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 "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 "Epetra_Time.h"
#include "Epetra_Map.h"
#include "Epetra_SerialComm.h"
#include "Epetra_Import.h"
#include "Epetra_Export.h"
#include "Epetra_CrsMatrix.h"
#include "Epetra_FECrsMatrix.h"
#include "Epetra_FEVector.h"
#include "Epetra_LinearProblem.h"
#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_DefaultComm.hpp"
#include "Shards_CellTopology.hpp"
#include "EpetraExt_RowMatrixOut.h"
#include "EpetraExt_MultiVectorOut.h"
#include "EpetraExt_VectorOut.h"
#include "EpetraExt_MatrixMatrix.h"
#include "AztecOO.h"
#include "ml_MultiLevelPreconditioner.h"
#include "ml_RefMaxwell_11_Operator.h"
#include "ml_RefMaxwell.h"
#include "ml_EdgeMatrixFreePreconditioner.h"
#include "ml_epetra_utils.h"
#include "create_inline_mesh.h"
#include "pamgen_im_exodusII_l.h"
#include "pamgen_im_ne_nemesisI_l.h"
#include "pamgen_extras.h"
#include "TrilinosCouplings_IntrepidPoissonExampleHelpers.hpp"

Include dependency graph for example_Maxwell.cpp:

Classes
struct	fecomp

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

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

Typedefs
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)

void	TestMultiLevelPreconditioner_Maxwell (char ProblemType[], Teuchos::ParameterList &MLList, Epetra_CrsMatrix &CurlCurl, Epetra_CrsMatrix &D0clean, Epetra_CrsMatrix &M0inv, Epetra_CrsMatrix &Ms, Epetra_CrsMatrix &M1, Epetra_MultiVector &xh, Epetra_MultiVector &b, double &TotalErrorResidual, double &TotalErrorExactSol)
	ML Preconditioner. More...

int	evalu (double &uExact0, double &uExact1, double &uExact2, double &x, double &y, double &z)
	ML Preconditioner. 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	body (int argc, char *argv[])

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

int	Multiply_Ones (const Epetra_CrsMatrix &A, const Epetra_Vector &x, Epetra_Vector &y)
	Multiplies Ax = y, where all non-zero entries of A are replaced with the value 1.0. More...

void	solution_test (string msg, const Epetra_Operator &A, const Epetra_MultiVector &lhs, const Epetra_MultiVector &rhs, const Epetra_MultiVector &xexact, Epetra_Time &Time, double &TotalErrorExactSol, double &TotalErrorResidual)
	Compute ML solution residual. More...

void	TestMueLuMultiLevelPreconditioner_Maxwell (char ProblemType[], Teuchos::ParameterList &MLList, Epetra_CrsMatrix &CurlCurl, Epetra_CrsMatrix &D0clean, Epetra_CrsMatrix &M0inv, Epetra_CrsMatrix &Ms, Epetra_CrsMatrix &M1, Epetra_MultiVector &coords, Epetra_MultiVector &xh, Epetra_MultiVector &b, double &TotalErrorResidual, double &TotalErrorExactSol)

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

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
	)

ML Preconditioner.

Parameters

ProblemType	[in] problem type
MLList	[in] ML 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 sigma
xh	[out] solution vector
b	[in] right-hand-side vector
TotalErrorResidual	[out] error residual
TotalErrorExactSol	[out] error in xhExact solution evaluation.
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

int Multiply_Ones	(	const Epetra_CrsMatrix &	A,
		const Epetra_Vector &	x,
		Epetra_Vector &	y
	)

Multiplies Ax = y, where all non-zero entries of A are replaced with the value 1.0.

Parameters

A	[in] matrix
x	[in] vector
y	[in] vector

void solution_test	(	string	msg,
		const Epetra_Operator &	A,
		const Epetra_MultiVector &	lhs,
		const Epetra_MultiVector &	rhs,
		const Epetra_MultiVector &	xexact,
		Epetra_Time &	Time,
		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)

void TestMultiLevelPreconditioner_Maxwell	(	char	ProblemType[],
		Teuchos::ParameterList &	MLList,
		Epetra_CrsMatrix &	CurlCurl,
		Epetra_CrsMatrix &	D0clean,
		Epetra_CrsMatrix &	M0inv,
		Epetra_CrsMatrix &	Ms,
		Epetra_CrsMatrix &	M1,
		Epetra_MultiVector &	xh,
		Epetra_MultiVector &	b,
		double &	TotalErrorResidual,
		double &	TotalErrorExactSol
	)

ML Preconditioner.

Parameters

ProblemType	[in] problem type
MLList	[in] ML 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 sigma
xh	[out] solution vector
b	[in] right-hand-side vector
TotalErrorResidual	[out] error residual
TotalErrorExactSol	[out] error in xh

References solution_test().

Classes

Macros

Typedefs

Functions

Detailed Description

Function Documentation