Demonstrate diagonalized mass matrices for H(grad) elements in 1d using Gauss-Legendre quadrature. More...

#include "Intrepid_FunctionSpaceTools.hpp"
#include "Intrepid_FieldContainer.hpp"
#include "Intrepid_CellTools.hpp"
#include "Intrepid_ArrayTools.hpp"
#include "Intrepid_HGRAD_QUAD_Cn_FEM.hpp"
#include "Intrepid_RealSpaceTools.hpp"
#include "Intrepid_DefaultCubatureFactory.hpp"
#include "Intrepid_Utils.hpp"
#include "Epetra_Time.h"
#include "Epetra_Map.h"
#include "Epetra_FECrsMatrix.h"
#include "Epetra_FEVector.h"
#include "Epetra_SerialComm.h"
#include "Teuchos_oblackholestream.hpp"
#include "Teuchos_RCP.hpp"
#include "Teuchos_BLAS.hpp"
#include "Shards_CellTopology.hpp"
#include "EpetraExt_RowMatrixOut.h"
#include "EpetraExt_MultiVectorOut.h"

Functions
double	evalu (double &x, double &y, double &z)

int	evalGradu (double &x, double &y, double &z, double &gradu1, double &gradu2, double &gradu3)

double	evalDivGradu (double &x, double &y, double &z)

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

Detailed Description

Demonstrate diagonalized mass matrices for H(grad) elements in 1d using Gauss-Legendre quadrature.

Example building stiffness matrix and right hand side for a Poisson equation using nodal (Hgrad) elements on squares. This uses higher order elements and builds a single reference stiffness matrix that is used for each element. The global matrix is constructed by specifying an upper bound on the number of nonzeros per row, but not preallocating the graph.

Author: Created by P. Bochev, R. Kirby D. Ridzal and K. Peterson.

Remarks

Usage

 ./Intrepid_example_Drivers_Example_03.exe max_deg verbose

    int min_deg         - beginning polynomial degree to check 
    int max_deg         - maximum polynomial degree to check
    verbose (optional)  - any character, indicates verbose output

Sample command line: checks mass matrix of degree 1,2,3

./Intrepid_example_Drivers_Example_03.exe 1 3

         div grad u = f in Omega
                  u = 0 on Gamma 

 Discrete linear system for nodal coefficients(x):
    
             Kx = b

        K - HGrad stiffness matrix
        b - right hand side vector

Author: Created by P. Bochev, R. Kirby, D. Ridzal and K. Peterson.

Remarks

Usage

 ./Intrepid_example_Drivers_Example_05.exe N verbose
    int deg             - polynomial degree
    int NX              - num intervals in x direction (assumed box domain, 0,1)
    int NY              - num intervals in x direction (assumed box domain, 0,1)
    verbose (optional)  - any character, indicates verbose output

Sample command line

./Intrepid_example_Drivers_Example_05.exe 2 10 10

Definition in file example_05.cpp.

Function Documentation

◆ evalDivGradu()

double evalDivGradu	(	double &	x,
		double &	y,
		double &	z
	)

Definition at line 486 of file example_05.cpp.

◆ evalGradu()

int evalGradu	(	double &	x,
		double &	y,
		double &	z,
		double &	gradu1,
		double &	gradu2,
		double &	gradu3
	)

Definition at line 465 of file example_05.cpp.

◆ evalu()

double evalu	(	double &	x,
		double &	y,
		double &	z
	)

Definition at line 451 of file example_05.cpp.

◆ main()

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