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rAKA/src/fe_engine/shape_lagrange.hh
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shape_lagrange.hh
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/**
* @file shape_lagrange.hh
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
* @author Mohit Pundir <mohit.pundir@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Tue Feb 15 2011
* @date last modification: Fri May 14 2021
*
* @brief lagrangian shape functions 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 "shape_lagrange_base.hh"
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_SHAPE_LAGRANGE_HH_
#define AKANTU_SHAPE_LAGRANGE_HH_
namespace akantu {
/* -------------------------------------------------------------------------- */
template <class Shape> class ShapeCohesive;
class ShapeIGFEM;
template <ElementKind kind> class ShapeLagrange : public ShapeLagrangeBase {
/* ------------------------------------------------------------------------ */
/* Constructors/Destructors */
/* ------------------------------------------------------------------------ */
public:
ShapeLagrange(const Mesh & mesh, Int spatial_dimension,
const ID & id = "shape_lagrange");
~ShapeLagrange() override = default;
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
public:
/// initialization function for structural elements not yet implemented
template <typename D>
inline void
initShapeFunctions(const Array<Real> & nodes,
const Eigen::MatrixBase<D> & integration_points,
ElementType type, GhostType ghost_type);
/// computes the shape functions derivatives for given interpolation points
template <ElementType type, typename D>
void computeShapeDerivativesOnIntegrationPoints(
const Array<Real> & nodes,
const Eigen::MatrixBase<D> & integration_points,
Array<Real> & shape_derivatives, GhostType ghost_type,
const Array<Idx> & filter_elements = empty_filter) const;
void computeShapeDerivativesOnIntegrationPoints(
const Array<Real> & nodes, const Ref<const MatrixXr> integration_points,
Array<Real> & shape_derivatives, ElementType type, GhostType ghost_type,
const Array<Idx> & filter_elements) const override;
/// 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, Int nb_degree_of_freedom,
GhostType ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const;
template <ElementType type>
void interpolateOnIntegrationPoints(
const Array<Real> & in_u, Array<Real> & out_uq, Int nb_degree_of_freedom,
const Array<Real> & shapes, GhostType ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const;
/// interpolate on physical point
template <ElementType type, typename D1, typename D2, typename D3,
std::enable_if_t<aka::are_vectors<D1, D3>::value> * = nullptr>
void interpolate(const Eigen::MatrixBase<D1> & real_coords, Idx elem,
const Eigen::MatrixBase<D2> & nodal_values,
Eigen::MatrixBase<D3> & 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, Int nb_degree_of_freedom,
GhostType ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const;
template <ElementType type>
void computeBtD(const Array<Real> & Ds, Array<Real> & BtDs,
GhostType ghost_type,
const Array<Idx> & filter_elements) const;
template <ElementType type,
std::enable_if_t<ElementClass<type>::getNaturalSpaceDimension() !=
0> * = nullptr>
void computeBtDB(const Array<Real> & Ds, Array<Real> & BtDBs, Int order_d,
GhostType ghost_type,
const Array<Idx> & filter_elements) const;
template <ElementType type,
std::enable_if_t<ElementClass<type>::getNaturalSpaceDimension() ==
0> * = nullptr>
void computeBtDB(const Array<Real> & /*Ds*/, Array<Real> & /*BtDBs*/,
Int /*order_d*/, GhostType /*ghost_type*/,
const Array<Idx> & /*filter_elements*/) const {
AKANTU_TO_IMPLEMENT();
}
/// multiply a field by shape functions @f$ fts_{ij} = f_i * \varphi_j @f$
template <ElementType type>
void computeNtb(const Array<Real> & bs, Array<Real> & Ntbs,
GhostType ghost_type,
const Array<Idx> & filter_elements = empty_filter) const;
template <ElementType type>
void computeNtbN(const Array<Real> & bs, Array<Real> & NtbNs,
GhostType ghost_type,
const Array<Idx> & filter_elements) const;
/// find natural coords from real coords provided an element
template <ElementType type, typename D1, typename D2>
void inverseMap(const Eigen::MatrixBase<D1> & real_coords, Idx element,
const Eigen::MatrixBase<D2> & natural_coords,
GhostType ghost_type = _not_ghost) const;
/// return true if the coordinates provided are inside the element, false
/// otherwise
template <ElementType type, typename D,
std::enable_if_t<aka::is_vector_v<D>> *>
bool contains(const Eigen::MatrixBase<D> & real_coords, Idx elem,
GhostType ghost_type) const;
/// compute the shape on a provided point
template <ElementType type, typename D1, typename D2>
void computeShapes(const Eigen::MatrixBase<D1> & real_coords, Idx elem,
Eigen::MatrixBase<D2> & shapes,
GhostType ghost_type) const;
/// compute the shape derivatives on a provided point
template <ElementType type, typename D>
void computeShapeDerivatives(const Eigen::MatrixBase<D> & real_coords,
Idx elem, Tensor3Base<Real> & shapes,
GhostType ghost_type) const;
protected:
/// compute the shape derivatives on integration points for a given element
template <ElementType type, typename D1, typename D2>
inline void computeShapeDerivativesOnCPointsByElement(
const Eigen::MatrixBase<D1> & node_coords,
const Eigen::MatrixBase<D2> & natural_coords,
Tensor3Base<Real> & shapesd) const;
};
} // namespace akantu
/* -------------------------------------------------------------------------- */
/* inline functions */
/* -------------------------------------------------------------------------- */
#include "shape_lagrange_inline_impl.hh"
#endif /* AKANTU_SHAPE_LAGRANGE_HH_ */
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