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shape_igfem.hh
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/**
* @file shape_igfem.hh
*
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
*
*
* @brief shape functions for interface-enriched generalized FEM
*
*
* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
*/
/* -------------------------------------------------------------------------- */
#include "aka_array.hh"
#include "shape_functions.hh"
#ifndef AKANTU_SHAPE_IGFEM_HH_
#define AKANTU_SHAPE_IGFEM_HH_
namespace akantu {
/* -------------------------------------------------------------------------- */
template <> class ShapeLagrange<_ek_igfem> : public ShapeFunctions {
/* ------------------------------------------------------------------------ */
/* Constructors/Destructors */
/* ------------------------------------------------------------------------ */
public:
ShapeLagrange(const Mesh & mesh, const ID & id = "shape_igfem");
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
public:
inline void initShapeFunctions(const Array<Real> & nodes,
const Matrix<Real> & integration_points,
const Matrix<Real> & integration_points_1,
const Matrix<Real> & integration_points_2,
ElementType type,
GhostType ghost_type);
inline void
interpolateEnrichmentsAllTypes(const Array<Real> & src, Array<Real> & dst,
ElementType type,
GhostType ghost_type) const;
template <ElementType type>
inline void precomputeShapesOnEnrichedNodes(const Array<Real> & nodes,
GhostType ghost_type);
template <ElementType type>
void interpolateAtEnrichedNodes(const Array<Real> & src, Array<Real> & dst,
GhostType ghost_type) const;
/// pre compute all shapes on the element integration points from natural
/// coordinates
template <ElementType type>
void precomputeShapesOnIntegrationPoints(const Array<Real> & nodes,
GhostType ghost_type);
/// pre compute all shape derivatives on the element integration points from
/// natural coordinates
template <ElementType type>
void precomputeShapeDerivativesOnIntegrationPoints(const Array<Real> & nodes,
GhostType ghost_type);
/// interpolate nodal values on the integration points
template <ElementType type>
void interpolateOnIntegrationPoints(
const Array<Real> & u, Array<Real> & uq, UInt nb_degree_of_freedom,
GhostType ghost_type = _not_ghost,
const Array<UInt> & filter_elements = empty_filter) const;
/// interpolate on physical point
template <ElementType type>
void interpolate(const Vector<Real> & real_coords, UInt elem,
const Matrix<Real> & nodal_values,
Vector<Real> & interpolated,
GhostType ghost_type) const;
/// compute the gradient of u on the integration points
template <ElementType type>
void gradientOnIntegrationPoints(
const Array<Real> & u, Array<Real> & nablauq, UInt nb_degree_of_freedom,
GhostType ghost_type = _not_ghost,
const Array<UInt> & filter_elements = empty_filter) const;
/// multiply a field by shape functions @f$ fts_{ij} = f_i * \varphi_j @f$
template <ElementType type>
void fieldTimesShapes(const Array<Real> & field,
Array<Real> & field_times_shapes,
GhostType ghost_type) const;
/// find natural coords in parent element from real coords provided an element
template <ElementType type>
void inverseMap(const Vector<Real> & real_coords, UInt element,
Vector<Real> & natural_coords,
GhostType ghost_type = _not_ghost) const;
/// find natural coords in sub-element from real coords provided an element
template <ElementType type>
void inverseMap(const Vector<Real> & real_coords, UInt element,
Vector<Real> & natural_coords, UInt sub_element,
GhostType ghost_type = _not_ghost) const;
/// return true if the coordinates provided are inside the element, false
/// otherwise
template <ElementType type>
bool contains(const Vector<Real> & real_coords, UInt elem,
GhostType ghost_type) const;
/// compute the shape on a provided point
template <ElementType type>
void computeShapes(const Vector<Real> & real_coords, UInt elem,
Vector<Real> & shapes, GhostType ghost_type) const;
/// compute the shape derivatives on a provided point
template <ElementType type>
void computeShapeDerivatives(const Matrix<Real> & real_coords, UInt elem,
Tensor3<Real> & shapes,
GhostType ghost_type) const;
/// interpolate a field on a given physical point
template <ElementType type>
void interpolateOnPhysicalPoint(const Vector<Real> & real_coords, UInt elem,
const Array<Real> & field,
Vector<Real> & interpolated,
GhostType ghost_type) const;
/// function to extract values at standard nodes and zero-out enriched values
/// of a nodal field
void extractValuesAtStandardNodes(const Array<Real> & nodal_values,
Array<Real> & extracted_values,
GhostType ghost_type) const;
/// function to print the containt of the class
virtual void printself(std::ostream & stream, int indent = 0) const;
protected:
/// compute the shape derivatives on integration points for a given element
template <ElementType type>
inline void
computeShapeDerivativesOnCPointsByElement(const Matrix<Real> & node_coords,
const Matrix<Real> & natural_coords,
Tensor3<Real> & shapesd) const;
/* ------------------------------------------------------------------------ */
/* Accessors */
/* ------------------------------------------------------------------------ */
public:
/// get a the shapes vector
inline const Array<Real> &
getShapes(ElementType el_type,
GhostType ghost_type = _not_ghost) const;
/// get a the shapes derivatives vector
inline const Array<Real> &
getShapesDerivatives(ElementType el_type,
GhostType ghost_type = _not_ghost) const;
/// get a the shapes vector
inline const Array<Real> &
getShapesAtEnrichedNodes(ElementType el_type,
GhostType ghost_type = _not_ghost) const;
/* ------------------------------------------------------------------------ */
/* Class Members */
/* ------------------------------------------------------------------------ */
protected:
/// shape functions for all elements
ElementTypeMapArray<Real, InterpolationType> shapes;
/// shape functions derivatives for all elements
ElementTypeMapArray<Real, InterpolationType> shapes_derivatives;
/// additional integration points for the IGFEM formulation
ElementTypeMapArray<Real> igfem_integration_points;
/// values of shape functions for all elements on the enriched nodes
ElementTypeMapArray<Real, InterpolationType> shapes_at_enrichments;
};
} // namespace akantu
/* -------------------------------------------------------------------------- */
/* inline functions */
/* -------------------------------------------------------------------------- */
#include "shape_igfem_inline_impl.hh"
/// standard output stream operator
// template <class ShapeFunction>
// inline std::ostream & operator <<(std::ostream & stream, const
// ShapeIGFEM<ShapeFunction> & _this)
// {
// _this.printself(stream);
// return stream;
// }
#endif /* AKANTU_SHAPE_IGFEM_HH_ */
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