
• ML to solve the linear system.

 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.

Remarks

Usage:

./TrilinosCouplings_examples_scaling_example_Poisson.exe [--meshfile filename]

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

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

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

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

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 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 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).

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(), and exactSolutionGrad().

TestMultiLevelPreconditionerLaplace()

int TestMultiLevelPreconditionerLaplace	(	char	ProblemType[],
		Teuchos::ParameterList &	MLList,
		Epetra_CrsMatrix &	A,
		const Epetra_MultiVector &	xexact,
		Epetra_MultiVector &	b,
		Epetra_MultiVector &	uh,
		double &	TotalErrorResidual,
		double &	TotalErrorExactSol
	)

ML Preconditioner.

Parameters

ProblemType	[in] problem type
MLList	[in] ML parameter list
A	[in] discrete operator matrix
xexact	[in] exact solution
b	[in] right-hand-side vector
uh	[out] solution vector
TotalErrorResidual	[out] error residual
TotalErrorExactSol	[out] error in uh