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element_class.hh
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/**
* @file element_class.hh
*
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Jun 18 2010
* @date last modification: Tue Feb 20 2018
*
* @brief Declaration of the ElementClass main class and the
* Integration and Interpolation elements
*
*
* Copyright (©) 2010-2018 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 const GeometricalType geometrical_type{_gt_not_defined};
static const InterpolationType interpolation_type{_itp_not_defined};
static const ElementKind element_kind{_ek_regular};
static const UInt spatial_dimension{0};
static const GaussIntegrationType gauss_integration_type{_git_not_defined};
static const UInt 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 const GeometricalType geometrical_type{geom_type}; \
static const InterpolationType interpolation_type{interp_type}; \
static const ElementKind element_kind{elem_kind}; \
static const UInt spatial_dimension{sp}; \
static const GaussIntegrationType gauss_integration_type{gauss_int_type}; \
static const UInt 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 const 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 coor
template <class vector_type>
static inline bool contains(const vector_type & 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 const 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
static inline Real getInradius(const Matrix<Real> & /*coord*/) {
AKANTU_TO_IMPLEMENT();
}
/// true if the natural coordinates are in the element
template <class vector_type>
static inline bool contains(const vector_type & coord);
public:
static AKANTU_GET_MACRO_NOT_CONST(SpatialDimension,
geometrical_property::spatial_dimension,
UInt);
static AKANTU_GET_MACRO_NOT_CONST(NbNodesPerElement,
geometrical_property::nb_nodes_per_element,
UInt);
static inline constexpr auto getNbFacetTypes() {
return geometrical_property::nb_facet_types;
};
static inline UInt getNbFacetsPerElement(UInt t);
static inline UInt getNbFacetsPerElement();
static inline constexpr auto getFacetLocalConnectivityPerElement(UInt t = 0);
};
/* -------------------------------------------------------------------------- */
/* 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 UInt nb_nodes_per_element{nb_nodes}; \
static constexpr UInt 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
static inline void computeShapes(const Matrix<Real> & natural_coord,
Matrix<Real> & N);
/// compute the shape values for a given point in natural coordinates
template <class vector_type>
static inline void computeShapes(const vector_type &, vector_type &) {
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
*/
static inline void computeDNDS(const Matrix<Real> & natural_coord,
Tensor3<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 vector_type, class matrix_type>
static inline void computeDNDS(const vector_type &, matrix_type &) {
AKANTU_TO_IMPLEMENT();
}
/**
* compute @f$ @f$
**/
static inline void computeDN2DS2(const Matrix<Real> & natural_coord,
Tensor3<Real> & dn2ds2);
/**
* 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 computeDN2DS2(const vector_type &, matrix_type &) {
AKANTU_TO_IMPLEMENT();
}
/// compute jacobian (or integration variable change factor) for a given point
/// in the case of spatial_dimension != natural_space_dimension
static inline void computeSpecialJacobian(const Matrix<Real> &, Real &) {
AKANTU_TO_IMPLEMENT();
}
/// interpolate a field given (arbitrary) natural coordinates
static inline void
interpolateOnNaturalCoordinates(const Vector<Real> & natural_coords,
const Matrix<Real> & nodal_values,
Vector<Real> & interpolated);
/// interpolate a field given the shape functions on the interpolation point
static inline void interpolate(const Matrix<Real> & nodal_values,
const Vector<Real> & shapes,
Vector<Real> & interpolated);
/// interpolate a field given the shape functions on the interpolations points
static inline void interpolate(const Matrix<Real> & nodal_values,
const Matrix<Real> & shapes,
Matrix<Real> & interpolated);
/// compute the gradient of a given field on the given natural coordinates
static inline void
gradientOnNaturalCoordinates(const Vector<Real> & natural_coords,
const Matrix<Real> & f, Matrix<Real> & gradient);
public:
static AKANTU_GET_MACRO_NOT_CONST(
ShapeSize,
InterpolationProperty<interpolation_type>::nb_nodes_per_element, UInt);
static AKANTU_GET_MACRO_NOT_CONST(
ShapeDerivativesSize,
(InterpolationProperty<interpolation_type>::nb_nodes_per_element *
InterpolationProperty<interpolation_type>::natural_space_dimension),
UInt);
static AKANTU_GET_MACRO_NOT_CONST(
NaturalSpaceDimension,
InterpolationProperty<interpolation_type>::natural_space_dimension, UInt);
static AKANTU_GET_MACRO_NOT_CONST(
NbNodesPerInterpolationElement,
InterpolationProperty<interpolation_type>::nb_nodes_per_element, UInt);
};
/* -------------------------------------------------------------------------- */
/* Integration */
/* -------------------------------------------------------------------------- */
template <GaussIntegrationType git_class, UInt 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,
UInt n = ElementClassProperty<type>::polynomial_degree>
class GaussIntegrationElement {
public:
static UInt getNbQuadraturePoints();
static const Matrix<Real> getQuadraturePoints();
static const Vector<Real> 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
*/
static inline void computeJMat(const Matrix<Real> & dnds,
const Matrix<Real> & node_coords,
Matrix<Real> & J);
/**
* 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
*/
static inline void computeJMat(const Tensor3<Real> & dnds,
const Matrix<Real> & node_coords,
Tensor3<Real> & J);
/// compute the jacobians of a serie of natural coordinates
static inline void computeJacobian(const Matrix<Real> & natural_coords,
const Matrix<Real> & node_coords,
Vector<Real> & jacobians);
/// compute jacobian (or integration variable change factor) for a set of
/// points
static inline void computeJacobian(const Tensor3<Real> & J,
Vector<Real> & jacobians);
/// compute jacobian (or integration variable change factor) for a given point
static inline void computeJacobian(const Matrix<Real> & J, Real & jacobians);
/// compute shape derivatives (input is dxds) for a set of points
static inline void computeShapeDerivatives(const Tensor3<Real> & J,
const Tensor3<Real> & dnds,
Tensor3<Real> & shape_deriv);
/// compute shape derivatives (input is dxds) for a given point
static inline void computeShapeDerivatives(const Matrix<Real> & J,
const Matrix<Real> & dnds,
Matrix<Real> & shape_deriv);
/// compute the normal of a surface defined by the function f
static inline void
computeNormalsOnNaturalCoordinates(const Matrix<Real> & coord,
Matrix<Real> & f, Matrix<Real> & normals);
/// get natural coordinates from real coordinates
static inline void inverseMap(const Vector<Real> & real_coords,
const Matrix<Real> & node_coords,
Vector<Real> & natural_coords,
UInt max_iterations = 100,
Real tolerance = 1e-10);
/// get natural coordinates from real coordinates
static inline void inverseMap(const Matrix<Real> & real_coords,
const Matrix<Real> & node_coords,
Matrix<Real> & natural_coords,
UInt max_iterations = 100,
Real tolerance = 1e-10);
public:
static AKANTU_GET_MACRO_NOT_CONST(Kind, element_kind, ElementKind);
static constexpr AKANTU_GET_MACRO_NOT_CONST(
SpatialDimension, ElementClassProperty<element_type>::spatial_dimension,
UInt);
using element_class_extra_geom_property =
ElementClassExtraGeometryProperties<element_type>;
static constexpr auto getP1ElementType() {
return element_class_extra_geom_property::p1_type;
}
static constexpr auto getFacetType(UInt t = 0) {
return element_class_extra_geom_property::facet_type[t];
}
static constexpr auto getFacetTypes();
};
/* -------------------------------------------------------------------------- */
} // namespace akantu
/* -------------------------------------------------------------------------- */
#include "geometrical_element_property.hh"
#include "interpolation_element_tmpl.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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