example_08.cpp File Reference

Example building stiffness matrix and right hand side for a Poisson equation using nodal (Hgrad) elements on squares. This code transforms the basis function gradients to each cell and performs 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"

Go to the source code of this file.

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

Example building stiffness matrix and right hand side for a Poisson equation using nodal (Hgrad) elements on squares. This code transforms the basis function gradients to each cell and performs quadrature.

Example of applying stiffness matrix for a Poisson equation using nodal (Hgrad) elements on squares. We are using a tensor-product decomposition of the element Poisson operator.

         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 

         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_09.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_09.exe 2 10 10 

Definition in file example_08.cpp.