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/**
* @file fe_engine.hh
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
* @author Sébastien Hartmann <sebastien.hartmann@epfl.ch>
* @author Mohit Pundir <mohit.pundir@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Jun 18 2010
* @date last modification: Fri May 14 2021
*
* @brief FEM 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 "element_type_map.hh"
#include "mesh_events.hh"
/* -------------------------------------------------------------------------- */
#include <functional>
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_FE_ENGINE_HH_
#define AKANTU_FE_ENGINE_HH_
namespace akantu {
class Mesh;
class Integrator;
class ShapeFunctions;
class DOFManager;
class Element;
} // namespace akantu
/* -------------------------------------------------------------------------- */
namespace akantu {
/* -------------------------------------------------------------------------- */
/**
* The generic FEEngine class derived in a FEEngineTemplate class
* containing the
* shape functions and the integration method
*/
class FEEngine : public MeshEventHandler {
/* ------------------------------------------------------------------------ */
/* Constructors/Destructors */
/* ------------------------------------------------------------------------ */
public:
FEEngine(Mesh & mesh, Int element_dimension = _all_dimensions,
const ID & id = "fem");
~FEEngine() override;
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
public:
/// pre-compute all the shape functions, their derivatives and the jacobians
virtual void
initShapeFunctions(GhostType ghost_type = _not_ghost) = 0;
/// extract the nodal values and store them per element
template <typename T>
static void
extractNodalToElementField(const Mesh & mesh, const Array<T> & nodal_f,
Array<T> & elemental_f, const ElementType & type,
const GhostType & ghost_type = _not_ghost,
const Array<Int> & filter_elements = empty_filter);
/// filter a field
template <typename T>
static void
filterElementalData(const Mesh & mesh, const Array<T> & quad_f,
Array<T> & filtered_f, const ElementType & type,
const GhostType & ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter);
/* ------------------------------------------------------------------------ */
/* Integration method bridges */
/* ------------------------------------------------------------------------ */
/// integrate f for all elements of type "type"
virtual void
integrate(const Array<Real> & f, Array<Real> & intf, Int nb_degree_of_freedom,
const ElementType & type, const GhostType & ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const = 0;
/// integrate a scalar value f on all elements of type "type"
virtual Real
integrate(const Array<Real> & f, const ElementType & type,
const GhostType & ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const = 0;
/// integrate f for all integration points of type "type" but don't sum over
/// all integration points
virtual void integrateOnIntegrationPoints(
const Array<Real> & f, Array<Real> & intf, Int nb_degree_of_freedom,
const ElementType & type, const GhostType & ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const = 0;
/// integrate one element scalar value on all elements of type "type"
Real integrate(const Ref<const VectorXr> & f, const Element & element) const {
return integrate(f, element.type, element.element, element.ghost_type);
}
private:
virtual Real integrate(const Ref<const VectorXr> & f,
const ElementType & type, Idx index,
const GhostType & ghost_type = _not_ghost) const = 0;
/* ------------------------------------------------------------------------ */
/* compatibility with old FEEngine fashion */
/* ------------------------------------------------------------------------ */
public:
/// get the number of integration points
virtual Int
getNbIntegrationPoints(ElementType type,
GhostType ghost_type = _not_ghost) const = 0;
/// get the precomputed shapes
const virtual Array<Real> &
getShapes(const ElementType & type, const GhostType & ghost_type = _not_ghost,
Idx id = 0) const = 0;
/// get the derivatives of shapes
virtual const Array<Real> &
getShapesDerivatives(const ElementType & type,
const GhostType & ghost_type = _not_ghost,
Idx id = 0) const = 0;
/// get integration points
const virtual MatrixXr &
getIntegrationPoints(ElementType type,
GhostType ghost_type = _not_ghost) const = 0;
/* ------------------------------------------------------------------------ */
/* Shape method bridges */
/* ------------------------------------------------------------------------ */
/// Compute the gradient nablauq on the integration points of an element type
/// from nodal values u
virtual void gradientOnIntegrationPoints(
const Array<Real> & u, Array<Real> & nablauq, Int nb_degree_of_freedom,
const ElementType & type, const GhostType & ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const = 0;
/// Interpolate a nodal field u at the integration points of an element type
/// -> uq
virtual void interpolateOnIntegrationPoints(
const Array<Real> & u, Array<Real> & uq, Int nb_degree_of_freedom,
const ElementType & type, const GhostType & ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const = 0;
/// Interpolate a nodal field u at the integration points of many element
/// types -> uq
virtual void interpolateOnIntegrationPoints(
const Array<Real> & u, ElementTypeMapArray<Real> & uq,
const ElementTypeMapArray<Idx> * filter_elements = nullptr) const = 0;
/// pre multiplies a tensor by the shapes derivaties
virtual void
computeBtD(const Array<Real> & Ds, Array<Real> & BtDs,
const ElementType & type,
const GhostType & ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const = 0;
/// left and right multiplies a tensor by the shapes derivaties
virtual void
computeBtDB(const Array<Real> & Ds, Array<Real> & BtDBs, Int order_d,
const ElementType & type,
const GhostType & ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const = 0;
/// left multiples a vector by the shape functions
virtual void
computeNtb(const Array<Real> & bs, Array<Real> & Ntbs,
const ElementType & type,
const GhostType & ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const = 0;
/// left and right multiplies a tensor by the shapes
virtual void
computeNtbN(const Array<Real> & bs, Array<Real> & NtbNs,
ElementType type, GhostType ghost_type = _not_ghost,
const Array<UInt> & filter_elements = empty_filter) const = 0;
/// Compute the interpolation point position in the global coordinates for
/// many element types
virtual void computeIntegrationPointsCoordinates(
ElementTypeMapArray<Real> & integration_points_coordinates,
const ElementTypeMapArray<Idx> * filter_elements = nullptr) const = 0;
/// Compute the interpolation point position in the global coordinates for an
/// element type
virtual void computeIntegrationPointsCoordinates(
Array<Real> & integration_points_coordinates, const ElementType & type,
const GhostType & ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const = 0;
/// Build pre-computed matrices for interpolation of field form integration
/// points at other given positions (interpolation_points)
virtual void initElementalFieldInterpolationFromIntegrationPoints(
const ElementTypeMapArray<Real> & interpolation_points_coordinates,
ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
ElementTypeMapArray<Real> & integration_points_coordinates_inv_matrices,
const ElementTypeMapArray<Idx> * element_filter) const = 0;
/// interpolate field at given position (interpolation_points) from given
/// values of this field at integration points (field)
virtual void interpolateElementalFieldFromIntegrationPoints(
const ElementTypeMapArray<Real> & field,
const ElementTypeMapArray<Real> & interpolation_points_coordinates,
ElementTypeMapArray<Real> & result, const GhostType ghost_type,
const ElementTypeMapArray<Idx> * element_filter) const = 0;
/// Interpolate field at given position from given values of this field at
/// integration points (field)
/// using matrices precomputed with
/// initElementalFieldInterplationFromIntegrationPoints
virtual void interpolateElementalFieldFromIntegrationPoints(
const ElementTypeMapArray<Real> & field,
const ElementTypeMapArray<Real> &
interpolation_points_coordinates_matrices,
const ElementTypeMapArray<Real> &
integration_points_coordinates_inv_matrices,
ElementTypeMapArray<Real> & result, const GhostType ghost_type,
const ElementTypeMapArray<Idx> * element_filter) const = 0;
/// interpolate on a phyiscal point inside an element
virtual void interpolate(const Ref<const VectorXr> & real_coords,
const Ref<const MatrixXr> & nodal_values,
Ref<VectorXr> interpolated,
const Element & element) const = 0;
/// compute the shape on a provided point
virtual void
computeShapes(const Ref<const VectorXr> & real_coords, Int elem,
const ElementType & type, Ref<VectorXr> shapes,
const GhostType & ghost_type = _not_ghost) const = 0;
/// compute the shape derivatives on a provided point
virtual void
computeShapeDerivatives(const Ref<const VectorXr> & real_coords, Int element,
const ElementType & type,
Ref<MatrixXr> shape_derivatives,
const GhostType & ghost_type = _not_ghost) const = 0;
/// assembles the lumped version of @f[ \int N^t rho N @f]
virtual void assembleFieldLumped(
const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
ElementType type, GhostType ghost_type = _not_ghost) const = 0;
/// assembles the matrix @f[ \int N^t rho N @f]
virtual void assembleFieldMatrix(
const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
ElementType type, GhostType ghost_type = _not_ghost) const = 0;
/* ------------------------------------------------------------------------ */
/* Other methods */
/* ------------------------------------------------------------------------ */
/// pre-compute normals on integration points
virtual void computeNormalsOnIntegrationPoints(
GhostType ghost_type = _not_ghost) = 0;
/// pre-compute normals on integration points
virtual void computeNormalsOnIntegrationPoints(
const Array<Real> & /*field*/,
GhostType /*ghost_type*/ = _not_ghost) {
AKANTU_TO_IMPLEMENT();
}
/// pre-compute normals on integration points
virtual void computeNormalsOnIntegrationPoints(
const Array<Real> & /*field*/, Array<Real> & /*normal*/,
ElementType /*type*/,
GhostType /*ghost_type*/ = _not_ghost) const {
AKANTU_TO_IMPLEMENT();
}
/// function to print the containt of the class
virtual void printself(std::ostream & stream, int indent = 0) const;
private:
/// initialise the class
void init();
/* ------------------------------------------------------------------------ */
/* Accessors */
/* ------------------------------------------------------------------------ */
public:
using ElementTypesIteratorHelper =
ElementTypeMapArray<Real, ElementType>::ElementTypesIteratorHelper;
ElementTypesIteratorHelper elementTypes(Int dim = _all_dimensions,
GhostType ghost_type = _not_ghost,
ElementKind kind = _ek_regular) const;
/// get the dimension of the element handeled by this fe_engine object
AKANTU_GET_MACRO_AUTO(ElementDimension, element_dimension);
/// get the mesh contained in the fem object
AKANTU_GET_MACRO_AUTO(Mesh, mesh);
/// get the mesh contained in the fem object
AKANTU_GET_MACRO_NOT_CONST(Mesh, mesh, Mesh &);
/// get the in-radius of an element
static inline constexpr Real getElementInradius(const Ref<const MatrixXr> & coord,
ElementType type);
inline Real getElementInradius(const Element & element) const;
/// get the normals on integration points
AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(NormalsOnIntegrationPoints,
normals_on_integration_points, Real);
/// get cohesive element type for a given facet type
static inline constexpr auto
getCohesiveElementType(const ElementType & type_facet);
/// get igfem element type for a given regular type
static inline Vector<ElementType>
getIGFEMElementTypes(ElementType type);
/// get the interpolation element associated to an element type
static inline constexpr auto
getInterpolationType(const ElementType & el_type);
/// get the shape function class (probably useless: see getShapeFunction in
/// fe_engine_template.hh)
virtual const ShapeFunctions & getShapeFunctionsInterface() const = 0;
/// get the integrator class (probably useless: see getIntegrator in
/// fe_engine_template.hh)
virtual const Integrator & getIntegratorInterface() const = 0;
AKANTU_GET_MACRO(ID, id, ID);
/* ------------------------------------------------------------------------ */
/* Class Members */
/* ------------------------------------------------------------------------ */
protected:
ID id;
/// spatial dimension of the problem
Int element_dimension;
/// the mesh on which all computation are made
Mesh & mesh;
/// normals at integration points
ElementTypeMapArray<Real> normals_on_integration_points;
};
/* -------------------------------------------------------------------------- */
/* inline functions */
/* -------------------------------------------------------------------------- */
/// standard output stream operator
inline std::ostream & operator<<(std::ostream & stream,
const FEEngine & _this) {
_this.printself(stream);
return stream;
}
} // namespace akantu
#include "fe_engine_inline_impl.hh"
#include "fe_engine_template.hh"
#endif /* AKANTU_FE_ENGINE_HH_ */
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