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. More...

template<typename Scalar >
const Scalar	exactSolution (const Scalar &x, const Scalar &y, const Scalar &z)
	User-defined exact solution. More...

template<typename Scalar >
void	materialTensor (Scalar material[][3], const Scalar &x, const Scalar &y, const Scalar &z)
	User-defined material tensor. More...

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. More...

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. More...

template<class ArrayOut , class ArrayIn >
void	evaluateMaterialTensor (ArrayOut &worksetMaterialValues, const ArrayIn &evaluationPoints)
	Computation of the material tensor at array of points in physical space. More...

template<class ArrayOut , class ArrayIn >
void	evaluateSourceTerm (ArrayOut &sourceTermValues, const ArrayIn &evaluationPoints)
	Computation of the source term at array of points in physical space. More...

template<class ArrayOut , class ArrayIn >
void	evaluateExactSolution (ArrayOut &exactSolutionValues, const ArrayIn &evaluationPoints)
	Computation of the exact solution at array of points in physical space. More...

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. More...

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.
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

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

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

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

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

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)

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().

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).

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().

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

Typedefs

Functions

Detailed Description

Function Documentation