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shape_functions.hh
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/**
* @file shape_functions.hh
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Jun 18 2010
* @date last modification: Tue Sep 29 2020
*
* @brief shape function class
*
*
* @section LICENSE
*
* Copyright (©) 2010-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* Akantu is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "mesh.hh"
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_SHAPE_FUNCTIONS_HH_
#define AKANTU_SHAPE_FUNCTIONS_HH_
namespace akantu {
/* -------------------------------------------------------------------------- */
class ShapeFunctions {
/* ------------------------------------------------------------------------ */
/* Constructors/Destructors */
/* ------------------------------------------------------------------------ */
public:
ShapeFunctions(const Mesh & mesh, Int spatial_dimension,
const ID & id = "shape");
virtual ~ShapeFunctions() = default;
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
public:
/// function to print the contain of the class
virtual void printself(std::ostream & stream, int indent = 0) const {
std::string space(indent, AKANTU_INDENT);
stream << space << "Shapes [" << std::endl;
integration_points.printself(stream, indent + 1);
// shapes.printself(stream, indent + 1);
// shapes_derivatives.printself(stream, indent + 1);
stream << space << "]" << std::endl;
}
/// set the integration points for a given element
template <ElementType type, class D1>
void
setIntegrationPointsByType(const Eigen::MatrixBase<D1> & integration_points,
GhostType ghost_type);
/// Build pre-computed matrices for interpolation of field form integration
/// points at other given positions (interpolation_points)
void initElementalFieldInterpolationFromIntegrationPoints(
const ElementTypeMapArray<Real> & interpolation_points_coordinates,
ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
const ElementTypeMapArray<Real> & quadrature_points_coordinates,
const ElementTypeMapArray<Idx> * element_filter) const;
/// Interpolate field at given position from given values of this field at
/// integration points (field)
/// using matrices precomputed with
/// initElementalFieldInterplationFromIntegrationPoints
void interpolateElementalFieldFromIntegrationPoints(
const ElementTypeMapArray<Real> & field,
const ElementTypeMapArray<Real> &
interpolation_points_coordinates_matrices,
const ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
ElementTypeMapArray<Real> & result, GhostType ghost_type,
const ElementTypeMapArray<Idx> * element_filter) const;
protected:
/// interpolate nodal values stored by element on the integration points
template <ElementType type>
void interpolateElementalFieldOnIntegrationPoints(
const Array<Real> & u_el, Array<Real> & uq, GhostType ghost_type,
const Array<Real> & shapes,
const Array<Idx> & filter_elements = empty_filter) const;
/// gradient of nodal values stored by element on the control points
template <ElementType type,
std::enable_if_t<ElementClass<type>::getNaturalSpaceDimension() !=
0> * = nullptr>
void gradientElementalFieldOnIntegrationPoints(
const Array<Real> & u_el, Array<Real> & out_nablauq, GhostType ghost_type,
const Array<Real> & shapes_derivatives,
const Array<Idx> & filter_elements) const;
template <ElementType type,
std::enable_if_t<ElementClass<type>::getNaturalSpaceDimension() ==
0> * = nullptr>
void gradientElementalFieldOnIntegrationPoints(
const Array<Real> & /*u_el*/, Array<Real> & out_nablauq,
GhostType ghost_type, const Array<Real> & /*shapes_derivatives*/,
const Array<Idx> & /*filter_elements*/) const {
auto nb_points = integration_points(type, ghost_type).cols();
auto nb_element = mesh.getNbElement(type, ghost_type);
out_nablauq.resize(nb_element * nb_points);
out_nablauq.zero();
}
protected:
/// By element versions of non-templated eponym methods
template <ElementType type>
inline void interpolateElementalFieldFromIntegrationPoints(
const Array<Real> & field,
const Array<Real> & interpolation_points_coordinates_matrices,
const Array<Real> & quad_points_coordinates_inv_matrices,
ElementTypeMapArray<Real> & result, GhostType ghost_type,
const Array<Idx> & element_filter) const;
/// Interpolate field at given position from given values of this field at
/// integration points (field)
/// using matrices precomputed with
/// initElementalFieldInterplationFromIntegrationPoints
template <ElementType type>
inline void initElementalFieldInterpolationFromIntegrationPoints(
const Array<Real> & interpolation_points_coordinates,
ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
const Array<Real> & quadrature_points_coordinates, GhostType ghost_type,
const Array<Idx> & element_filter) const;
/// build matrix for the interpolation of field form integration points
template <ElementType type, typename D1, typename D2>
inline void buildElementalFieldInterpolationMatrix(
const Eigen::MatrixBase<D1> & coordinates,
Eigen::MatrixBase<D2> & coordMatrix,
Int integration_order =
ElementClassProperty<type>::polynomial_degree) const;
/// build the so called interpolation matrix (first collumn is 1, then the
/// other collumns are the traansposed coordinates)
template <typename D1, typename D2>
inline void
buildInterpolationMatrix(const Eigen::MatrixBase<D1> & coordinates,
Eigen::MatrixBase<D2> & coordMatrix,
Int integration_order) const;
template <ElementType type>
friend struct BuildElementalFieldInterpolationMatrix;
public:
virtual void onElementsAdded(const Array<Element> & /*unused*/) {
AKANTU_TO_IMPLEMENT();
}
virtual void onElementsRemoved(const Array<Element> & /*unused*/,
const ElementTypeMapArray<Idx> & /*unused*/) {
AKANTU_TO_IMPLEMENT();
}
/* ------------------------------------------------------------------------ */
/* Accessors */
/* ------------------------------------------------------------------------ */
public:
/// get the size of the shapes returned by the element class
static inline Int getShapeSize(ElementType type);
/// get the size of the shapes derivatives returned by the element class
static inline Int getShapeDerivativesSize(ElementType type);
inline const Matrix<Real> & getIntegrationPoints(ElementType type,
GhostType ghost_type) const {
return integration_points(type, ghost_type);
}
/* ------------------------------------------------------------------------ */
/* 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;
/* ------------------------------------------------------------------------ */
/* Class Members */
/* ------------------------------------------------------------------------ */
protected:
/// shape functions for all elements
ElementTypeMapArray<Real, InterpolationType> shapes;
/// shape functions derivatives for all elements
ElementTypeMapArray<Real, InterpolationType> shapes_derivatives;
/// associated mesh
const Mesh & mesh;
// spatial dimension of the elements to consider
Int _spatial_dimension;
/// shape functions for all elements
ElementTypeMap<Matrix<Real>> integration_points;
};
/* -------------------------------------------------------------------------- */
/* inline functions */
/* -------------------------------------------------------------------------- */
/// standard output stream operator
inline std::ostream & operator<<(std::ostream & stream,
const ShapeFunctions & _this) {
_this.printself(stream);
return stream;
}
} // namespace akantu
#include "shape_functions_inline_impl.hh"
#endif /* AKANTU_SHAPE_FUNCTIONS_HH_ */
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