fe_engine.hh
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Created: Mon, May 27, 23:17

fe_engine.hh
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	/**
	* Copyright (©) 2010-2023 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* This file is part of Akantu
	*
	* 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, ElementType type,
	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, ElementType type,
	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,
	ElementType type, 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"
	[[nodiscard]] virtual Real
	integrate(const Array<Real> & f, ElementType type,
	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,
	ElementType type, 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"
	[[nodiscard]] Real integrate(const Ref<const VectorXr> f,
	const Element & element) const {
	return integrate(f, element.type, element.element, element.ghost_type);
	}

	private:
	[[nodiscard]] virtual Real
	integrate(const Ref<const VectorXr> f, ElementType type, Idx index,
	GhostType ghost_type = _not_ghost) const = 0;

	/* ------------------------------------------------------------------------ */
	/* compatibility with old FEEngine fashion */
	/* ------------------------------------------------------------------------ */
	public:
	/// get the number of integration points
	[[nodiscard]] virtual Int
	getNbIntegrationPoints(ElementType type,
	GhostType ghost_type = _not_ghost) const = 0;

	/// get the precomputed shapes
	[[nodiscard]] const virtual Array<Real> &
	getShapes(ElementType type, GhostType ghost_type = _not_ghost,
	Idx id = 0) const = 0;

	/// get the derivatives of shapes
	[[nodiscard]] virtual const Array<Real> &
	getShapesDerivatives(ElementType type, GhostType ghost_type = _not_ghost,
	Idx id = 0) const = 0;

	/// get integration points
	[[nodiscard]] virtual const 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,
	ElementType type, 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,
	ElementType type, 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, ElementType type,
	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,
	ElementType type, 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, ElementType type,
	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<Idx> & 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, ElementType type,
	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,
	ElementType type, Ref<VectorXr> shapes,
	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,
	ElementType type, Ref<MatrixXr> shape_derivatives,
	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;

	[[nodiscard]] 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
	template <class Derived>
	[[nodiscard]] static inline Real
	getElementInradius(const Eigen::MatrixBase<Derived> & coord,
	ElementType type);

	[[nodiscard]] 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
	[[nodiscard]] static inline constexpr ElementType
	getCohesiveElementType(ElementType type_facet);

	/// get igfem element type for a given regular type
	[[nodiscard]] static inline Vector<ElementType>
	getIGFEMElementTypes(ElementType type);

	/// get the interpolation element associated to an element type
	[[nodiscard]] static inline constexpr auto
	getInterpolationType(ElementType el_type);

	/// get the shape function class (probably useless: see getShapeFunction in
	/// fe_engine_template.hh)
	[[nodiscard]] virtual const ShapeFunctions &
	getShapeFunctionsInterface() const = 0;
	/// get the integrator class (probably useless: see getIntegrator in
	/// fe_engine_template.hh)
	[[nodiscard]] 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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