NumLib::TemplateIsoparametric< ShapeFunctionType_, ShapeMatrixTypes_ > Class Template Reference

Detailed Description

template<class ShapeFunctionType_, class ShapeMatrixTypes_>
class NumLib::TemplateIsoparametric< ShapeFunctionType_, ShapeMatrixTypes_ >

Template class for isoparametric elements.

Template Parameters

ShapeFunctionType_	The shape function type.
ShapeMatrixTypes_	An aggregate of shape matrix types.

Definition at line 32 of file TemplateIsoparametric.h.

#include <TemplateIsoparametric.h>

Collaboration diagram for NumLib::TemplateIsoparametric< ShapeFunctionType_, ShapeMatrixTypes_ >:

Public Types
using	ShapeFunctionType = ShapeFunctionType_
using	ShapeMatrices = typename ShapeMatrixTypes_::ShapeMatrices
	Coordinate mapping matrices type.
using	NaturalCoordsMappingType

Public Member Functions
	TemplateIsoparametric ()
	TemplateIsoparametric (const MeshLib::Element &e)
const MeshLib::Element *	getMeshElement () const
	return current mesh element
void	setMeshElement (const MeshLib::Element &e)
	Sets the mesh element.
void	computeShapeFunctions (const double *natural_pt, ShapeMatrices &shape, const unsigned global_dim, bool is_axially_symmetric) const
template<ShapeMatrixType T_SHAPE_MATRIX_TYPE>
void	computeShapeFunctions (const double *natural_pt, ShapeMatrices &shape, const unsigned global_dim, bool is_axially_symmetric) const
double	interpolateZerothCoordinate (typename ShapeMatrices::ShapeType const &N) const
std::array< double, 3 >	interpolateCoordinates (typename ShapeMatrices::ShapeType const &N) const
	Interpolates the coordinates of the element with the given shape matrix.

Private Member Functions
void	computeIntegralMeasure (bool is_axially_symmetric, ShapeMatrices &shape) const

Private Attributes
const MeshLib::Element *	_ele

Member Typedef Documentation

NaturalCoordsMappingType

template<class ShapeFunctionType_, class ShapeMatrixTypes_>

using NumLib::TemplateIsoparametric< ShapeFunctionType_, ShapeMatrixTypes_ >::NaturalCoordsMappingType

Initial value:

 
        NaturalCoordinatesMapping<ShapeFunctionType, ShapeMatrices>

Natural coordinates mapping tools specialization for specific MeshElement and ShapeFunction types.

Definition at line 42 of file TemplateIsoparametric.h.

ShapeFunctionType

template<class ShapeFunctionType_, class ShapeMatrixTypes_>

using NumLib::TemplateIsoparametric< ShapeFunctionType_, ShapeMatrixTypes_ >::ShapeFunctionType = ShapeFunctionType_

Definition at line 35 of file TemplateIsoparametric.h.

ShapeMatrices

template<class ShapeFunctionType_, class ShapeMatrixTypes_>

using NumLib::TemplateIsoparametric< ShapeFunctionType_, ShapeMatrixTypes_ >::ShapeMatrices = typename ShapeMatrixTypes_::ShapeMatrices

Coordinate mapping matrices type.

Definition at line 38 of file TemplateIsoparametric.h.

Constructor & Destructor Documentation

TemplateIsoparametric() [1/2]

template<class ShapeFunctionType_, class ShapeMatrixTypes_>

NumLib::TemplateIsoparametric< ShapeFunctionType_, ShapeMatrixTypes_ >::TemplateIsoparametric ( )

inline

Constructor without specifying a mesh element. setMeshElement() must be called afterwards.

Definition at line 49 of file TemplateIsoparametric.h.

: _ele(nullptr) {}

TemplateIsoparametric() [2/2]

template<class ShapeFunctionType_, class ShapeMatrixTypes_>

NumLib::TemplateIsoparametric< ShapeFunctionType_, ShapeMatrixTypes_ >::TemplateIsoparametric ( const MeshLib::Element & e )

inlineexplicit

Construct this object for the given mesh element.

Parameters

e	Mesh element object

Definition at line 56 of file TemplateIsoparametric.h.

: _ele(&e) {}

Member Function Documentation

computeIntegralMeasure()

template<class ShapeFunctionType_, class ShapeMatrixTypes_>

void NumLib::TemplateIsoparametric< ShapeFunctionType_, ShapeMatrixTypes_ >::computeIntegralMeasure ( bool is_axially_symmetric, ShapeMatrices & shape ) const

inlineprivate

Definition at line 135 of file TemplateIsoparametric.h.

    {
        if (!is_axially_symmetric)
        {
            shape.integralMeasure = 1.0;
            return;
        }
 
        // Note: If an integration point is located at the rotation axis, r will
        // be zero which might lead to problems with the assembled equation
        // system.
        // E.g., for triangle elements, if an integration point is
        // located at edge of the unit triangle, it is possible that
        // r becomes zero.
        auto const r = interpolateZerothCoordinate(shape.N);
        shape.integralMeasure = 2. * std::numbers::pi * r;
    }

Referenced by NumLib::TemplateIsoparametric< ShapePoint1, T_SHAPE_MATRIX_POLICY< ShapePoint1 > >::computeShapeFunctions().

computeShapeFunctions() [1/2]

template<class ShapeFunctionType_, class ShapeMatrixTypes_>

void NumLib::TemplateIsoparametric< ShapeFunctionType_, ShapeMatrixTypes_ >::computeShapeFunctions ( const double * natural_pt, ShapeMatrices & shape, const unsigned global_dim, bool is_axially_symmetric ) const

inline

compute shape functions

Parameters

natural_pt	position in natural coordinates
shape	evaluated shape function matrices
global_dim	global dimension
is_axially_symmetric	if true, the integral measure for cylinder coordinates is used, and 1 otherwise.

Definition at line 72 of file TemplateIsoparametric.h.

    {
        NaturalCoordsMappingType::computeShapeMatrices(*_ele, natural_pt, shape,
                                                       global_dim);
        computeIntegralMeasure(is_axially_symmetric, shape);
    }

computeShapeFunctions() [2/2]

template<class ShapeFunctionType_, class ShapeMatrixTypes_>

template<ShapeMatrixType T_SHAPE_MATRIX_TYPE>

void NumLib::TemplateIsoparametric< ShapeFunctionType_, ShapeMatrixTypes_ >::computeShapeFunctions ( const double * natural_pt, ShapeMatrices & shape, const unsigned global_dim, bool is_axially_symmetric ) const

inline

compute shape functions

Template Parameters

T_SHAPE_MATRIX_TYPE

shape matrix types to be calculated

Parameters

natural_pt	position in natural coordinates
shape	evaluated shape function matrices
global_dim	global dimension
is_axially_symmetric	if true, the integral measure for cylinder coordinates is used, and 1 otherwise.

Definition at line 92 of file TemplateIsoparametric.h.

    {
        NaturalCoordsMappingType::template computeShapeMatrices<
            T_SHAPE_MATRIX_TYPE>(*_ele, natural_pt, shape, global_dim);
        computeIntegralMeasure(is_axially_symmetric, shape);
    }

getMeshElement()

template<class ShapeFunctionType_, class ShapeMatrixTypes_>

const MeshLib::Element * NumLib::TemplateIsoparametric< ShapeFunctionType_, ShapeMatrixTypes_ >::getMeshElement ( ) const

inline

return current mesh element

Definition at line 59 of file TemplateIsoparametric.h.

{ return _ele; }

interpolateCoordinates()

template<class ShapeFunctionType_, class ShapeMatrixTypes_>

std::array< double, 3 > NumLib::TemplateIsoparametric< ShapeFunctionType_, ShapeMatrixTypes_ >::interpolateCoordinates ( typename ShapeMatrices::ShapeType const & N ) const

inline

Interpolates the coordinates of the element with the given shape matrix.

Definition at line 117 of file TemplateIsoparametric.h.

    {
        auto* nodes = _ele->getNodes();
        typename ShapeMatrices::ShapeType rs(N.size());
        std::array<double, 3> interpolated_coords;
        for (int d = 0; d < 3; ++d)
        {
            for (int i = 0; i < rs.size(); ++i)
            {
                rs[i] = (*nodes[i])[d];
            }
            interpolated_coords[d] = N.dot(rs);
        }
        return interpolated_coords;
    }

Referenced by ProcessLib::BoundaryConditionAndSourceTerm::Python::BcAndStLocalAssemblerImpl< BcOrStData, ShapeFunction, LowerOrderShapeFunction, GlobalDim >::interpolateCoords().

interpolateZerothCoordinate()

template<class ShapeFunctionType_, class ShapeMatrixTypes_>

double NumLib::TemplateIsoparametric< ShapeFunctionType_, ShapeMatrixTypes_ >::interpolateZerothCoordinate ( typename ShapeMatrices::ShapeType const & N ) const

inline

Interpolates the x coordinate of the element with the given shape matrix.

Definition at line 103 of file TemplateIsoparametric.h.

    {
        auto* nodes = _ele->getNodes();
        typename ShapeMatrices::ShapeType rs(N.size());
        for (int i = 0; i < rs.size(); ++i)
        {
            rs[i] = (*nodes[i])[0];
        }
        auto const r = N.dot(rs);
        return r;
    }

Referenced by NumLib::TemplateIsoparametric< ShapePoint1, T_SHAPE_MATRIX_POLICY< ShapePoint1 > >::computeIntegralMeasure().

setMeshElement()

template<class ShapeFunctionType_, class ShapeMatrixTypes_>

void NumLib::TemplateIsoparametric< ShapeFunctionType_, ShapeMatrixTypes_ >::setMeshElement ( const MeshLib::Element & e )

inline

Sets the mesh element.

Definition at line 62 of file TemplateIsoparametric.h.

{ this->_ele = &e; }

Member Data Documentation

_ele

template<class ShapeFunctionType_, class ShapeMatrixTypes_>

const MeshLib::Element* NumLib::TemplateIsoparametric< ShapeFunctionType_, ShapeMatrixTypes_ >::_ele

private

Definition at line 154 of file TemplateIsoparametric.h.

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

• NumLib/Fem/FiniteElement/TemplateIsoparametric.h