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element_class.hh
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/**
* @file element_class.hh
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@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 Dec 11 2020
*
* @brief Declaration of the ElementClass main class and the
* Integration and Interpolation elements
*
*
* @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 "aka_common.hh"
#include "aka_types.hh"
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_ELEMENT_CLASS_HH_
#define AKANTU_ELEMENT_CLASS_HH_
namespace akantu {
/* -------------------------------------------------------------------------- */
/// default element class structure
template <ElementType element_type> struct ElementClassProperty {
static constexpr GeometricalType geometrical_type{_gt_not_defined};
static constexpr InterpolationType interpolation_type{_itp_not_defined};
static constexpr ElementKind element_kind{_ek_regular};
static constexpr Int spatial_dimension{0};
static constexpr GaussIntegrationType gauss_itegration_type{_git_not_defined};
static constexpr Int polynomial_degree{0};
};
#if !defined(DOXYGEN)
/// Macro to generate the element class structures for different element types
#define AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(elem_type, geom_type, \
interp_type, elem_kind, sp, \
gauss_int_type, min_int_order) \
template <> struct ElementClassProperty<elem_type> { \
static constexpr GeometricalType geometrical_type{geom_type}; \
static constexpr InterpolationType interpolation_type{interp_type}; \
static constexpr ElementKind element_kind{elem_kind}; \
static constexpr Int spatial_dimension{sp}; \
static constexpr GaussIntegrationType gauss_integration_type{ \
gauss_int_type}; \
static constexpr Int polynomial_degree{min_int_order}; \
}
#else
#define AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY(elem_type, geom_type, \
interp_type, elem_kind, sp, \
gauss_int_type, min_int_order)
#endif
/* -------------------------------------------------------------------------- */
/* Geometry */
/* -------------------------------------------------------------------------- */
/// Default GeometricalShape structure
template <GeometricalType geometrical_type> struct GeometricalShape {
static constexpr GeometricalShapeType shape{_gst_point};
};
/// Templated GeometricalShape with function contains
template <GeometricalShapeType shape> struct GeometricalShapeContains {
/// Check if the point (vector in 2 and 3D) at natural coordinate coord
template <class D>
static inline bool contains(const Eigen::MatrixBase<D> & coord);
};
#if !defined(DOXYGEN)
/// Macro to generate the GeometricalShape structures for different geometrical
/// types
#define AKANTU_DEFINE_SHAPE(geom_type, geom_shape) \
template <> struct GeometricalShape<geom_type> { \
static constexpr GeometricalShapeType shape{geom_shape}; \
}
AKANTU_DEFINE_SHAPE(_gt_hexahedron_20, _gst_square);
AKANTU_DEFINE_SHAPE(_gt_hexahedron_8, _gst_square);
AKANTU_DEFINE_SHAPE(_gt_pentahedron_15, _gst_prism);
AKANTU_DEFINE_SHAPE(_gt_pentahedron_6, _gst_prism);
AKANTU_DEFINE_SHAPE(_gt_point, _gst_point);
AKANTU_DEFINE_SHAPE(_gt_quadrangle_4, _gst_square);
AKANTU_DEFINE_SHAPE(_gt_quadrangle_8, _gst_square);
AKANTU_DEFINE_SHAPE(_gt_segment_2, _gst_square);
AKANTU_DEFINE_SHAPE(_gt_segment_3, _gst_square);
AKANTU_DEFINE_SHAPE(_gt_tetrahedron_10, _gst_triangle);
AKANTU_DEFINE_SHAPE(_gt_tetrahedron_4, _gst_triangle);
AKANTU_DEFINE_SHAPE(_gt_triangle_3, _gst_triangle);
AKANTU_DEFINE_SHAPE(_gt_triangle_6, _gst_triangle);
#endif
/* -------------------------------------------------------------------------- */
template <GeometricalType geometrical_type>
struct GeometricalElementProperty {};
template <ElementType element_type>
struct ElementClassExtraGeometryProperties {};
/* -------------------------------------------------------------------------- */
/// Templated GeometricalElement with function getInradius
template <GeometricalType geometrical_type,
GeometricalShapeType shape =
GeometricalShape<geometrical_type>::shape>
class GeometricalElement {
using geometrical_property = GeometricalElementProperty<geometrical_type>;
public:
/// compute the in-radius: \todo should be renamed for characteristic length
template <class D>
static inline Real getInradius(const Eigen::MatrixBase<D> & /*X*/) {
return 0.;
}
/// compute the normal to the element
template <class D1, class D2>
static inline void getNormal(const Eigen::MatrixBase<D1> & /*X*/,
Eigen::MatrixBase<D2> & n) {
n.zero();
}
/// true if the natural coordinates are in the element
template <class D>
static inline bool contains(const Eigen::MatrixBase<D> & coord);
public:
static constexpr auto getSpatialDimension() {
return geometrical_property::spatial_dimension;
}
static constexpr auto getNbNodesPerElement() {
return geometrical_property::nb_nodes_per_element;
}
static inline constexpr auto getNbFacetTypes() {
return geometrical_property::nb_facet_types;
};
static inline constexpr Int getNbFacetsPerElement(Idx t);
static inline constexpr Int getNbFacetsPerElement();
static inline constexpr decltype(auto)
getFacetLocalConnectivityPerElement(Idx t = 0);
template <Idx t,
std::size_t size = std::tuple_size<
decltype(geometrical_property::nb_facets)>::value,
std::enable_if_t<(t < size)> * = nullptr>
static inline constexpr decltype(auto) getFacetLocalConnectivityPerElement();
template <Idx t,
std::size_t size = std::tuple_size<
decltype(geometrical_property::nb_facets)>::value,
std::enable_if_t<not(t < size)> * = nullptr>
static inline constexpr decltype(auto) getFacetLocalConnectivityPerElement();
};
/* -------------------------------------------------------------------------- */
/* Interpolation */
/* -------------------------------------------------------------------------- */
/// default InterpolationProperty structure
template <InterpolationType interpolation_type> struct InterpolationProperty {};
#if !defined(DOXYGEN)
/// Macro to generate the InterpolationProperty structures for different
/// interpolation types
#define AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(itp_type, itp_kind, \
nb_nodes, ndim) \
template <> struct InterpolationProperty<itp_type> { \
static constexpr InterpolationKind kind{itp_kind}; \
static constexpr Int nb_nodes_per_element{nb_nodes}; \
static constexpr Int natural_space_dimension{ndim}; \
}
#else
#define AKANTU_DEFINE_INTERPOLATION_TYPE_PROPERTY(itp_type, itp_kind, \
nb_nodes, ndim)
#endif
/* -------------------------------------------------------------------------- */
/// Generic (templated by the enum InterpolationType which specifies the order
/// and the dimension of the interpolation) class handling the elemental
/// interpolation
template <InterpolationType interpolation_type,
InterpolationKind kind =
InterpolationProperty<interpolation_type>::kind>
class InterpolationElement {
public:
using interpolation_property = InterpolationProperty<interpolation_type>;
/// compute the shape values for a given set of points in natural coordinates
template <class D1, class D2,
aka::enable_if_t<aka::are_matrices<D1, D2>::value> * = nullptr>
static inline void computeShapes(const Eigen::MatrixBase<D1> & Xs,
const Eigen::MatrixBase<D2> & N_);
/// compute the shape values for a given point in natural coordinates
template <class D1, class D2,
aka::enable_if_t<aka::are_vectors<D1, D2>::value> * = nullptr>
static inline void computeShapes(const Eigen::MatrixBase<D1> & /*Xs*/,
Eigen::MatrixBase<D2> & /*N_*/) {
AKANTU_TO_IMPLEMENT();
}
/**
* compute @f$ B_{ij} = \frac{\partial N_j}{\partial S_i} @f$ the variation of
* shape functions along with variation of natural coordinates on a given set
* of points in natural coordinates
*/
template <class D>
static inline void computeDNDS(const Eigen::MatrixBase<D> & Xs,
Tensor3Base<Real> & dnds);
/**
* compute @f$ B_{ij} = \frac{\partial N_j}{\partial S_i} @f$ the variation of
* shape functions along with
* variation of natural coordinates on a given point in natural
* coordinates
*/
template <class D1, class D2>
static inline void computeDNDS(const Eigen::MatrixBase<D1> & /*Xs*/,
Eigen::MatrixBase<D2> & /*dNdS*/) {
AKANTU_TO_IMPLEMENT();
}
/**
* compute @f$ @f$
**/
static inline void computeD2NDS2(const Matrix<Real> & natural_coord,
Tensor3<Real> & d2nds2);
/**
* compute @f$ B_{ij} = \frac{\partial N_j}{\partial S_i} @f$ the
* second variation of
* shape functions along with
* variation of natural coordinates on a given point in natural
* coordinates
*/
template <class vector_type, class matrix_type>
static inline void computeD2NDS2(const vector_type & /*unused*/,
matrix_type & /*unused*/) {
AKANTU_TO_IMPLEMENT();
}
/// compute jacobian (or integration variable change factor) for a given point
/// in the case of spatial_dimension != natural_space_dimension
template <class D>
static inline Real computeSpecialJacobian(const Eigen::MatrixBase<D> &) {
AKANTU_TO_IMPLEMENT();
}
/// interpolate a field given (arbitrary) natural coordinates
template <class Derived1, class Derived2>
static inline decltype(auto) interpolateOnNaturalCoordinates(
const Eigen::MatrixBase<Derived1> & natural_coords,
const Eigen::MatrixBase<Derived2> & nodal_values) {
using interpolation = InterpolationProperty<interpolation_type>;
Eigen::Matrix<Real, interpolation::nb_nodes_per_element, 1> shapes;
computeShapes(natural_coords, shapes);
Matrix<Real, Eigen::Dynamic, 1> res;
res.noalias() = interpolate(nodal_values, shapes);
return res;
}
/// interpolate a field given the shape functions on the interpolation point
template <class Derived1, class Derived2>
static inline auto
interpolate(const Eigen::MatrixBase<Derived1> & nodal_values,
const Eigen::MatrixBase<Derived2> & shapes);
/// interpolate a field given the shape functions on the interpolations points
template <class Derived1, class Derived2, class Derived3>
static inline void
interpolate(const Eigen::MatrixBase<Derived1> & nodal_values,
const Eigen::MatrixBase<Derived2> & Ns,
const Eigen::MatrixBase<Derived3> & interpolated);
/// compute the gradient of a given field on the given natural coordinates
template <class D1, class D2, class D3>
static inline void
gradientOnNaturalCoordinates(const Eigen::MatrixBase<D1> & natural_coords,
const Eigen::MatrixBase<D2> & f,
const Eigen::MatrixBase<D3> & dfds);
public:
static constexpr auto getShapeSize() {
return InterpolationProperty<interpolation_type>::nb_nodes_per_element;
}
static constexpr auto getShapeDerivativesSize() {
return (InterpolationProperty<interpolation_type>::nb_nodes_per_element *
InterpolationProperty<interpolation_type>::natural_space_dimension);
}
static constexpr auto getNaturalSpaceDimension() {
return InterpolationProperty<interpolation_type>::natural_space_dimension;
}
static constexpr auto getNbNodesPerInterpolationElement() {
return InterpolationProperty<interpolation_type>::nb_nodes_per_element;
}
};
/* -------------------------------------------------------------------------- */
/* Integration */
/* -------------------------------------------------------------------------- */
template <GaussIntegrationType git_class, Int nb_points>
struct GaussIntegrationTypeData {
/// quadrature points in natural coordinates
static Real quad_positions[];
/// weights for the Gauss integration
static Real quad_weights[];
};
template <ElementType type,
Int n = ElementClassProperty<type>::polynomial_degree>
class GaussIntegrationElement {
static constexpr InterpolationType itp_type =
ElementClassProperty<type>::interpolation_type;
using interpolation_property = InterpolationProperty<itp_type>;
public:
static constexpr Int getNbQuadraturePoints();
static constexpr auto getQuadraturePoints();
static constexpr auto getWeights();
};
/* -------------------------------------------------------------------------- */
/* ElementClass */
/* -------------------------------------------------------------------------- */
template <ElementType element_type,
ElementKind element_kind =
ElementClassProperty<element_type>::element_kind>
class ElementClass
: public GeometricalElement<
ElementClassProperty<element_type>::geometrical_type>,
public InterpolationElement<
ElementClassProperty<element_type>::interpolation_type> {
protected:
using geometrical_element =
GeometricalElement<ElementClassProperty<element_type>::geometrical_type>;
using interpolation_element = InterpolationElement<
ElementClassProperty<element_type>::interpolation_type>;
using element_property = ElementClassProperty<element_type>;
using interpolation_property =
typename interpolation_element::interpolation_property;
public:
/**
* compute @f$ J = \frac{\partial x_j}{\partial s_i} @f$ the variation of real
* coordinates along with variation of natural coordinates on a given point in
* natural coordinates
*/
template <class D1, class D2>
static inline decltype(auto)
computeJMat(const Eigen::MatrixBase<D1> & dnds,
const Eigen::MatrixBase<D2> & node_coords);
/**
* compute the Jacobian matrix by computing the variation of real coordinates
* along with variation of natural coordinates on a given set of points in
* natural coordinates
*/
template <class D>
static inline void computeJMat(const Tensor3Base<Real> & dnds,
const Eigen::MatrixBase<D> & node_coords,
Tensor3Base<Real> & J);
/// compute the jacobians of a serie of natural coordinates
template <class D1, class D2, class D3>
static inline void
computeJacobian(const Eigen::MatrixBase<D1> & natural_coords,
const Eigen::MatrixBase<D2> & node_coords,
Eigen::MatrixBase<D3> & jacobians);
/// compute jacobian (or integration variable change factor) for a set of
/// points
template <class D>
static inline void computeJacobian(const Tensor3Base<Real> & J,
Eigen::MatrixBase<D> & jacobians);
/// compute jacobian (or integration variable change factor) for a given point
template <class D>
static inline Real computeJacobian(const Eigen::MatrixBase<D> & J);
/// compute shape derivatives (input is dxds) for a set of points
static inline void computeShapeDerivatives(const Tensor3Base<Real> & J,
const Tensor3Base<Real> & dnds,
Tensor3Base<Real> & shape_deriv);
/// compute shape derivatives (input is dxds) for a given point
template <class D1, class D2, class D3>
static inline void
computeShapeDerivatives(const Eigen::MatrixBase<D1> & J,
const Eigen::MatrixBase<D2> & dnds,
Eigen::MatrixBase<D3> & shape_deriv);
/// compute the normal of a surface defined by the function f
template <class D1, class D2, class D3>
static inline void
computeNormalsOnNaturalCoordinates(const Eigen::MatrixBase<D1> & coord,
const Eigen::MatrixBase<D2> & f,
Eigen::MatrixBase<D3> & normals);
/// get natural coordinates from real coordinates
template <class D1, class D2, class D3,
aka::enable_if_vectors_t<D1, D3> * = nullptr>
static inline void inverseMap(const Eigen::MatrixBase<D1> & real_coords,
const Eigen::MatrixBase<D2> & node_coords,
const Eigen::MatrixBase<D3> & natural_coords,
Int max_iterations = 100,
Real tolerance = 1e-10);
/// get natural coordinates from real coordinates
template <class D1, class D2, class D3,
aka::enable_if_matrices_t<D1, D3> * = nullptr>
static inline void inverseMap(const Eigen::MatrixBase<D1> & real_coords,
const Eigen::MatrixBase<D2> & node_coords,
const Eigen::MatrixBase<D3> & natural_coords_,
Int max_iterations = 100,
Real tolerance = 1e-10);
public:
static constexpr auto getKind() { return element_kind; }
static constexpr auto getSpatialDimension() {
return ElementClassProperty<element_type>::spatial_dimension;
}
using element_class_extra_geom_property =
ElementClassExtraGeometryProperties<element_type>;
static constexpr decltype(auto) getP1ElementType() {
return element_class_extra_geom_property::p1_type;
}
static constexpr decltype(auto) getFacetType(UInt t = 0) {
return element_class_extra_geom_property::facet_type[t];
}
static constexpr decltype(auto) getFacetTypes();
};
/* -------------------------------------------------------------------------- */
} // namespace akantu
/* -------------------------------------------------------------------------- */
#include "interpolation_element_tmpl.hh"
/* -------------------------------------------------------------------------- */
#include "geometrical_element_property.hh"
/* -------------------------------------------------------------------------- */
#include "element_class_tmpl.hh"
/* -------------------------------------------------------------------------- */
#include "element_class_hexahedron_8_inline_impl.hh"
#include "element_class_pentahedron_6_inline_impl.hh"
/* keep order */
#include "element_class_hexahedron_20_inline_impl.hh"
#include "element_class_pentahedron_15_inline_impl.hh"
#include "element_class_point_1_inline_impl.hh"
#include "element_class_quadrangle_4_inline_impl.hh"
#include "element_class_quadrangle_8_inline_impl.hh"
#include "element_class_segment_2_inline_impl.hh"
#include "element_class_segment_3_inline_impl.hh"
#include "element_class_tetrahedron_10_inline_impl.hh"
#include "element_class_tetrahedron_4_inline_impl.hh"
#include "element_class_triangle_3_inline_impl.hh"
#include "element_class_triangle_6_inline_impl.hh"
/* -------------------------------------------------------------------------- */
#if defined(AKANTU_STRUCTURAL_MECHANICS)
#include "element_class_structural.hh"
#endif
#if defined(AKANTU_COHESIVE_ELEMENT)
#include "cohesive_element.hh"
#endif
#if defined(AKANTU_IGFEM)
#include "element_class_igfem.hh"
#endif
#endif /* AKANTU_ELEMENT_CLASS_HH_ */
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