Chaste Release::3.1
Static Public Member Functions
QuadraticBasisFunction< ELEMENT_DIM > Class Template Reference

#include <QuadraticBasisFunction.hpp>

List of all members.

Static Public Member Functions

static double ComputeBasisFunction (const ChastePoint< ELEMENT_DIM > &rPoint, unsigned basisIndex)
static c_vector< double,
ELEMENT_DIM > 		ComputeBasisFunctionDerivative (const ChastePoint< ELEMENT_DIM > &rPoint, unsigned basisIndex)
static void ComputeBasisFunctions (const ChastePoint< ELEMENT_DIM > &rPoint, c_vector< double,(ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2 > &rReturnValue)
static void ComputeBasisFunctionDerivatives (const ChastePoint< ELEMENT_DIM > &rPoint, c_matrix< double, ELEMENT_DIM,(ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2 > &rReturnValue)
static void ComputeTransformedBasisFunctionDerivatives (const ChastePoint< ELEMENT_DIM > &rPoint, const c_matrix< double, ELEMENT_DIM, ELEMENT_DIM > &rInverseJacobian, c_matrix< double, ELEMENT_DIM,(ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2 > &rReturnValue)

Detailed Description

template<unsigned ELEMENT_DIM>
class QuadraticBasisFunction< ELEMENT_DIM >

Quadratic basis functions for the finite element method, computed on a canonical element.

Definition at line 47 of file QuadraticBasisFunction.hpp.

Member Function Documentation

template<unsigned ELEMENT_DIM>
double QuadraticBasisFunction< ELEMENT_DIM >::ComputeBasisFunction ( const ChastePoint< ELEMENT_DIM > &  rPoint,
unsigned  basisIndex 
) [static]

Compute a basis function at a point within an element.

Parameters:
rPointThe point at which to compute the basis function. The results are undefined if this is not within the canonical element.
basisIndexWhich basis function to compute. This is a local index within a canonical element.
Returns:
The value of the basis function.

Definition at line 80 of file QuadraticBasisFunction.cpp.

References NEVER_REACHED.

Referenced by QuadraticBasisFunction< 0 >::ComputeBasisFunctions().

template<unsigned ELEMENT_DIM>
c_vector< double, ELEMENT_DIM > QuadraticBasisFunction< ELEMENT_DIM >::ComputeBasisFunctionDerivative ( const ChastePoint< ELEMENT_DIM > &  rPoint,
unsigned  basisIndex 
) [static]

Compute the derivative of a basis function at a point within an canonical element.

Parameters:
rPointThe point at which to compute the basis function. The results are undefined if this is not within the canonical element.
basisIndexWhich basis function to compute. This is a local index within a canonical element.
Returns:
The derivative of the basis function. This is a vector (c_vector instance) giving the derivative along each axis.

Definition at line 192 of file QuadraticBasisFunction.cpp.

References NEVER_REACHED.

template<unsigned ELEMENT_DIM>
void QuadraticBasisFunction< ELEMENT_DIM >::ComputeBasisFunctionDerivatives ( const ChastePoint< ELEMENT_DIM > &  rPoint,
c_matrix< double, ELEMENT_DIM,(ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2 > &  rReturnValue 
) [static]

Compute the derivatives of all basis functions at a point within an element.

Parameters:
rPointThe point at which to compute the basis functions. The results are undefined if this is not within the canonical element.
rReturnValueThe derivatives of the basis functions, in local index order. Each column of the matrix gives the derivative along each axis.

Definition at line 345 of file QuadraticBasisFunction.cpp.

template<unsigned ELEMENT_DIM>
void QuadraticBasisFunction< ELEMENT_DIM >::ComputeBasisFunctions ( const ChastePoint< ELEMENT_DIM > &  rPoint,
c_vector< double,(ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2 > &  rReturnValue 
) [static]

Compute all basis functions at a point within an element.

Parameters:
rPointThe point at which to compute the basis functions. The results are undefined if this is not within the canonical element.
rReturnValueThe values of the basis functions, in local index order.

Definition at line 324 of file QuadraticBasisFunction.cpp.

Referenced by ContinuumMechanicsNeumannBcsAssembler< DIM >::AssembleOnBoundaryElement(), AbstractNonlinearElasticitySolver< DIM >::AssembleOnBoundaryElement(), AbstractNonlinearElasticitySolver< DIM >::AssembleOnBoundaryElementForPressureOnDeformedBc(), IncompressibleNonlinearElasticitySolver< DIM >::AssembleOnElement(), CompressibleNonlinearElasticitySolver< DIM >::AssembleOnElement(), and AbstractContinuumMechanicsAssembler< DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX >::AssembleOnElement().

template<unsigned ELEMENT_DIM>
void QuadraticBasisFunction< ELEMENT_DIM >::ComputeTransformedBasisFunctionDerivatives ( const ChastePoint< ELEMENT_DIM > &  rPoint,
const c_matrix< double, ELEMENT_DIM, ELEMENT_DIM > &  rInverseJacobian,
c_matrix< double, ELEMENT_DIM,(ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2 > &  rReturnValue 
) [static]

Compute the derivatives of all basis functions at a point within an element. This method will transform the results, for use within gaussian quadrature for example.

Parameters:
rPointThe point at which to compute the basis functions. The results are undefined if this is not within the canonical element.
rInverseJacobianThe inverse of the Jacobian matrix mapping the real element into the canonical element.
rReturnValueThe derivatives of the basis functions, in local index order. Each entry is a vector (VectorDouble instance) giving the derivative along each axis.

Definition at line 371 of file QuadraticBasisFunction.cpp.

Referenced by AbstractNonlinearElasticitySolver< DIM >::AssembleOnBoundaryElementForPressureOnDeformedBc(), IncompressibleNonlinearElasticitySolver< DIM >::AssembleOnElement(), CompressibleNonlinearElasticitySolver< DIM >::AssembleOnElement(), AbstractContinuumMechanicsAssembler< DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX >::AssembleOnElement(), and AbstractNonlinearElasticitySolver< DIM >::GetElementCentroidDeformationGradient().

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