#include <fei2dlinelin.h>

Inheritance diagram for oofem::FEI2dLineLin:

Collaboration diagram for oofem::FEI2dLineLin:

Public Member Functions
	FEI2dLineLin (int ind1, int ind2)
integrationDomain	giveIntegrationDomain (const Element_Geometry_Type) const override
const Element_Geometry_Type	giveGeometryType () const override
const Element_Geometry_Type	giveBoundaryGeometryType (int boundary) const override
integrationDomain	giveBoundaryIntegrationDomain (int ib, const Element_Geometry_Type) const override
	Returns boundary integration domain.
integrationDomain	giveBoundarySurfaceIntegrationDomain (int isurf, const Element_Geometry_Type) const override
	Returns boundary integration domain.
integrationDomain	giveBoundaryEdgeIntegrationDomain (int iedge, const Element_Geometry_Type) const override
	Returns boundary integration domain.
double	giveArea (const FEICellGeometry &cellgeo) const override
void	local2global (FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
int	global2local (FloatArray &answer, const FloatArray &gcoords, const FEICellGeometry &cellgeo) const override
int	giveNumberOfEdges (const Element_Geometry_Type) const override
void	giveCellDofMans (IntArray &nodes, IntArray &internalDofMans, Element *elem) const override
	Returns list of element nodes (and list of internal dof managers) (including on edges and surfaces) defining the approximation.
void	evalN (FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	evaldNdx (FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
void	evaldNdxi (FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	giveTransformationJacobian (const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
IntArray	boundaryEdgeGiveNodes (int boundary, const Element_Geometry_Type, bool includeHierarchical=false) const override
IntArray	computeLocalEdgeMapping (int iedge) const override
void	edgeEvalN (FloatArray &answer, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	edgeEvalNormal (FloatArray &normal, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
void	edgeEvaldNds (FloatArray &answer, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
void	edgeLocal2global (FloatArray &answer, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	evalNXIntegral (int iEdge, const FEICellGeometry &cellgeo) const override
int	giveNumberOfNodes (const Element_Geometry_Type) const override
std::unique_ptr< IntegrationRule >	giveIntegrationRule (int order, const Element_Geometry_Type) const override
void	surfaceEvaldNdxi (FloatMatrix &answer, const FloatArray &lcoords) const override
void	surfaceEvald2Ndxi2 (FloatMatrix &answer, const FloatArray &lcoords) const override
Public Member Functions inherited from oofem::FEInterpolation2d
	FEInterpolation2d (int o, int ind1, int ind2)
int	giveNsd (const Element_Geometry_Type) const override
virtual double	giveCharacteristicLength (const FEICellGeometry &cellgeo) const
int	global2local (FloatArray &answer, const FloatArray &gcoords, const FEICellGeometry &cellgeo) const override
void	giveJacobianMatrixAt (FloatMatrix &jacobianMatrix, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
virtual bool	inside (const FloatArray &lcoords) const
IntArray	boundaryEdgeGiveNodes (int boundary, const Element_Geometry_Type, bool includeHierarchical=false) const override
void	boundaryEdgeEvalN (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	boundaryEdgeEvalNormal (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	boundaryEdgeGiveTransformationJacobian (int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
void	boundaryEdgeLocal2Global (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
IntArray	boundaryGiveNodes (int boundary, const Element_Geometry_Type) const override
void	boundaryEvalN (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	boundaryEvalNormal (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	boundaryGiveTransformationJacobian (int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
void	boundaryLocal2Global (FloatArray &answer, int boundary, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
void	boundarySurfaceEvalN (FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
void	boundarySurfaceEvaldNdx (FloatMatrix &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	boundarySurfaceEvalNormal (FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
void	boundarySurfaceLocal2global (FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
double	boundarySurfaceGiveTransformationJacobian (int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const override
IntArray	boundarySurfaceGiveNodes (int boundary, const Element_Geometry_Type, bool includeHierarchical=false) const override
virtual FloatArrayF< 2 >	surfaceEvalBaseVectorsAt (int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
IntArray	computeEdgeMapping (const IntArray &elemNodes, int iedge) const
virtual double	edgeGiveTransformationJacobian (int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
Public Member Functions inherited from oofem::FEInterpolation
	FEInterpolation (int o)
virtual	~FEInterpolation ()=default
virtual void	initializeFrom (InputRecord &ir, ParameterManager &pm, int elnum, int priority)
	Initializes receiver according to object description stored in input record.
virtual void	postInitialize (ParameterManager &pm, int elnum)
int	giveInterpolationOrder () const
virtual void	evald2Ndx2 (FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
virtual void	giveLocalNodeCoords (FloatMatrix &answer, const Element_Geometry_Type) const
virtual std::unique_ptr< IntegrationRule >	giveBoundaryEdgeIntegrationRule (int order, int boundary, const Element_Geometry_Type) const
virtual std::unique_ptr< IntegrationRule >	giveBoundarySurfaceIntegrationRule (int order, int boundary, const Element_Geometry_Type) const
virtual std::unique_ptr< IntegrationRule >	giveBoundaryIntegrationRule (int order, int boundary, const Element_Geometry_Type) const
virtual int	giveKnotSpanBasisFuncMask (const IntArray &knotSpan, IntArray &mask) const
virtual int	giveNumberOfKnotSpanBasisFunctions (const IntArray &knotSpan) const
virtual bool	hasSubPatchFormulation () const
virtual const FloatArray *	giveKnotVector () const
virtual int	giveNumberOfKnotSpans (int dim) const
virtual const FloatArray *	giveKnotValues (int dim) const
virtual const IntArray *	giveKnotMultiplicity (int dim) const
virtual void	initializeCell (Element *e) const
std::string	errorInfo (const char *func) const

Static Public Member Functions
static FloatArrayF< 2 >	evalN (double xi)

Protected Member Functions
double	edgeComputeLength (const IntArray &edgeNodes, const FEICellGeometry &cellgeo) const

Additional Inherited Members
Protected Attributes inherited from oofem::FEInterpolation2d
int	xind
int	yind
Protected Attributes inherited from oofem::FEInterpolation
int	order = 0

Detailed Description

Class representing a 2d line with linear interpolation.

Todo

Author: Mikael Öhman

Definition at line 46 of file fei2dlinelin.h.

Constructor & Destructor Documentation

◆ FEI2dLineLin()

oofem::FEI2dLineLin::FEI2dLineLin	(	int	ind1,
		int	ind2 )

inline

Definition at line 49 of file fei2dlinelin.h.

References oofem::FEInterpolation2d::FEInterpolation2d().

Member Function Documentation

◆ boundaryEdgeGiveNodes()

IntArray oofem::FEI2dLineLin::boundaryEdgeGiveNodes	(	int	boundary,
		const Element_Geometry_Type	,
		bool	includeHierarchical = false ) const

overridevirtual

Gives the boundary nodes for requested boundary number.

Parameters

answer	Array to be filled with the boundary nodes.
boundary	Boundary number.
includeHierarchical	If true, include hierarchical nodes, introduced by interpolations on universal cells (mpm)

Implements oofem::FEInterpolation.

Definition at line 133 of file fei2dlinelin.C.

◆ computeLocalEdgeMapping()

IntArray oofem::FEI2dLineLin::computeLocalEdgeMapping ( int iedge ) const

overridevirtual

Implements oofem::FEInterpolation2d.

Definition at line 138 of file fei2dlinelin.C.

References OOFEM_ERROR.

◆ edgeComputeLength()

double oofem::FEI2dLineLin::edgeComputeLength	(	const IntArray &	edgeNodes,
		const FEICellGeometry &	cellgeo ) const

protected

Definition at line 152 of file fei2dlinelin.C.

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

◆ edgeEvaldNds()

void oofem::FEI2dLineLin::edgeEvaldNds	(	FloatArray &	answer,
		int	iedge,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo ) const

overridevirtual

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 100 of file fei2dlinelin.C.

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

◆ edgeEvalN()

void oofem::FEI2dLineLin::edgeEvalN	(	FloatArray &	answer,
		int	iedge,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo ) const

overridevirtual

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 147 of file fei2dlinelin.C.

References evalN().

◆ edgeEvalNormal()

double oofem::FEI2dLineLin::edgeEvalNormal	(	FloatArray &	answer,
		int	iedge,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo ) const

overridevirtual

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 118 of file fei2dlinelin.C.

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

◆ edgeLocal2global()

void oofem::FEI2dLineLin::edgeLocal2global	(	FloatArray &	answer,
		int	iedge,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo ) const

inlineoverridevirtual

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 82 of file fei2dlinelin.h.

◆ evaldNdx()

double oofem::FEI2dLineLin::evaldNdx	(	FloatMatrix &	answer,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo ) const

overridevirtual

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 57 of file fei2dlinelin.C.

References oofem::FloatMatrix::clear().

◆ evaldNdxi()

void oofem::FEI2dLineLin::evaldNdxi	(	FloatMatrix &	answer,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo ) const

overridevirtual

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 64 of file fei2dlinelin.C.

References oofem::FloatMatrix::resize().

◆ evalN() [1/2]

FloatArrayF< 2 > oofem::FEI2dLineLin::evalN ( double xi )

static

Definition at line 44 of file fei2dlinelin.C.

Referenced by edgeEvalN(), and local2global().

◆ evalN() [2/2]

void oofem::FEI2dLineLin::evalN	(	FloatArray &	answer,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo ) const

overridevirtual

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.

Definition at line 49 of file fei2dlinelin.C.

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

◆ evalNXIntegral()

double oofem::FEI2dLineLin::evalNXIntegral	(	int	boundary,
		const FEICellGeometry &	cellgeo ) const

overridevirtual

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 159 of file fei2dlinelin.C.

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

◆ giveArea()

double oofem::FEI2dLineLin::giveArea ( const FEICellGeometry & cellgeo ) const

inlineoverridevirtual

Computes the exact area.

Parameters

cellgeo Cell geometry for the element.

Returns: Area of geometry.

Reimplemented from oofem::FEInterpolation2d.

Definition at line 59 of file fei2dlinelin.h.

◆ giveBoundaryEdgeIntegrationDomain()

integrationDomain oofem::FEI2dLineLin::giveBoundaryEdgeIntegrationDomain	(	int	boundary,
		const Element_Geometry_Type	) const

inlineoverridevirtual

Returns boundary integration domain.

Implements oofem::FEInterpolation.

Definition at line 57 of file fei2dlinelin.h.

References oofem::_Line.

◆ giveBoundaryGeometryType()

const Element_Geometry_Type oofem::FEI2dLineLin::giveBoundaryGeometryType ( int boundary ) const

inlineoverridevirtual

Returns boundary geometry type

Implements oofem::FEInterpolation.

Definition at line 53 of file fei2dlinelin.h.

◆ giveBoundaryIntegrationDomain()

integrationDomain oofem::FEI2dLineLin::giveBoundaryIntegrationDomain	(	int	boundary,
		const Element_Geometry_Type	) const

inlineoverridevirtual

Returns boundary integration domain.

Implements oofem::FEInterpolation.

Definition at line 55 of file fei2dlinelin.h.

References oofem::_Point.

◆ giveBoundarySurfaceIntegrationDomain()

integrationDomain oofem::FEI2dLineLin::giveBoundarySurfaceIntegrationDomain	(	int	boundary,
		const Element_Geometry_Type	) const

inlineoverridevirtual

Returns boundary integration domain.

Implements oofem::FEInterpolation.

Definition at line 56 of file fei2dlinelin.h.

References oofem::_UnknownIntegrationDomain.

◆ giveCellDofMans()

void oofem::FEI2dLineLin::giveCellDofMans	(	IntArray &	nodes,
		IntArray &	internalDofMans,
		Element *	elem ) const

inlineoverridevirtual

Returns list of element nodes (and list of internal dof managers) (including on edges and surfaces) defining the approximation.

Returns local element node numbers defining the approximation. Typically this corresponds to all element nodes. But for elements with mixed interpolation, we need to select subset of nodes (quadratic triangle with linear interpolation). This method can query element geometry type (from given element) and compile the nodal set.

Note: Required by mpm module

Reimplemented from oofem::FEInterpolation.

Definition at line 65 of file fei2dlinelin.h.

◆ giveGeometryType()

const Element_Geometry_Type oofem::FEI2dLineLin::giveGeometryType ( ) const

inlineoverridevirtual

Returns the geometry type fo the interpolator.

Implements oofem::FEInterpolation.

Definition at line 52 of file fei2dlinelin.h.

◆ giveIntegrationDomain()

integrationDomain oofem::FEI2dLineLin::giveIntegrationDomain ( const Element_Geometry_Type ) const

inlineoverridevirtual

Returns the integration domain of the interpolator.

Implements oofem::FEInterpolation.

Definition at line 51 of file fei2dlinelin.h.

References oofem::_Line.

◆ giveIntegrationRule()

std::unique_ptr< IntegrationRule > oofem::FEI2dLineLin::giveIntegrationRule	(	int	order,
		const Element_Geometry_Type	egt ) const

overridevirtual

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.

Definition at line 172 of file fei2dlinelin.C.

References oofem::_Line, and oofem::FEInterpolation::order.

◆ giveNumberOfEdges()

int oofem::FEI2dLineLin::giveNumberOfEdges ( const Element_Geometry_Type ) const

inlineoverridevirtual

Returns number of edges.

Reimplemented from oofem::FEInterpolation.

Definition at line 64 of file fei2dlinelin.h.

◆ giveNumberOfNodes()

int oofem::FEI2dLineLin::giveNumberOfNodes ( const Element_Geometry_Type ) const

inlineoverridevirtual

Returns the number of geometric nodes of the receiver.

Reimplemented from oofem::FEInterpolation.

Definition at line 85 of file fei2dlinelin.h.

◆ giveTransformationJacobian()

double oofem::FEI2dLineLin::giveTransformationJacobian	(	const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo ) const

overridevirtual

Evaluates the determinant of the transformation.

Parameters

lcoords	Array containing (local) coordinates.
cellgeo	Underlying cell geometry.

Returns: Determinant of the transformation.

Reimplemented from oofem::FEInterpolation.

Definition at line 126 of file fei2dlinelin.C.

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

◆ global2local()

int oofem::FEI2dLineLin::global2local	(	FloatArray &	answer,
		const FloatArray &	gcoords,
		const FEICellGeometry &	cellgeo ) const

overridevirtual

Evaluates local coordinates from given global ones. If local coordinates cannot be found (generate elements, or point far outside geometry, then the center coordinate will be used as a last resort, and the return value will be zero.

Parameters

answer	Contains evaluated local coordinates.
gcoords	Array containing global coordinates.
cellgeo	Underlying cell geometry.

Returns: Nonzero is returned if point is within the element geometry, zero otherwise.

Implements oofem::FEInterpolation.

Definition at line 83 of file fei2dlinelin.C.

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

◆ local2global()

void oofem::FEI2dLineLin::local2global	(	FloatArray &	answer,
		const FloatArray &	lcoords,
		const FEICellGeometry &	cellgeo ) const

overridevirtual

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 71 of file fei2dlinelin.C.

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

◆ surfaceEvald2Ndxi2()

void oofem::FEI2dLineLin::surfaceEvald2Ndxi2	(	FloatMatrix &	answer,
		const FloatArray &	lcoords ) const

overridevirtual

Evaluates the matrix of second derivatives of surface interpolation functions (shape functions) wrt parametric coordinates at given point.

Parameters

answer	Contains resulting matrix of derivatives, the member at i,j position contains value of dNj/dxi.
lcoords	Array containing (local) coordinates.

Reimplemented from oofem::FEInterpolation2d.

Definition at line 189 of file fei2dlinelin.C.

References oofem::FloatMatrix::resize().

◆ surfaceEvaldNdxi()

void oofem::FEI2dLineLin::surfaceEvaldNdxi	(	FloatMatrix &	answer,
		const FloatArray &	lcoords ) const

overridevirtual

Evaluates the matrix of derivatives of surface interpolation functions (shape functions) wrt parametric coordinates at given point.

Parameters

answer	Contains resulting matrix of derivatives, the member at i,j position contains value of dNj/dxi.
lcoords	Array containing (local) coordinates.

Reimplemented from oofem::FEInterpolation2d.

Definition at line 181 of file fei2dlinelin.C.

References oofem::FloatMatrix::resize().

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

Public Member Functions

Static Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ FEI2dLineLin()

Member Function Documentation

◆ boundaryEdgeGiveNodes()

◆ computeLocalEdgeMapping()

◆ edgeComputeLength()

◆ edgeEvaldNds()

◆ edgeEvalN()

◆ edgeEvalNormal()

◆ edgeLocal2global()

◆ evaldNdx()

◆ evaldNdxi()

◆ evalN() [1/2]

◆ evalN() [2/2]

◆ evalNXIntegral()

◆ giveArea()

◆ giveBoundaryEdgeIntegrationDomain()

◆ giveBoundaryGeometryType()

◆ giveBoundaryIntegrationDomain()

◆ giveBoundarySurfaceIntegrationDomain()

◆ giveCellDofMans()

◆ giveGeometryType()

◆ giveIntegrationDomain()

◆ giveIntegrationRule()

◆ giveNumberOfEdges()

◆ giveNumberOfNodes()

◆ giveTransformationJacobian()

◆ global2local()

◆ local2global()

◆ surfaceEvald2Ndxi2()

◆ surfaceEvaldNdxi()