Class representing a 2d quadrilateral with quadratic interpolation based on isoparametric coordinates. More...

#include <fei2dquadquad.h>

Inheritance diagram for oofem::FEI2dQuadQuad:

Collaboration diagram for oofem::FEI2dQuadQuad:

Public Member Functions
	FEI2dQuadQuad (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 double	giveArea (const FEICellGeometry &cellgeo) const
	Computes the exact area. 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	local2global (FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates global coordinates from given local ones. More...

virtual int	giveNumberOfNodes () const
	Returns the number of geometric nodes of the receiver. More...

virtual double	giveCharacteristicLength (const FEICellGeometry &cellgeo) const
	Returns a characteristic length of the geometry, typically a diagonal or edge length. More...

virtual bool	inside (const FloatArray &lcoords) const

virtual void	computeLocalEdgeMapping (IntArray &edgeNodes, int iedge)

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 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	edgeEvalNormal (FloatArray &normal, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo)
	Evaluates the normal on the given edge. More...

virtual double	evalNXIntegral (int iEdge, const FEICellGeometry &cellgeo)
	Computes the integral $\int_S n \cdot x \mathrm{d}s$ . More...

virtual IntegrationRule *	giveIntegrationRule (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 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	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	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 IntegrationRule *	giveBoundaryEdgeIntegrationRule (int order, int boundary)
	Sets up a suitable integration rule for integrating over the requested boundary. More...

virtual IntegrationRule *	giveBoundarySurfaceIntegrationRule (int order, int boundary)
	Sets up a suitable integration rule for integrating over the requested boundary. More...

virtual IntegrationRule *	giveBoundaryIntegrationRule (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 FloatArray *	giveKnotValues (int dim)
	Returns the knot values of the receiver. More...

virtual const IntArray *	giveKnotMultiplicity (int dim)
	Returns the knot multiplicity of the receiver. More...

virtual int	giveNumberOfEdges () const
	Returns number of edges. More...

Additional Inherited Members
Protected Attributes inherited from oofem::FEInterpolation2d
int	xind

int	yind

Protected Attributes inherited from oofem::FEInterpolation
int	order

Detailed Description

Class representing a 2d quadrilateral with quadratic interpolation based on isoparametric coordinates.

Local Node Numbering (4)–(7)–(3) | | | | (8) (6) | | | | (1)–(5)–(2)

Definition at line 52 of file fei2dquadquad.h.

Constructor & Destructor Documentation

oofem::FEI2dQuadQuad::FEI2dQuadQuad	(	int	ind1,
		int	ind2
	)

inline

Definition at line 55 of file fei2dquadquad.h.

Member Function Documentation

void oofem::FEI2dQuadQuad::computeLocalEdgeMapping	(	IntArray &	edgeNodes,
		int	iedge
	)

virtual

Implements oofem::FEInterpolation2d.

Definition at line 201 of file fei2dquadquad.C.

References oofem::IntArray::at(), OOFEM_ERROR, and oofem::IntArray::resize().

Referenced by edgeEvalNormal(), oofem::FEI2dQuadQuadAxi::edgeGiveTransformationJacobian(), edgeLocal2global(), and evalNXIntegral().

void oofem::FEI2dQuadQuad::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

answer	Contains resulting array of derivatives, the member at i position contains value of $\frac{\mathrm{d}N_i}{\mathrm{d}s}$ .
iedge	Determines the edge number.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation2d.

Definition at line 174 of file fei2dquadquad.C.

References oofem::FloatArray::at().

void oofem::FEI2dQuadQuad::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

answer	Contains resulting array of evaluated interpolation functions.
iedge	Edge number.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation2d.

Definition at line 163 of file fei2dquadquad.C.

References oofem::FloatArray::at().

Referenced by oofem::FEI2dQuadQuadAxi::edgeGiveTransformationJacobian(), and edgeLocal2global().

double oofem::FEI2dQuadQuad::edgeEvalNormal	(	FloatArray &	answer,
		int	iedge,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

virtual

Evaluates the normal on the given edge.

Parameters

answer	Contains the evaluated normal.
iedge	Determines the edge number.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation2d.

Definition at line 231 of file fei2dquadquad.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::FEI2dQuadQuad::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

answer	Contains resulting global coordinates.
iedge	Determines edge number.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation2d.

Definition at line 182 of file fei2dquadquad.C.

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

double oofem::FEI2dQuadQuad::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

answer	Contains resulting matrix of derivatives, the member at i,j position contains value of dNi/dxj.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Returns: Determinant of the Jacobian.

Implements oofem::FEInterpolation.

Definition at line 104 of file fei2dquadquad.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::Quad2PlateSubSoil::computeBmatrixAt().

void oofem::FEI2dQuadQuad::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

answer	Contains resulting matrix of derivatives, the member at i,j position contains value of dNi/dxij.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Reimplemented from oofem::FEInterpolation.

Definition at line 254 of file fei2dquadquad.C.

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

Referenced by evaldNdx().

void oofem::FEI2dQuadQuad::evalN	(	FloatArray &	answer,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

virtual

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

Parameters

answer	Contains resulting array of evaluated interpolation functions.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation.

Reimplemented in oofem::FEI2dQuadBiQuad.

Definition at line 84 of file fei2dquadquad.C.

References oofem::FloatArray::at().

Referenced by oofem::Quad2PlateSubSoil::computeBmatrixAt(), oofem::FEI2dQuadQuadAxi::giveTransformationJacobian(), and local2global().

double oofem::FEI2dQuadQuad::evalNXIntegral	(	int	boundary,
		const FEICellGeometry &	cellgeo
	)

virtual

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

Parameters

boundary	Boundary number.
cellgeo	Underlying cell geometry.

Returns: Evaluated integral.

Reimplemented from oofem::FEInterpolation.

Definition at line 283 of file fei2dquadquad.C.

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

double oofem::FEI2dQuadQuad::giveArea ( const FEICellGeometry & cellgeo ) const

virtual

Computes the exact area.

Parameters

cellgeo Cell geometry for the element.

Returns: Area of geometry.

Reimplemented from oofem::FEInterpolation2d.

Definition at line 43 of file fei2dquadquad.C.

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

virtual integrationDomain oofem::FEI2dQuadQuad::giveBoundaryEdgeIntegrationDomain ( int boundary ) const

inlinevirtual

Returns boundary integration domain.

Implements oofem::FEInterpolation.

Definition at line 61 of file fei2dquadquad.h.

References oofem::_Line.

virtual integrationDomain oofem::FEI2dQuadQuad::giveBoundaryIntegrationDomain ( int boundary ) const

inlinevirtual

Returns boundary integration domain.

Implements oofem::FEInterpolation.

Definition at line 59 of file fei2dquadquad.h.

References oofem::_Line.

virtual integrationDomain oofem::FEI2dQuadQuad::giveBoundarySurfaceIntegrationDomain ( int boundary ) const

inlinevirtual

Returns boundary integration domain.

Implements oofem::FEInterpolation.

Definition at line 60 of file fei2dquadquad.h.

References oofem::_Square.

double oofem::FEI2dQuadQuad::giveCharacteristicLength ( const FEICellGeometry & cellgeo ) const

virtual

Returns a characteristic length of the geometry, typically a diagonal or edge length.

Parameters

cellgeo underlying cell geometry

Returns: distance from node 1 to 3

Reimplemented from oofem::FEInterpolation2d.

Definition at line 139 of file fei2dquadquad.C.

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

virtual Element_Geometry_Type oofem::FEI2dQuadQuad::giveGeometryType ( ) const

inlinevirtual

Returns the geometry type fo the interpolator.

Implements oofem::FEInterpolation.

Definition at line 58 of file fei2dquadquad.h.

virtual integrationDomain oofem::FEI2dQuadQuad::giveIntegrationDomain ( ) const

inlinevirtual

Returns the integration domain of the interpolator.

Implements oofem::FEInterpolation.

Definition at line 57 of file fei2dquadquad.h.

References oofem::_Square.

IntegrationRule * oofem::FEI2dQuadQuad::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

order Polynomial order of integrand (should NOT including determinant of jacobian).

Reimplemented from oofem::FEInterpolation.

Reimplemented in oofem::FEI2dQuadBiQuad.

Definition at line 308 of file fei2dquadquad.C.

References oofem::_Square, oofem::IntegrationRule::getRequiredNumberOfIntegrationPoints(), and oofem::IntegrationRule::SetUpPointsOnSquare().

virtual int oofem::FEI2dQuadQuad::giveNumberOfNodes ( ) const

inlinevirtual

Returns the number of geometric nodes of the receiver.

Reimplemented from oofem::FEInterpolation.

Reimplemented in oofem::FEI2dQuadBiQuad.

Definition at line 69 of file fei2dquadquad.h.

bool oofem::FEI2dQuadQuad::inside ( const FloatArray & lcoords ) const

virtual

Reimplemented from oofem::FEInterpolation2d.

Definition at line 146 of file fei2dquadquad.C.

References oofem::FloatArray::at().

void oofem::FEI2dQuadQuad::local2global	(	FloatArray &	answer,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo
	)

virtual

Evaluates global coordinates from given local ones.

Parameters

answer	Contains resulting global coordinates.
lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Implements oofem::FEInterpolation.

Definition at line 125 of file fei2dquadquad.C.

References oofem::FloatArray::at(), evalN(), oofem::FloatArray::giveSize(), 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:

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation