BELFEM 0.9.0
Berkeley Lab Finite Element Framework
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belfem::fem::InterpolationFunctionTemplate< G, T, D, B > Class Template Reference

shape function templated class G : Geometry T : Type D : Dimension B : Number of Basis More...

#include <cl_IF_InterpolationFunctionTemplate.hpp>

Inheritance diagram for belfem::fem::InterpolationFunctionTemplate< G, T, D, B >:
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Collaboration diagram for belfem::fem::InterpolationFunctionTemplate< G, T, D, B >:
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Public Member Functions

 InterpolationFunctionTemplate ()=default
 trivial constructor
 ~InterpolationFunctionTemplate () override=default
 trivial destructor
void param_coords (Matrix< real > &aXiHat) const override
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const override
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const override
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const override
 calculates the second derivative of the shape function in parameter space
uint number_of_bases () const override
 returns the number of bases for this shape function
uint number_of_dimensions () const override
 returns the number of dimensions for this shape function
InterpolationOrder interpolation_order () const override
 returns the interpolation order
InterpolationType interpolation_type () const override
 returns the interpolation type
GeometryType geometry_type () const override
 returns the geometry type
ElementType element_type () const override
 returns the element type
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Bubble function for TET10 element, side 0, following the EXODUSII numbering scheme.
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Bubble function for TET10 element, side 1, following the EXODUSII numbering scheme.
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Bubble function for TET10 element, side 2, following the EXODUSII numbering scheme.
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Bubble function for TET10 element, side 3, following the EXODUSII numbering scheme.
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Bubble function for TET4 element, side 0, following the EXODUSII numbering scheme.
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Bubble function for TET4 element, side 1, following the EXODUSII numbering scheme.
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Bubble function for TET4 element, side 2, following the EXODUSII numbering scheme.
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Bubble function for TET4 element, side 3, following the EXODUSII numbering scheme.
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Bubble function for TRI3 element, side 0 \(4\,\xi \,\eta\).
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Bubble function for TRI3 element, side 1 \(4\,\eta \,\zeta\).
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Bubble function for TRI3 element, side 2 \(4\,\xi \,\zeta\).
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Bubble function for TRI6 element, side 0, following the EXODUSII numbering scheme.
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Bubble function for TRI6 element, side 1, following the EXODUSII numbering scheme.
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Bubble function for TRI6 element, side 2, following the EXODUSII numbering scheme.
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Lagrange function for linear tet element, following the EXODUSII node numbering.
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Lagrange function for linear Triangle element, following the EXODUSII node numbering.
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 Lagrange function for quadratic Triangle element, following the EXODUSII node numbering.
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
InterpolationOrder interpolation_order () const
 returns the interpolation order
ElementType element_type () const
 returns the element type
void param_coords (Matrix< real > &aXiHat) const
 returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >
void N (const Vector< real > &aXi, Matrix< real > &aN) const
 evaluates the shape function at a given point
void dNdXi (const Vector< real > &aXi, Matrix< real > &adNdXi) const
 calculates the first derivative of the shape function in parameter space
void d2NdXi2 (const Vector< real > &aXi, Matrix< real > &ad2NdXi2) const
 calculates the second derivative of the shape function in parameter space
Public Member Functions inherited from belfem::fem::InterpolationFunction
 InterpolationFunction ()=default
 trivial constructor
virtual ~InterpolationFunction ()=default
 trivial destructor

Detailed Description

template<GeometryType G, InterpolationType T, uint D, uint B>
class belfem::fem::InterpolationFunctionTemplate< G, T, D, B >

shape function templated class G : Geometry T : Type D : Dimension B : Number of Basis

Constructor & Destructor Documentation

◆ InterpolationFunctionTemplate()

template<GeometryType G, InterpolationType T, uint D, uint B>
belfem::fem::InterpolationFunctionTemplate< G, T, D, B >::InterpolationFunctionTemplate ( )
default

trivial constructor

◆ ~InterpolationFunctionTemplate()

trivial destructor

Member Function Documentation

◆ d2NdXi2() [1/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::LINE, InterpolationType::BERNSTEIN, 1, 3 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [2/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::BERNSTEIN, 2, 6 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [3/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::BubbleFace0, 3, 3 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [4/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::BubbleFace1, 3, 3 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [5/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::BubbleFace2, 3, 3 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [6/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::BubbleFace3, 3, 3 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [7/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::BubbleFace0, 3, 1 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [8/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::BubbleFace1, 3, 1 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [9/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::BubbleFace2, 3, 1 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [10/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::BubbleFace3, 3, 1 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [11/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::BubbleEdge0, 2, 1 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [12/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::BubbleEdge1, 2, 1 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [13/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::BubbleEdge2, 2, 1 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [14/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::BubbleEdge0, 2, 2 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [15/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::BubbleEdge1, 2, 2 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [16/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::BubbleEdge2, 2, 2 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [17/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::LINE, InterpolationType::HERMITE, 1, 4 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [18/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::QUAD, InterpolationType::HERMITE, 2, 16 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [19/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::HEX, InterpolationType::LAGRANGE, 3, 20 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [20/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::HEX, InterpolationType::LAGRANGE, 3, 27 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [21/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::HEX, InterpolationType::LAGRANGE, 3, 64 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [22/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::HEX, InterpolationType::LAGRANGE, 3, 8 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
inlinevirtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [23/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::LINE, InterpolationType::LAGRANGE, 1, 2 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [24/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::LINE, InterpolationType::LAGRANGE, 1, 3 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [25/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::LINE, InterpolationType::LAGRANGE, 1, 4 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [26/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::LINE, InterpolationType::LAGRANGE, 1, 5 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [27/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 15 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [28/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 18 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [29/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 6 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [30/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::PYRA, InterpolationType::LAGRANGE, 3, 13 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [31/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::PYRA, InterpolationType::LAGRANGE, 3, 14 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [32/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::PYRA, InterpolationType::LAGRANGE, 3, 5 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [33/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 16 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [34/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 4 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
inlinevirtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [35/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 8 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [36/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 9 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [37/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::LAGRANGE, 3, 10 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [38/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::LAGRANGE, 3, 20 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [39/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::LAGRANGE, 3, 35 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [40/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::LAGRANGE, 3, 4 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [41/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::LAGRANGE, 2, 10 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [42/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::LAGRANGE, 2, 15 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [43/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::LAGRANGE, 2, 3 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [44/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::LAGRANGE, 2, 6 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [45/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::LINE, InterpolationType::BERNSTEIN, 1, 3 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [46/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::BERNSTEIN, 2, 6 >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
virtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ d2NdXi2() [47/47]

template<GeometryType G, InterpolationType T, uint D, uint B>
void belfem::fem::InterpolationFunctionTemplate< G, T, D, B >::d2NdXi2 ( const Vector< real > & aXi,
Matrix< real > & ad2NdXi2 ) const
inlineoverridevirtual

calculates the second derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]ad2NdXi2( <number of second-derivative components> x <number of bases> ): 1 x n in 1D, 3 x n in 2D ( xi², eta², xi·eta ), 6 x n in 3D ( xi², eta², zeta², eta·zeta, xi·zeta, xi·eta )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [1/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::LINE, InterpolationType::BERNSTEIN, 1, 3 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [2/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::BERNSTEIN, 2, 6 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [3/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::BubbleFace0, 3, 3 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [4/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::BubbleFace1, 3, 3 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [5/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::BubbleFace2, 3, 3 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [6/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::BubbleFace3, 3, 3 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [7/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::BubbleFace0, 3, 1 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [8/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::BubbleFace1, 3, 1 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [9/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::BubbleFace2, 3, 1 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [10/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::BubbleFace3, 3, 1 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [11/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::BubbleEdge0, 2, 1 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [12/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::BubbleEdge1, 2, 1 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [13/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::BubbleEdge2, 2, 1 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [14/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::BubbleEdge0, 2, 2 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [15/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::BubbleEdge1, 2, 2 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [16/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::BubbleEdge2, 2, 2 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [17/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::LINE, InterpolationType::HERMITE, 1, 4 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [18/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::QUAD, InterpolationType::HERMITE, 2, 16 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [19/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::HEX, InterpolationType::LAGRANGE, 3, 20 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [20/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::HEX, InterpolationType::LAGRANGE, 3, 27 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [21/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::HEX, InterpolationType::LAGRANGE, 3, 64 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [22/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::HEX, InterpolationType::LAGRANGE, 3, 8 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
inlinevirtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [23/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::LINE, InterpolationType::LAGRANGE, 1, 2 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [24/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::LINE, InterpolationType::LAGRANGE, 1, 3 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [25/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::LINE, InterpolationType::LAGRANGE, 1, 4 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [26/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::LINE, InterpolationType::LAGRANGE, 1, 5 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [27/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 15 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [28/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 18 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [29/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::PENTA, InterpolationType::LAGRANGE, 3, 6 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [30/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::PYRA, InterpolationType::LAGRANGE, 3, 13 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [31/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::PYRA, InterpolationType::LAGRANGE, 3, 14 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [32/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::PYRA, InterpolationType::LAGRANGE, 3, 5 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [33/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 16 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [34/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 4 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
inlinevirtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [35/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 8 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [36/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 9 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [37/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::LAGRANGE, 3, 10 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [38/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::LAGRANGE, 3, 20 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [39/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::LAGRANGE, 3, 35 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [40/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::LAGRANGE, 3, 4 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [41/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::LAGRANGE, 2, 10 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [42/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::LAGRANGE, 2, 15 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [43/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::LAGRANGE, 2, 3 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [44/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::LAGRANGE, 2, 6 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [45/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::LINE, InterpolationType::BERNSTEIN, 1, 3 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [46/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::BERNSTEIN, 2, 6 >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
virtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ dNdXi() [47/47]

template<GeometryType G, InterpolationType T, uint D, uint B>
void belfem::fem::InterpolationFunctionTemplate< G, T, D, B >::dNdXi ( const Vector< real > & aXi,
Matrix< real > & adNdXi ) const
inlineoverridevirtual

calculates the first derivative of the shape function in parameter space

Parameters
[in]aXipoint where function is evaluated ( <number of dimensions> x 1 )
[out]adNdXi( <number of dimensions> x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ element_type() [1/47]

◆ element_type() [2/47]

◆ element_type() [3/47]

◆ element_type() [4/47]

◆ element_type() [5/47]

◆ element_type() [6/47]

◆ element_type() [7/47]

◆ element_type() [8/47]

◆ element_type() [9/47]

◆ element_type() [10/47]

◆ element_type() [11/47]

◆ element_type() [12/47]

◆ element_type() [13/47]

◆ element_type() [14/47]

◆ element_type() [15/47]

◆ element_type() [16/47]

◆ element_type() [17/47]

◆ element_type() [18/47]

◆ element_type() [19/47]

◆ element_type() [20/47]

◆ element_type() [21/47]

◆ element_type() [22/47]

returns the element type

Implements belfem::fem::InterpolationFunction.

◆ element_type() [23/47]

◆ element_type() [24/47]

◆ element_type() [25/47]

◆ element_type() [26/47]

◆ element_type() [27/47]

◆ element_type() [28/47]

◆ element_type() [29/47]

◆ element_type() [30/47]

◆ element_type() [31/47]

◆ element_type() [32/47]

◆ element_type() [33/47]

◆ element_type() [34/47]

returns the element type

Implements belfem::fem::InterpolationFunction.

◆ element_type() [35/47]

◆ element_type() [36/47]

◆ element_type() [37/47]

◆ element_type() [38/47]

◆ element_type() [39/47]

◆ element_type() [40/47]

◆ element_type() [41/47]

◆ element_type() [42/47]

◆ element_type() [43/47]

◆ element_type() [44/47]

◆ element_type() [45/47]

◆ element_type() [46/47]

◆ element_type() [47/47]

template<GeometryType G, InterpolationType T, uint D, uint B>
ElementType belfem::fem::InterpolationFunctionTemplate< G, T, D, B >::element_type ( ) const
inlineoverridevirtual

returns the element type

Implements belfem::fem::InterpolationFunction.

◆ geometry_type()

template<GeometryType G, InterpolationType T, uint D, uint B>
GeometryType belfem::fem::InterpolationFunctionTemplate< G, T, D, B >::geometry_type ( ) const
inlineoverridevirtual

returns the geometry type

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [1/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [2/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [3/47]

Bubble function for TET10 element, side 0, following the EXODUSII numbering scheme.

\begin{align} N_1 & = 64.8 \, \xi \, \eta \, \tau \, \left( 2 \, \eta^2 - \xi^2 - \tau^2 \right) \\[2ex] N_2 & = 64.8 \, \xi \, \eta \, \tau \, \left( 2 \, \xi^2 - \eta^2 - \tau^2 \right) \\[2ex] N_3 & = 64.8 \, \xi \, \eta \, \tau \, \left( 2 \, \tau^2 - \xi^2 - \eta^2 \right) \end{align}

.

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [4/47]

Bubble function for TET10 element, side 1, following the EXODUSII numbering scheme.

\begin{align} N_1 & = 64.8 \, \eta \, \zeta \, \tau \, \left( 2 \, \zeta^2 - \eta^2 - \tau^2 \right) \\[2ex] N_2 & = 64.8 \, \eta \, \zeta \, \tau \, \left( 2 \, \eta^2 - \zeta^2 - \tau^2 \right) \\[2ex] N_3 & = 64.8 \, \eta \, \zeta \, \tau \, \left( 2 \, \tau^2 - \eta^2 - \zeta^2 \right) \end{align}

.

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [5/47]

Bubble function for TET10 element, side 2, following the EXODUSII numbering scheme.

\begin{align} N_1 & = 64.8 \, \xi \, \zeta \, \tau \, \left( 2 \, \tau^2 - \xi^2 - \zeta^2 \right) \\[2ex] N_2 & = 64.8 \, \xi \, \zeta \, \tau \, \left( 2 \, \xi^2 - \zeta^2 - \tau^2 \right) \\[2ex] N_3 & = 64.8 \, \xi \, \zeta \, \tau \, \left( 2 \, \zeta^2 - \xi^2 - \tau^2 \right) \end{align}

.

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [6/47]

Bubble function for TET10 element, side 3, following the EXODUSII numbering scheme.

\begin{align} N_1 & = 64.8 \, \xi \, \eta \, \zeta \, \left( 2 \, \zeta^2 - \xi^2 - \eta^2 \right)\\[2ex] N_2 & = 64.8 \, \xi \, \eta \, \zeta \, \left( 2 \, \xi^2 - \zeta^2 - \eta^2 \right) \\[2ex] N_3 & = 64.8 \, \xi \, \eta \, \zeta \, \left( 2 \, \eta^2 - \xi^2 - \zeta^2 \right) \end{align}

.

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [7/47]

Bubble function for TET4 element, side 0, following the EXODUSII numbering scheme.

\begin{align} N & = 27 \, \xi \, \eta \, ( 1 - \xi - \eta ) \end{align}

.

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [8/47]

Bubble function for TET4 element, side 1, following the EXODUSII numbering scheme.

\begin{align} N & = 27 \, \eta \, \zeta \, ( 1 - \eta - \zeta ) \end{align}

.

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [9/47]

Bubble function for TET4 element, side 2, following the EXODUSII numbering scheme.

\begin{align} N & = 27 \, \xi \, \zeta \, ( 1 - \xi - \zeta ) \end{align}

.

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [10/47]

Bubble function for TET4 element, side 3, following the EXODUSII numbering scheme.

\begin{align} N & = 27 \, \xi \, \eta \, \zeta \end{align}

.

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [11/47]

Bubble function for TRI3 element, side 0 \(4\,\xi \,\eta\).

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [12/47]

Bubble function for TRI3 element, side 1 \(4\,\eta \,\zeta\).

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [13/47]

Bubble function for TRI3 element, side 2 \(4\,\xi \,\zeta\).

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [14/47]

Bubble function for TRI6 element, side 0, following the EXODUSII numbering scheme.

\begin{align} N_1 & =\frac{32}{3} \, \xi \, \eta \, \left(\xi^2-\eta^2\right) \\[2ex]  N_2 & =\frac{32}{3} \, \xi \, \eta \, \left(\eta^2-\xi^2\right) \end{align}

.

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [15/47]

Bubble function for TRI6 element, side 1, following the EXODUSII numbering scheme.

\begin{align} N_1 & =\frac{32}{3} \, \eta \, \zeta \, \left(\eta^2-\zeta^2\right) \\[2ex]  N_2 & =\frac{32}{3} \, \eta \, \zeta \, \left(\zeta^2-\eta^2\right) \end{align}

.

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [16/47]

Bubble function for TRI6 element, side 2, following the EXODUSII numbering scheme.

\begin{align} N_1 & =\frac{32}{3} \, \xi \, \zeta \, \left(\zeta^2-\xi^2\right) \\[2ex]  N_2 & =\frac{32}{3} \, \xi \, \zeta \, \left(\xi^2-\zeta^2\right) \end{align}

.

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [17/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [18/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [19/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [20/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [21/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [22/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [23/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [24/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [25/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [26/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [27/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [28/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [29/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [30/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [31/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [32/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [33/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [34/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [35/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [36/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [37/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [38/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [39/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [40/47]

Lagrange function for linear tet element, following the EXODUSII node numbering.

\begin{align} N_1 & = \xi \\ N_2 & = \zeta \\ N_3 & = \eta \\ N_4 & = 1 - \xi - \eta - \zeta \end{align}

.

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [41/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [42/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [43/47]

Lagrange function for linear Triangle element, following the EXODUSII node numbering.

\begin{align} N_1 &= \xi \\ N_2 &= \eta & N_3 &= 1 - \xi - \eta \end{align}

.

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [44/47]

Lagrange function for quadratic Triangle element, following the EXODUSII node numbering.

\begin{align} N_1 & = \xi \,\left(2\,\xi -1\right) \\  N_2 & = \eta \,\left(2\,\eta -1\right) \\ N_3 & = \zeta \,\left(2\,\zeta -1\right) \\ N_4 & = 4 \, \xi \, \eta \\ N_5 & = 4 \, \eta \, \zeta \\ N_6 & = 4 \, \xi \, \zeta \end{align}

.

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [45/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [46/47]

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_order() [47/47]

template<GeometryType G, InterpolationType T, uint D, uint B>
InterpolationOrder belfem::fem::InterpolationFunctionTemplate< G, T, D, B >::interpolation_order ( ) const
inlineoverridevirtual

returns the interpolation order

Implements belfem::fem::InterpolationFunction.

◆ interpolation_type()

template<GeometryType G, InterpolationType T, uint D, uint B>
InterpolationType belfem::fem::InterpolationFunctionTemplate< G, T, D, B >::interpolation_type ( ) const
inlineoverridevirtual

returns the interpolation type

Implements belfem::fem::InterpolationFunction.

◆ N() [1/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [2/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [3/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [4/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [5/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [6/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [7/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [8/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [9/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [10/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [11/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [12/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [13/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [14/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [15/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [16/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [17/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [18/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [19/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [20/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [21/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [22/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::HEX, InterpolationType::LAGRANGE, 3, 8 >::N ( const Vector< real > & aXi,
Matrix< real > & aN ) const
inlinevirtual

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [23/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [24/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [25/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [26/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [27/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [28/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [29/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [30/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [31/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [32/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [33/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [34/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 4 >::N ( const Vector< real > & aXi,
Matrix< real > & aN ) const
inlinevirtual

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [35/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [36/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [37/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [38/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [39/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [40/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [41/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [42/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [43/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [44/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [45/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [46/47]

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ N() [47/47]

template<GeometryType G, InterpolationType T, uint D, uint B>
void belfem::fem::InterpolationFunctionTemplate< G, T, D, B >::N ( const Vector< real > & aXi,
Matrix< real > & aN ) const
inlineoverridevirtual

evaluates the shape function at a given point

Parameters
[in]aXiparameter coordinates ( <number of dimensions> x 1 )
[out]aNshape function as ( 1 x <number of bases> )

Implements belfem::fem::InterpolationFunction.

◆ number_of_bases()

template<GeometryType G, InterpolationType T, uint D, uint B>
uint belfem::fem::InterpolationFunctionTemplate< G, T, D, B >::number_of_bases ( ) const
inlineoverridevirtual

returns the number of bases for this shape function

Implements belfem::fem::InterpolationFunction.

◆ number_of_dimensions()

template<GeometryType G, InterpolationType T, uint D, uint B>
uint belfem::fem::InterpolationFunctionTemplate< G, T, D, B >::number_of_dimensions ( ) const
inlineoverridevirtual

returns the number of dimensions for this shape function

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [1/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [2/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [3/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [4/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [5/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [6/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [7/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [8/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [9/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [10/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [11/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [12/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [13/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [14/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [15/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [16/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [17/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::LINE, InterpolationType::HERMITE, 1, 4 >::param_coords ( Matrix< real > & aXiHat) const
virtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [18/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::QUAD, InterpolationType::HERMITE, 2, 16 >::param_coords ( Matrix< real > & aXiHat) const
virtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [19/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::HEX, InterpolationType::LAGRANGE, 3, 20 >::param_coords ( Matrix< real > & aXiHat) const
virtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [20/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::HEX, InterpolationType::LAGRANGE, 3, 27 >::param_coords ( Matrix< real > & aXiHat) const
virtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [21/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::HEX, InterpolationType::LAGRANGE, 3, 64 >::param_coords ( Matrix< real > & aXiHat) const
virtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [22/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::HEX, InterpolationType::LAGRANGE, 3, 8 >::param_coords ( Matrix< real > & aXiHat) const
inlinevirtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [23/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [24/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [25/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [26/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [27/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [28/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [29/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [30/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::PYRA, InterpolationType::LAGRANGE, 3, 13 >::param_coords ( Matrix< real > & aXiHat) const
virtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [31/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::PYRA, InterpolationType::LAGRANGE, 3, 14 >::param_coords ( Matrix< real > & aXiHat) const
virtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [32/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [33/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 16 >::param_coords ( Matrix< real > & aXiHat) const
virtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [34/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::QUAD, InterpolationType::LAGRANGE, 2, 4 >::param_coords ( Matrix< real > & aXiHat) const
inlinevirtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [35/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [36/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [37/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::LAGRANGE, 3, 10 >::param_coords ( Matrix< real > & aXiHat) const
virtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [38/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::LAGRANGE, 3, 20 >::param_coords ( Matrix< real > & aXiHat) const
virtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [39/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::LAGRANGE, 3, 35 >::param_coords ( Matrix< real > & aXiHat) const
virtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [40/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TET, InterpolationType::LAGRANGE, 3, 4 >::param_coords ( Matrix< real > & aXiHat) const
virtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [41/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::LAGRANGE, 2, 10 >::param_coords ( Matrix< real > & aXiHat) const
virtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [42/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::LAGRANGE, 2, 15 >::param_coords ( Matrix< real > & aXiHat) const
virtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [43/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::LAGRANGE, 2, 3 >::param_coords ( Matrix< real > & aXiHat) const
virtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [44/47]

void belfem::fem::InterpolationFunctionTemplate< GeometryType::TRI, InterpolationType::LAGRANGE, 2, 6 >::param_coords ( Matrix< real > & aXiHat) const
virtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [45/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [46/47]

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.

◆ param_coords() [47/47]

template<GeometryType G, InterpolationType T, uint D, uint B>
void belfem::fem::InterpolationFunctionTemplate< G, T, D, B >::param_coords ( Matrix< real > & aXiHat) const
inlineoverridevirtual

returns a matrix containing the parameter coordinates of the nodes < number of dimensions x number of nodes >

Implements belfem::fem::InterpolationFunction.


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