LinearBasisFunction< ELEMENT_DIM > Class Template Reference

#include <LinearBasisFunction.hpp>

List of all members.

Public Member Functions

template<>
double ComputeBasisFunction (const ChastePoint< 3 > &rPoint, unsigned basisIndex)
template<>
double ComputeBasisFunction (const ChastePoint< 2 > &rPoint, unsigned basisIndex)
template<>
double ComputeBasisFunction (const ChastePoint< 1 > &rPoint, unsigned basisIndex)
template<>
c_vector< double, 3 > ComputeBasisFunctionDerivative (const ChastePoint< 3 > &rPoint, unsigned basisIndex)
template<>
c_vector< double, 2 > ComputeBasisFunctionDerivative (const ChastePoint< 2 > &rPoint, unsigned basisIndex)
template<>
c_vector< double, 1 > ComputeBasisFunctionDerivative (const ChastePoint< 1 > &rPoint, unsigned basisIndex)

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 > &rReturnValue)
static void ComputeBasisFunctionDerivatives (const ChastePoint< ELEMENT_DIM > &rPoint, c_matrix< double, ELEMENT_DIM, ELEMENT_DIM+1 > &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 > &rReturnValue)

Detailed Description

template<unsigned ELEMENT_DIM>
class LinearBasisFunction< ELEMENT_DIM >

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

Definition at line 39 of file LinearBasisFunction.hpp.

Member Function Documentation

template<>
double LinearBasisFunction< 1 >::ComputeBasisFunction ( const ChastePoint< 1 > &  rPoint,
unsigned  basisIndex 
) [inline]

Compute a basis function at a point within an element (1d case).

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

Definition at line 113 of file LinearBasisFunction.cpp.

template<>
double LinearBasisFunction< 2 >::ComputeBasisFunction ( const ChastePoint< 2 > &  rPoint,
unsigned  basisIndex 
) [inline]

Compute a basis function at a point within an element (2d case).

Parameters:
rPoint The point at which to compute the basis function. The results are undefined if this is not within the canonical element.
basisIndex Which 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 LinearBasisFunction.cpp.

template<>
double LinearBasisFunction< 3 >::ComputeBasisFunction ( const ChastePoint< 3 > &  rPoint,
unsigned  basisIndex 
) [inline]

Compute a basis function at a point within an element (3d case).

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

Definition at line 44 of file LinearBasisFunction.cpp.

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

Compute a basis function at a point within an element.

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

Referenced by LinearBasisFunction< 0 >::ComputeBasisFunctions(), and LinearBasisFunction< ELEMENT_DIM >::ComputeBasisFunctions().

template<>
c_vector< double, 1 > LinearBasisFunction< 1 >::ComputeBasisFunctionDerivative ( const ChastePoint< 1 > &  rPoint,
unsigned  basisIndex 
) [inline]

Compute the derivative of a basis function at a point within a canonical element (1d case).

Parameters:
rPoint (unused) The point at which to compute the basis function. The results are undefined if this is not within the canonical element.
basisIndex Which 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<double, ELEMENT_DIM> instance) giving the derivative along each axis.

Definition at line 249 of file LinearBasisFunction.cpp.

template<>
c_vector< double, 2 > LinearBasisFunction< 2 >::ComputeBasisFunctionDerivative ( const ChastePoint< 2 > &  rPoint,
unsigned  basisIndex 
) [inline]

Compute the derivative of a basis function at a point within a canonical element (2d case).

Parameters:
rPoint (unused) The point at which to compute the basis function. The results are undefined if this is not within the canonical element.
basisIndex Which 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<double, ELEMENT_DIM> instance) giving the derivative along each axis.

Definition at line 209 of file LinearBasisFunction.cpp.

template<>
c_vector< double, 3 > LinearBasisFunction< 3 >::ComputeBasisFunctionDerivative ( const ChastePoint< 3 > &  rPoint,
unsigned  basisIndex 
) [inline]

Compute the derivative of a basis function at a point within a canonical element (3d case).

Parameters:
rPoint (unused) The point at which to compute the basis function. The results are undefined if this is not within the canonical element.
basisIndex Which 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<double, ELEMENT_DIM> instance) giving the derivative along each axis.

Definition at line 161 of file LinearBasisFunction.cpp.

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

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

Parameters:
rPoint (unused) The point at which to compute the basis function. The results are undefined if this is not within the canonical element.
basisIndex Which 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<double, ELEMENT_DIM> instance) giving the derivative along each axis.

Referenced by LinearBasisFunction< ELEMENT_DIM >::ComputeBasisFunctionDerivatives().

template<unsigned ELEMENT_DIM>
void LinearBasisFunction< ELEMENT_DIM >::ComputeBasisFunctionDerivatives ( const ChastePoint< ELEMENT_DIM > &  rPoint,
c_matrix< double, ELEMENT_DIM, ELEMENT_DIM+1 > &  rReturnValue 
) [inline, static]

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

Parameters:
rPoint The point at which to compute the basis functions. The results are undefined if this is not within the canonical element.
rReturnValue A reference to a vector, to be filled in
Returns:
The derivatives of the basis functions as the column vectors of a matrix in local index order.

Definition at line 313 of file LinearBasisFunction.cpp.

References LinearBasisFunction< ELEMENT_DIM >::ComputeBasisFunctionDerivative().

Referenced by LinearBasisFunction< ELEMENT_DIM >::ComputeTransformedBasisFunctionDerivatives().

template<unsigned ELEMENT_DIM>
void LinearBasisFunction< ELEMENT_DIM >::ComputeBasisFunctions ( const ChastePoint< ELEMENT_DIM > &  rPoint,
c_vector< double, ELEMENT_DIM+1 > &  rReturnValue 
) [inline, static]

Compute all basis functions at a point within an element.

Parameters:
rPoint The point at which to compute the basis functions. The results are undefined if this is not within the canonical element.
rReturnValue A reference to a vector, to be filled in

Definition at line 279 of file LinearBasisFunction.cpp.

References LinearBasisFunction< ELEMENT_DIM >::ComputeBasisFunction().

Referenced by AbstractStaticAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, NON_HEART, CONCRETE >::AssembleOnElement(), and AbstractStaticAssembler< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, NON_HEART, CONCRETE >::AssembleOnSurfaceElement().

template<unsigned ELEMENT_DIM>
void LinearBasisFunction< 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 > &  rReturnValue 
) [inline, 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:
rPoint The point at which to compute the basis functions. The results are undefined if this is not within the canonical element.
rInverseJacobian The inverse of the Jacobian matrix mapping the real element into the canonical element.
rReturnValue A reference to a vector, to be filled in
Returns:
The derivatives of the basis functions, in local index order. Each entry is a vector (c_vector<double, SPACE_DIM> instance) giving the derivative along each axis.

Definition at line 340 of file LinearBasisFunction.cpp.

References LinearBasisFunction< ELEMENT_DIM >::ComputeBasisFunctionDerivatives().

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