OOFEM  2.4
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oofem::FEI2dTrQuad Class Reference

Second order triangular interpolation in 2D (6 nodes). More...

#include <fei2dtrquad.h>

+ Inheritance diagram for oofem::FEI2dTrQuad:
+ Collaboration diagram for oofem::FEI2dTrQuad:

Public Member Functions

 FEI2dTrQuad (int ind1, int ind2)
 
virtual integrationDomain giveIntegrationDomain () const
 Returns the integration domain of the interpolator. More...
 
virtual Element_Geometry_Type giveGeometryType () const
 Returns the geometry type fo the interpolator. More...
 
virtual integrationDomain giveBoundaryIntegrationDomain (int ib) const
 Returns boundary integration domain. More...
 
virtual integrationDomain giveBoundarySurfaceIntegrationDomain (int isurf) const
 Returns boundary integration domain. More...
 
virtual integrationDomain giveBoundaryEdgeIntegrationDomain (int iedge) const
 Returns boundary integration domain. More...
 
virtual void evalN (FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the array of interpolation functions (shape functions) at given point. More...
 
virtual double evaldNdx (FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the matrix of derivatives of interpolation functions (shape functions) at given point. More...
 
virtual void evald2Ndx2 (FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the matrix of second derivatives of interpolation functions (shape functions) at given point. More...
 
virtual void local2global (FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates global coordinates from given local ones. More...
 
virtual double giveArea (const FEICellGeometry &cellgeo) const
 Computes the exact area. More...
 
virtual int giveNumberOfNodes () const
 Returns the number of geometric nodes of the receiver. More...
 
virtual bool inside (const FloatArray &lcoords) const
 
virtual void computeLocalEdgeMapping (IntArray &edgeNodes, int iedge)
 
virtual int giveNumberOfEdges () const
 Returns number of edges. More...
 
virtual void edgeEvalN (FloatArray &answer, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the array of edge interpolation functions (shape functions) at given point. More...
 
virtual double edgeEvalNormal (FloatArray &normal, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the normal on the given edge. More...
 
virtual void edgeEvaldNds (FloatArray &answer, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the matrix of derivatives of edge interpolation functions (shape functions) at given point. More...
 
virtual void edgeLocal2global (FloatArray &answer, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates edge global coordinates from given local ones. More...
 
virtual double evalNXIntegral (int iEdge, const FEICellGeometry &cellgeo)
 Computes the integral $ \int_S n \cdot x \mathrm{d}s $. More...
 
virtual IntegrationRulegiveIntegrationRule (int order)
 Sets up a suitable integration rule for numerical integrating over volume. More...
 
virtual void evaldNdxi (FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the matrix of derivatives of interpolation functions (shape functions) at given point. More...
 
- Public Member Functions inherited from oofem::FEInterpolation2d
 FEInterpolation2d (int o, int ind1, int ind2)
 
virtual int giveNsd ()
 Returns number of spatial dimensions. More...
 
virtual double giveCharacteristicLength (const FEICellGeometry &cellgeo) const
 Returns a characteristic length of the geometry, typically a diagonal or edge length. More...
 
virtual int global2local (FloatArray &answer, const FloatArray &gcoords, const FEICellGeometry &cellgeo)
 Default implementation using Newton's method to find the local coordinates. More...
 
virtual void giveJacobianMatrixAt (FloatMatrix &jacobianMatrix, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Gives the jacobian matrix at the local coordinates. More...
 
virtual void boundaryEdgeGiveNodes (IntArray &answer, int boundary)
 Gives the boundary nodes for requested boundary number. More...
 
virtual void boundaryEdgeEvalN (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the basis functions on the requested boundary. More...
 
virtual double boundaryEdgeGiveTransformationJacobian (int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the determinant of the transformation Jacobian on the requested boundary. More...
 
virtual void boundaryEdgeLocal2Global (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Maps the local boundary coordinates to global. More...
 
virtual void boundaryGiveNodes (IntArray &answer, int boundary)
 Gives the boundary nodes for requested boundary number. More...
 
virtual void boundaryEvalN (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the basis functions on the requested boundary. More...
 
virtual double boundaryEvalNormal (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the normal on the requested boundary. More...
 
virtual double boundaryGiveTransformationJacobian (int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the determinant of the transformation Jacobian on the requested boundary. More...
 
virtual void boundaryLocal2Global (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Maps the local boundary coordinates to global. More...
 
virtual void boundarySurfaceEvalN (FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the array of edge interpolation functions (shape functions) at given point. More...
 
virtual void boundarySurfaceEvaldNdx (FloatMatrix &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the matrix of derivatives of edge interpolation functions (shape functions) at given point. More...
 
virtual double boundarySurfaceEvalNormal (FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the normal out of the surface at given point. More...
 
virtual void boundarySurfaceLocal2global (FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates edge global coordinates from given local ones. More...
 
virtual double boundarySurfaceGiveTransformationJacobian (int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the edge jacobian of transformation between local and global coordinates. More...
 
virtual void boundarySurfaceGiveNodes (IntArray &answer, int boundary)
 Gives the boundary nodes for requested boundary number. More...
 
void computeEdgeMapping (IntArray &edgeNodes, IntArray &elemNodes, int iedge)
 
virtual double edgeGiveTransformationJacobian (int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the edge Jacobian of transformation between local and global coordinates. More...
 
- Public Member Functions inherited from oofem::FEInterpolation
 FEInterpolation (int o)
 
virtual ~FEInterpolation ()
 
virtual IRResultType initializeFrom (InputRecord *ir)
 Initializes receiver according to object description stored in input record. More...
 
std::string errorInfo (const char *func) const
 
int giveInterpolationOrder ()
 Returns the interpolation order. More...
 
virtual void giveLocalNodeCoords (FloatMatrix &answer)
 Returns a matrix containing the local coordinates for each node corresponding to the interpolation. More...
 
virtual double giveTransformationJacobian (const FloatArray &lcoords, const FEICellGeometry &cellgeo)
 Evaluates the determinant of the transformation. More...
 
virtual IntegrationRulegiveBoundaryEdgeIntegrationRule (int order, int boundary)
 Sets up a suitable integration rule for integrating over the requested boundary. More...
 
virtual IntegrationRulegiveBoundarySurfaceIntegrationRule (int order, int boundary)
 Sets up a suitable integration rule for integrating over the requested boundary. More...
 
virtual IntegrationRulegiveBoundaryIntegrationRule (int order, int boundary)
 Sets up a suitable integration rule for integrating over the requested boundary. More...
 
virtual int giveKnotSpanBasisFuncMask (const IntArray &knotSpan, IntArray &mask)
 Returns indices (zero based) of nonzero basis functions for given knot span. More...
 
virtual int giveNumberOfKnotSpanBasisFunctions (const IntArray &knotSpan)
 Returns the number of nonzero basis functions at individual knot span,. More...
 
virtual bool hasSubPatchFormulation ()
 Returns true, if receiver is formulated on sub-patch basis. More...
 
virtual const double *const * giveKnotVector ()
 Returns the subdivision of patch parametric space. More...
 
virtual int giveNumberOfKnotSpans (int dim)
 Returns the number of knot spans of the receiver. More...
 
virtual const FloatArraygiveKnotValues (int dim)
 Returns the knot values of the receiver. More...
 
virtual const IntArraygiveKnotMultiplicity (int dim)
 Returns the knot multiplicity of the receiver. More...
 

Protected Member Functions

double edgeComputeLength (IntArray &edgeNodes, const FEICellGeometry &cellgeo)
 

Additional Inherited Members

- Protected Attributes inherited from oofem::FEInterpolation2d
int xind
 
int yind
 
- Protected Attributes inherited from oofem::FEInterpolation
int order
 

Detailed Description

Second order triangular interpolation in 2D (6 nodes).

Definition at line 44 of file fei2dtrquad.h.

Constructor & Destructor Documentation

oofem::FEI2dTrQuad::FEI2dTrQuad ( int  ind1,
int  ind2 
)
inline

Definition at line 47 of file fei2dtrquad.h.

Member Function Documentation

double oofem::FEI2dTrQuad::edgeComputeLength ( IntArray edgeNodes,
const FEICellGeometry cellgeo 
)
protected
void oofem::FEI2dTrQuad::edgeEvaldNds ( FloatArray answer,
int  iedge,
const FloatArray lcoords,
const FEICellGeometry cellgeo 
)
virtual

Evaluates the matrix of derivatives of edge interpolation functions (shape functions) at given point.

These derivatives are in global coordinate system (where the nodal coordinates are defined).

Parameters
answerContains resulting array of derivatives, the member at i position contains value of $ \frac{\mathrm{d}N_i}{\mathrm{d}s} $.
iedgeDetermines the edge number.
lcoordsArray containing (local) coordinates.
cellgeoUnderlying cell geometry.

Implements oofem::FEInterpolation2d.

Definition at line 155 of file fei2dtrquad.C.

References oofem::IntArray::at(), oofem::FloatArray::at(), computeLocalEdgeMapping(), oofem::FloatArray::computeNorm(), oofem::FEInterpolation2d::edgeGiveTransformationJacobian(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FloatArray::times(), oofem::FEInterpolation2d::xind, and oofem::FEInterpolation2d::yind.

void oofem::FEI2dTrQuad::edgeEvalN ( FloatArray answer,
int  iedge,
const FloatArray lcoords,
const FEICellGeometry cellgeo 
)
virtual

Evaluates the array of edge interpolation functions (shape functions) at given point.

Parameters
answerContains resulting array of evaluated interpolation functions.
iedgeEdge number.
lcoordsArray containing (local) coordinates.
cellgeoUnderlying cell geometry.

Implements oofem::FEInterpolation2d.

Definition at line 146 of file fei2dtrquad.C.

References oofem::FloatArray::at().

Referenced by oofem::Tr21Stokes::computeBoundarySurfaceLoadVector(), oofem::TrPlanestressRotAllman::computeEgdeNMatrixAt(), and edgeLocal2global().

double oofem::FEI2dTrQuad::edgeEvalNormal ( FloatArray answer,
int  iedge,
const FloatArray lcoords,
const FEICellGeometry cellgeo 
)
virtual

Evaluates the normal on the given edge.

Parameters
answerContains the evaluated normal.
iedgeDetermines the edge number.
lcoordsArray containing (local) coordinates.
cellgeoUnderlying cell geometry.

Implements oofem::FEInterpolation2d.

Definition at line 192 of file fei2dtrquad.C.

References oofem::IntArray::at(), oofem::FloatArray::at(), computeLocalEdgeMapping(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FloatArray::normalize(), oofem::FloatArray::resize(), oofem::FEInterpolation2d::xind, and oofem::FEInterpolation2d::yind.

void oofem::FEI2dTrQuad::edgeLocal2global ( FloatArray answer,
int  iedge,
const FloatArray lcoords,
const FEICellGeometry cellgeo 
)
virtual

Evaluates edge global coordinates from given local ones.

These derivatives are in global coordinate system (where the nodal coordinates are defined).

Parameters
answerContains resulting global coordinates.
iedgeDetermines edge number.
lcoordsArray containing (local) coordinates.
cellgeoUnderlying cell geometry.

Implements oofem::FEInterpolation2d.

Definition at line 215 of file fei2dtrquad.C.

References oofem::IntArray::at(), oofem::FloatArray::at(), computeLocalEdgeMapping(), edgeEvalN(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FloatArray::resize(), oofem::FEInterpolation2d::xind, and oofem::FEInterpolation2d::yind.

Referenced by oofem::TR21_2D_SUPG::computeIntersection().

void oofem::FEI2dTrQuad::evald2Ndx2 ( FloatMatrix answer,
const FloatArray lcoords,
const FEICellGeometry cellgeo 
)
virtual

Evaluates the matrix of second derivatives of interpolation functions (shape functions) at given point.

These derivatives are in global coordinate system (where the nodal coordinates are defined)

Parameters
answerContains resulting matrix of derivatives, the member at i,j position contains value of dNi/dxj.
lcoordsArray containing (local) coordinates.
cellgeoUnderlying cell geometry.

Reimplemented from oofem::FEInterpolation.

Definition at line 81 of file fei2dtrquad.C.

References oofem::FloatArray::at(), oofem::FloatMatrix::at(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FloatMatrix::resize(), oofem::FEInterpolation2d::xind, and oofem::FEInterpolation2d::yind.

Referenced by oofem::TR21_2D_SUPG::computeDivTauMatrix().

double oofem::FEI2dTrQuad::evaldNdx ( FloatMatrix answer,
const FloatArray lcoords,
const FEICellGeometry cellgeo 
)
virtual

Evaluates the matrix of derivatives of interpolation functions (shape functions) at given point.

These derivatives are in global coordinate system (where the nodal coordinates are defined)

Parameters
answerContains resulting matrix of derivatives, the member at i,j position contains value of dNi/dxj.
lcoordsArray containing (local) coordinates.
cellgeoUnderlying cell geometry.
Returns
Determinant of the Jacobian.

Implements oofem::FEInterpolation.

Definition at line 60 of file fei2dtrquad.C.

References oofem::FloatArray::at(), oofem::FloatMatrix::at(), oofem::FloatMatrix::beInverseOf(), oofem::FloatMatrix::beProductTOf(), evaldNdxi(), oofem::FloatMatrix::giveNumberOfRows(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FEInterpolation2d::xind, and oofem::FEInterpolation2d::yind.

Referenced by oofem::TR21_2D_SUPG::computeBMatrix(), oofem::TrPlanestressRotAllman::computeBmatrixAt(), oofem::TR21_2D_SUPG::computeDivUMatrix(), oofem::TR21_2D_SUPG::computeGradUMatrix(), oofem::Tr21Stokes::computeInternalForcesVector(), oofem::Tr21Stokes::computeStiffnessMatrix(), oofem::TrPlanestressRotAllman::computeStiffnessMatrixZeroEnergyStabilization(), oofem::TR21_2D_SUPG::computeUDotGradUMatrix(), oofem::TR21_2D_SUPG::LS_PCS_computedN(), and oofem::TR21_2D_SUPG::LS_PCS_computeF().

void oofem::FEI2dTrQuad::evaldNdxi ( FloatMatrix answer,
const FloatArray lcoords,
const FEICellGeometry cellgeo 
)
virtual

Evaluates the matrix of derivatives of interpolation functions (shape functions) at given point.

These derivatives are wrt local (parent) coordinate system

Parameters
answerContains resulting matrix of derivatives, the member at i,j position contains value of dNi/dxij.
lcoordsArray containing (local) coordinates.
cellgeoUnderlying cell geometry.

Reimplemented from oofem::FEInterpolation.

Definition at line 262 of file fei2dtrquad.C.

References oofem::FloatArray::at(), oofem::FloatMatrix::at(), and oofem::FloatMatrix::resize().

Referenced by evaldNdx().

void oofem::FEI2dTrQuad::evalN ( FloatArray answer,
const FloatArray lcoords,
const FEICellGeometry cellgeo 
)
virtual

Evaluates the array of interpolation functions (shape functions) at given point.

Parameters
answerContains resulting array of evaluated interpolation functions.
lcoordsArray containing (local) coordinates.
cellgeoUnderlying cell geometry.

Implements oofem::FEInterpolation.

Definition at line 43 of file fei2dtrquad.C.

References oofem::FloatArray::at().

Referenced by oofem::Tr21Stokes::computeField(), oofem::Tr21Stokes::computeLoadVector(), oofem::TrPlanestressRotAllman::computeNmatrixAt(), oofem::TR21_2D_SUPG::computeNuMatrix(), local2global(), oofem::TR21_2D_SUPG::LS_PCS_computeS(), and oofem::TR21_2D_SUPG::LS_PCS_computeVOFFractions().

double oofem::FEI2dTrQuad::evalNXIntegral ( int  boundary,
const FEICellGeometry cellgeo 
)
virtual

Computes the integral $ \int_S n \cdot x \mathrm{d}s $.

Parameters
boundaryBoundary number.
cellgeoUnderlying cell geometry.
Returns
Evaluated integral.

Reimplemented from oofem::FEInterpolation.

Definition at line 338 of file fei2dtrquad.C.

References oofem::IntArray::at(), oofem::FloatArray::at(), computeLocalEdgeMapping(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FEInterpolation2d::xind, and oofem::FEInterpolation2d::yind.

double oofem::FEI2dTrQuad::giveArea ( const FEICellGeometry cellgeo) const
virtual

Computes the exact area.

Parameters
cellgeoCell geometry for the element.
Returns
Area of geometry.

Reimplemented from oofem::FEInterpolation2d.

Definition at line 288 of file fei2dtrquad.C.

References oofem::FloatArray::at(), and oofem::FEICellGeometry::giveVertexCoordinates().

virtual integrationDomain oofem::FEI2dTrQuad::giveBoundaryEdgeIntegrationDomain ( int  boundary) const
inlinevirtual

Returns boundary integration domain.

Implements oofem::FEInterpolation.

Definition at line 53 of file fei2dtrquad.h.

References oofem::_Line.

virtual integrationDomain oofem::FEI2dTrQuad::giveBoundaryIntegrationDomain ( int  boundary) const
inlinevirtual

Returns boundary integration domain.

Implements oofem::FEInterpolation.

Definition at line 51 of file fei2dtrquad.h.

References oofem::_Line.

virtual integrationDomain oofem::FEI2dTrQuad::giveBoundarySurfaceIntegrationDomain ( int  boundary) const
inlinevirtual

Returns boundary integration domain.

Implements oofem::FEInterpolation.

Definition at line 52 of file fei2dtrquad.h.

References oofem::_Triangle.

virtual Element_Geometry_Type oofem::FEI2dTrQuad::giveGeometryType ( ) const
inlinevirtual

Returns the geometry type fo the interpolator.

Implements oofem::FEInterpolation.

Definition at line 50 of file fei2dtrquad.h.

virtual integrationDomain oofem::FEI2dTrQuad::giveIntegrationDomain ( ) const
inlinevirtual

Returns the integration domain of the interpolator.

Implements oofem::FEInterpolation.

Definition at line 49 of file fei2dtrquad.h.

References oofem::_Triangle.

IntegrationRule * oofem::FEI2dTrQuad::giveIntegrationRule ( int  order)
virtual

Sets up a suitable integration rule for numerical integrating over volume.

The required polynomial order for the determinant of the jacobian is added automatically.

Parameters
orderPolynomial order of integrand (should NOT including determinant of jacobian).

Reimplemented from oofem::FEInterpolation.

Definition at line 362 of file fei2dtrquad.C.

References oofem::_Triangle, oofem::IntegrationRule::getRequiredNumberOfIntegrationPoints(), and oofem::IntegrationRule::SetUpPointsOnTriangle().

virtual int oofem::FEI2dTrQuad::giveNumberOfEdges ( ) const
inlinevirtual

Returns number of edges.

Reimplemented from oofem::FEInterpolation.

Definition at line 69 of file fei2dtrquad.h.

virtual int oofem::FEI2dTrQuad::giveNumberOfNodes ( ) const
inlinevirtual

Returns the number of geometric nodes of the receiver.

Reimplemented from oofem::FEInterpolation.

Definition at line 63 of file fei2dtrquad.h.

bool oofem::FEI2dTrQuad::inside ( const FloatArray lcoords) const
virtual

Reimplemented from oofem::FEInterpolation2d.

Definition at line 316 of file fei2dtrquad.C.

References oofem::FloatArray::at().

void oofem::FEI2dTrQuad::local2global ( FloatArray answer,
const FloatArray lcoords,
const FEICellGeometry cellgeo 
)
virtual

Evaluates global coordinates from given local ones.

Parameters
answerContains resulting global coordinates.
lcoordsArray containing (local) coordinates.
cellgeoUnderlying cell geometry.

Implements oofem::FEInterpolation.

Definition at line 131 of file fei2dtrquad.C.

References oofem::FloatArray::at(), evalN(), oofem::FEICellGeometry::giveVertexCoordinates(), oofem::FloatArray::resize(), oofem::FEInterpolation2d::xind, oofem::FEInterpolation2d::yind, and oofem::FloatArray::zero().


The documentation for this class was generated from the following files:

This page is part of the OOFEM documentation. Copyright (c) 2011 Borek Patzak
Project e-mail: info@oofem.org
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