Example solution of the eddy current Maxwell's equations using curl-conforming (edge) elements. More...

#include "TrilinosCouplings_config.h"
#include "TrilinosCouplings_Pamgen_Utils.hpp"
#include "TrilinosCouplings_Statistics.hpp"
#include "TrilinosCouplings_IntrepidPoissonExample_SolveWithBelos.hpp"
#include "Intrepid_FunctionSpaceTools.hpp"
#include "Intrepid_FieldContainer.hpp"
#include "Intrepid_CellTools.hpp"
#include "Intrepid_ArrayTools.hpp"
#include "Intrepid_HCURL_HEX_I1_FEM.hpp"
#include "Intrepid_HGRAD_HEX_C1_FEM.hpp"
#include "Intrepid_RealSpaceTools.hpp"
#include "Intrepid_DefaultCubatureFactory.hpp"
#include "Intrepid_Utils.hpp"
#include "Kokkos_Core.hpp"
#include "Tpetra_Map.hpp"
#include "Tpetra_Import.hpp"
#include "Tpetra_Export.hpp"
#include "Tpetra_CrsMatrix.hpp"
#include "Tpetra_FECrsMatrix.hpp"
#include "Tpetra_FECrsGraph.hpp"
#include "Tpetra_FEMultiVector.hpp"
#include "Tpetra_Assembly_Helpers.hpp"
#include "TpetraExt_MatrixMatrix.hpp"
#include "MatrixMarket_Tpetra.hpp"
#include "Tpetra_applyDirichletBoundaryCondition.hpp"
#include "Teuchos_oblackholestream.hpp"
#include "Teuchos_RCP.hpp"
#include "Teuchos_BLAS.hpp"
#include "Teuchos_GlobalMPISession.hpp"
#include "Teuchos_ParameterList.hpp"
#include "Teuchos_XMLParameterListHelpers.hpp"
#include "Teuchos_Comm.hpp"
#include "Teuchos_OrdinalTraits.hpp"
#include "Teuchos_StackedTimer.hpp"
#include "Shards_CellTopology.hpp"
#include <Xpetra_MultiVector.hpp>
#include <Xpetra_MultiVectorFactory.hpp>
#include <Xpetra_CrsMatrix.hpp>
#include <Xpetra_CrsMatrixWrap.hpp>
#include <Xpetra_Matrix.hpp>
#include <BelosConfigDefs.hpp>
#include <BelosLinearProblem.hpp>
#include <BelosSolverFactory.hpp>
#include <BelosXpetraAdapter.hpp>
#include <BelosMueLuAdapter.hpp>
#include <MueLu_RefMaxwell.hpp>
#include <MueLu_Exceptions.hpp>
#include "create_inline_mesh.h"
#include "pamgen_im_exodusII_l.h"
#include "pamgen_im_ne_nemesisI_l.h"
#include "pamgen_extras.h"

Include dependency graph for example_Maxwell_Tpetra.cpp:

Classes
struct	fecomp

Macros
#define	ABS(x) ((x)>0?(x):-(x))

#define	SQR(x) ((x)*(x))

#define	TC_sumAll(rcpComm, in, out) Teuchos::reduceAll(*rcpComm, Teuchos::REDUCE_SUM, in, Teuchos::outArg(out))

#define	TC_minAll(rcpComm, in, out) Teuchos::reduceAll(*rcpComm, Teuchos::REDUCE_MIN, in, Teuchos::outArg(out))

#define	TC_maxAll(rcpComm, in, out) Teuchos::reduceAll(*rcpComm, Teuchos::REDUCE_MAX, in, Teuchos::outArg(out))

Typedefs
typedef double	SC

typedef int	LO

typedef Tpetra::Map::global_ordinal_type	GO

typedef Tpetra::Map::node_type	Node

typedef Node	NO

typedef Tpetra::CrsMatrix< SC, LO, GO, Node >	Tpetra_CrsMatrix

typedef Tpetra::FECrsMatrix < SC, LO, GO, Node >	Tpetra_FECrsMatrix

typedef Tpetra::FECrsGraph< LO, GO, Node >	Tpetra_FECrsGraph

typedef Tpetra::MultiVector < SC, LO, GO, Node >	Tpetra_MultiVector

typedef Tpetra::FEMultiVector < SC, LO, GO, Node >	Tpetra_FEMultiVector

typedef Tpetra::Vector< SC, LO, GO, Node >	Tpetra_Vector

typedef Tpetra::Map< LO, GO, Node >	Tpetra_Map

typedef Tpetra::Import< LO, GO, Node >	Tpetra_Import

typedef Tpetra::Export< LO, GO, Node >	Tpetra_Export

typedef Tpetra::Operator< SC, LO, GO, Node >	Tpetra_Operator

typedef Xpetra::Operator< SC, LO, GO, Node >	Xpetra_Operator

typedef Xpetra::Matrix< SC, LO, GO, NO >	Matrix

typedef Xpetra::MultiVector < SC, LO, GO, NO >	Xpetra_MultiVector

typedef Intrepid::FunctionSpaceTools	IntrepidFSTools

typedef Intrepid::RealSpaceTools < double >	IntrepidRSTools

typedef Intrepid::CellTools < double >	IntrepidCTools

Functions
template<class Container >
double	distance (Container &nodeCoord, int i1, int i2)

RCP< Matrix >	toXpetra (RCP< Tpetra_CrsMatrix > &mat)

RCP< Xpetra_MultiVector >	toXpetra (RCP< Tpetra_MultiVector > &vec)

RCP< Xpetra_Operator >	BuildPreconditioner_MueLu (char ProblemType[], Teuchos::ParameterList &MLList, RCP< Tpetra_CrsMatrix > &CurlCurl, RCP< Tpetra_CrsMatrix > &D0clean, RCP< Tpetra_CrsMatrix > &M0inv, RCP< Tpetra_CrsMatrix > &Ms, RCP< Tpetra_CrsMatrix > &M1, RCP< Tpetra_MultiVector > &coords)
	MueLu Preconditioner. More...

int	evalu (double &uExact0, double &uExact1, double &uExact2, double &x, double &y, double &z)
	Exact solution evaluation. More...

int	evalCurlu (double &curlu0, double &curlu1, double &curlu2, double &x, double &y, double &z, double &mu)
	Curl of exact solution. More...

int	evalCurlCurlu (double &curlcurlu0, double &curlcurlu1, double &curlcurlu2, double &x, double &y, double &z, double &mu)
	CurlCurl of exact solution. More...

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

void	solution_test (string msg, const Tpetra_Operator &A, const Tpetra_MultiVector &lhs, const Tpetra_MultiVector &rhs, const Tpetra_MultiVector &xexact, double &TotalErrorExactSol, double &TotalErrorResidual)
	Compute ML solution residual. More...

Detailed Description

Example solution of the eddy current Maxwell's equations using curl-conforming (edge) elements.

This example uses the following Trilinos packages:

Pamgen to generate a Hexahedral mesh.
Intrepid to build the discretization matrices and right-hand side.
Epetra to handle the global matrix and vector.
ML to solve the linear system.

Maxwell System:

curl x mu^{-1} curl E + sigma E = f

Corresponding discrete linear system for edge element coeficients (x):

(Kc + Mc)x = b

Kc    - Hcurl stiffness matrix
Mc    - Hcurl mass 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_Maxwell.exe  inputfile.xml


inputfile.xml (optional)  -  xml input file containing Pamgen mesh description
and material parameters for each Pamgen block,
if not present code attempts to read Maxwell.xml.

Input files available in Trilinos for use with the Maxwell driver:

Maxwell.xml - basic input file with box mesh and one mesh block
Ninja.xml - input file with distorted mesh (shaped like Ninja star) and one mesh block
Maxwell_in_block.xml - input file with box mesh with a center block with different material values.

Function Documentation

RCP< Xpetra_Operator > BuildPreconditioner_MueLu	(	char	ProblemType[],
		Teuchos::ParameterList &	MLList,
		RCP< Tpetra_CrsMatrix > &	CurlCurl,
		RCP< Tpetra_CrsMatrix > &	D0clean,
		RCP< Tpetra_CrsMatrix > &	M0inv,
		RCP< Tpetra_CrsMatrix > &	Ms,
		RCP< Tpetra_CrsMatrix > &	M1,
		RCP< Tpetra_MultiVector > &	coords
	)

MueLu Preconditioner.

Parameters

ProblemType	[in] problem type
MLList	[in] Parameter list
CurlCurl	[in] H(curl) stiffness matrix
D0clean	[in] Edge to node stiffness matrix
M0inv	[in] H(grad) mass matrix inverse
Ms	[in] H(curl) mass matrix w/ sigma
M1	[in] H(curl) mass matrix w/o sigm

int evalCurlCurlu	(	double &	curlcurlu0,
		double &	curlcurlu1,
		double &	curlcurlu2,
		double &	x,
		double &	y,
		double &	z,
		double &	mu
	)

CurlCurl of exact solution.

Parameters

curlcurlu0	[out] first component of curl-curl of exact solution
curlcurlu1	[out] second component of curl-curl of exact solution
curlcurlu2	[out] third component of curl-curl of exact solution
x	[in] x coordinate
y	[in] y coordinate
z	[in] z coordinate
mu	[in] material parameter

int evalCurlu	(	double &	curlu0,
		double &	curlu1,
		double &	curlu2,
		double &	x,
		double &	y,
		double &	z,
		double &	mu
	)

Curl of exact solution.

Parameters

curlu0	[out] first component of curl of exact solution
curlu1	[out] second component of curl of exact solution
curlu2	[out] third component of curl of exact solution
x	[in] x coordinate
y	[in] y coordinate
z	[in] z coordinate
mu	[in] material parameter

int evalu	(	double &	uExact0,
		double &	uExact1,
		double &	uExact2,
		double &	x,
		double &	y,
		double &	z
	)

Exact solution evaluation.

Parameters

uExact0	[out] first component of exact solution at (x,y,z)
uExact1	[out] second component of exact solution at (x,y,z)
uExact2	[out] third component of exact solution at (x,y,z)
x	[in] x coordinate
y	[in] y coordinate
z	[in] z coordinate

void solution_test	(	string	msg,
		const Tpetra_Operator &	A,
		const Tpetra_MultiVector &	lhs,
		const Tpetra_MultiVector &	rhs,
		const Tpetra_MultiVector &	xexact,
		double &	TotalErrorExactSol,
		double &	TotalErrorResidual
	)

Compute ML solution residual.

Parameters

A	[in] discrete operator
lhs	[in] solution vector
rhs	[in] right hand side vector
Time	[in] elapsed time for output
TotalErrorResidual	[out] error residual
TotalErrorExactSol	[out] error in xh (not an appropriate measure for H(curl) basis functions)

Classes

Macros

Typedefs

Functions

Detailed Description

Function Documentation