mathcomp.assemble
Class LagrangeSquareAssembler

java.lang.Object
  mathcomp.monitor.DefaultReportable
      mathcomp.monitor.DefaultAlgorithm
          mathcomp.assemble.Assembler
              mathcomp.assemble.LagrangeSquareAssembler

All Implemented Interfaces:

java.lang.Runnable, Algorithm, Reportable

Direct Known Subclasses:

AbstractCDA_Square, SquareLaplaceAssembler

public abstract class LagrangeSquareAssembler
extends Assembler

An Assembler class for piecewise quadratic lagrange basis-functions.

Author:

pht

Field Summary

Fields inherited from class mathcomp.assemble.Assembler

dirichletBoundaryValues, solScale

Constructor Summary

LagrangeSquareAssembler()

Method Summary

void	createDof(Grid grid, java.util.Set dof) All global Objects, that represent a degreeOfFreedom are added to dof.
void	createDofExport(Triangle t, java.lang.Object[] result)
double[]	evalApproxGradient(Node gaussRef, Triangle t, Vector x) For H1 error calculations we need to know the gradient of the approximated solution in a node n.
double	evalApproxSolution(Node n, Triangle t, Vector x) Evaluates the FEM solution in a Node.
double	evalBasisFuncOnRef(Node u, int localBasisNumber) Returns the value of the Node u on the quadratic Basisfunktion with the local number localBasisNumber on the standart-triangle.
double	evalGradXBasisFuncOnRef(Node u, int localBasisNumber)
double	evalGradYBasisFuncOnRef(Node u, int localBasisNumber)
java.util.List	getLdof(Triangle t, java.util.List ldof) Every Assambler has to define the local DOFs for an element.
int	getLocalNodeNumber(Triangle t, Node n) Gets the local Node number to a Node on a quadratic triangle element.

Methods inherited from class mathcomp.assemble.Assembler

addDirichletNodes, assembleGlobal, calcDirichletBoundary, createSurfaces, createSurfaces, evalExactGradient, evalExactSolution, evalF, getDof, getElementMatrix, getEpsilon, getErrorCalculator, getExactPartialX, getExactPartialY, getGrid, getInfoUrl, getM, getPreferredGridFileName, getSolScale, getY, report, run, setEpsilon, setGrid, setM, setTauIndex, setY, toString

Methods inherited from class mathcomp.monitor.DefaultAlgorithm

algoAbortIfNeeded, algoCancel, algoClear, algoCount, algoIncrement, algoMax, isAlgoCancel, setAlgoCount, setAlgoMax

Methods inherited from class mathcomp.monitor.DefaultReportable

getReport, setReport

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface mathcomp.monitor.Reportable

getReport, setReport

Constructor Detail

LagrangeSquareAssembler

public LagrangeSquareAssembler()

Method Detail

createDof

public void createDof(Grid grid,
                      java.util.Set dof)

Description copied from class: Assembler

All global Objects, that represent a degreeOfFreedom are added to dof.

Specified by:

createDof in class Assembler

Parameters:

grid - the current grid

dof - the Set where the DOFs have to be put in

getLdof

public java.util.List getLdof(Triangle t,
                              java.util.List ldof)

Description copied from class: Assembler

Every Assambler has to define the local DOFs for an element. Depending on what FE-space you choose the local DOFs vary

Returns:

the List containing the local DOFs

createDofExport

public void createDofExport(Triangle t,
                            java.lang.Object[] result)

getLocalNodeNumber

public int getLocalNodeNumber(Triangle t,
                              Node n)

Gets the local Node number to a Node on a quadratic triangle element. By convention corner nodes have the local numbers 0,1 and 2 then the opposite edge middle node of corner node 0 is 3, and so on, so the edge middle nodes have local numbers 3,4 and 5. If the node is no local dof on this element we return -1.

Parameters:

t - the current triangle

n - the node to find the local number of

Returns:

the local node number on this element

evalApproxSolution

public double evalApproxSolution(Node n,
                                 Triangle t,
                                 Vector x)

Description copied from class: Assembler

Evaluates the FEM solution in a Node. To do that we do need the triangle. We need this method for an easy l2 and l\infty error calculation.

Specified by:

evalApproxSolution in class Assembler

Parameters:

n - Node where the solution has to be evaluated

t - the triangle that contains the Node n

x - the solution vector

Returns:

the value of the solution in n

evalBasisFuncOnRef

public double evalBasisFuncOnRef(Node u,
                                 int localBasisNumber)

Returns the value of the Node u on the quadratic Basisfunktion with the local number localBasisNumber on the standart-triangle.

evalGradXBasisFuncOnRef

public double evalGradXBasisFuncOnRef(Node u,
                                      int localBasisNumber)

evalGradYBasisFuncOnRef

public double evalGradYBasisFuncOnRef(Node u,
                                      int localBasisNumber)

evalApproxGradient

public double[] evalApproxGradient(Node gaussRef,
                                   Triangle t,
                                   Vector x)

Description copied from class: Assembler

For H1 error calculations we need to know the gradient of the approximated solution in a node n. If we don't know that, return [0.0,0.0] for every node n. TODO this should become abstract.

Overrides:

evalApproxGradient in class Assembler

Parameters:

gaussRef - node where the approximated gradient should be evaluated