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rAKA akantu
fe_engine.hh
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/**
* @file fe_engine.hh
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Jun 18 2010
* @date last modification: Tue Feb 20 2018
*
* @brief FEM class
*
*
* 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_memory.hh"
#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
:
protected
Memory
,
public
MeshEventHandler
{
/* ------------------------------------------------------------------------ */
/* Constructors/Destructors */
/* ------------------------------------------------------------------------ */
public
:
FEEngine
(
Mesh
&
mesh
,
UInt
element_dimension
=
_all_dimensions
,
const
ID
&
id
=
"fem"
,
MemoryID
memory_id
=
0
);
~
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
<
UInt
>
&
filter_elements
=
empty_filter
);
/// filter a field
template
<
typename
T
>
static
void
filterElementalData
(
const
Mesh
&
mesh
,
const
Array
<
T
>
&
elem_f
,
Array
<
T
>
&
filtered_f
,
ElementType
type
,
GhostType
ghost_type
=
_not_ghost
,
const
Array
<
UInt
>
&
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
,
UInt
nb_degree_of_freedom
,
ElementType
type
,
GhostType
ghost_type
=
_not_ghost
,
const
Array
<
UInt
>
&
filter_elements
=
empty_filter
)
const
=
0
;
/// integrate a scalar value f on all elements of type "type"
virtual
Real
integrate
(
const
Array
<
Real
>
&
f
,
ElementType
type
,
GhostType
ghost_type
=
_not_ghost
,
const
Array
<
UInt
>
&
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
,
UInt
nb_degree_of_freedom
,
ElementType
type
,
GhostType
ghost_type
=
_not_ghost
,
const
Array
<
UInt
>
&
filter_elements
=
empty_filter
)
const
=
0
;
/// integrate one element scalar value on all elements of type "type"
virtual
Real
integrate
(
const
Vector
<
Real
>
&
f
,
ElementType
type
,
UInt
index
,
GhostType
ghost_type
=
_not_ghost
)
const
=
0
;
/* ------------------------------------------------------------------------ */
/* compatibility with old FEEngine fashion */
/* ------------------------------------------------------------------------ */
/// get the number of integration points
virtual
UInt
getNbIntegrationPoints
(
ElementType
type
,
GhostType
ghost_type
=
_not_ghost
)
const
=
0
;
/// get the precomputed shapes
const
virtual
Array
<
Real
>
&
getShapes
(
ElementType
type
,
GhostType
ghost_type
=
_not_ghost
,
UInt
id
=
0
)
const
=
0
;
/// get the derivatives of shapes
const
virtual
Array
<
Real
>
&
getShapesDerivatives
(
ElementType
type
,
GhostType
ghost_type
=
_not_ghost
,
UInt
id
=
0
)
const
=
0
;
/// get integration points
const
virtual
Matrix
<
Real
>
&
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
,
UInt
nb_degree_of_freedom
,
ElementType
type
,
GhostType
ghost_type
=
_not_ghost
,
const
Array
<
UInt
>
&
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
,
UInt
nb_degree_of_freedom
,
ElementType
type
,
GhostType
ghost_type
=
_not_ghost
,
const
Array
<
UInt
>
&
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
<
UInt
>
*
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
<
UInt
>
&
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
,
UInt
order_d
,
ElementType
type
,
GhostType
ghost_type
=
_not_ghost
,
const
Array
<
UInt
>
&
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
<
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
<
UInt
>
*
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
<
UInt
>
&
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
<
UInt
>
*
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
,
GhostType
ghost_type
,
const
ElementTypeMapArray
<
UInt
>
*
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
,
GhostType
ghost_type
,
const
ElementTypeMapArray
<
UInt
>
*
element_filter
)
const
=
0
;
/// interpolate on a phyiscal point inside an element
virtual
void
interpolate
(
const
Vector
<
Real
>
&
real_coords
,
const
Matrix
<
Real
>
&
nodal_values
,
Vector
<
Real
>
&
interpolated
,
const
Element
&
element
)
const
=
0
;
/// compute the shape on a provided point
virtual
void
computeShapes
(
const
Vector
<
Real
>
&
real_coords
,
UInt
elem
,
ElementType
type
,
Vector
<
Real
>
&
shapes
,
GhostType
ghost_type
=
_not_ghost
)
const
=
0
;
/// compute the shape derivatives on a provided point
virtual
void
computeShapeDerivatives
(
const
Vector
<
Real
>
&
real_coords
,
UInt
element
,
ElementType
type
,
Matrix
<
Real
>
&
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
;
ElementTypesIteratorHelper
elementTypes
(
UInt
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
(
ElementDimension
,
element_dimension
,
UInt
);
/// get the mesh contained in the fem object
AKANTU_GET_MACRO
(
Mesh
,
mesh
,
const
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
Real
getElementInradius
(
const
Matrix
<
Real
>
&
coord
,
ElementType
type
);
/// 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
ElementType
getCohesiveElementType
(
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
InterpolationType
getInterpolationType
(
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
;
/* ------------------------------------------------------------------------ */
/* Class Members */
/* ------------------------------------------------------------------------ */
protected
:
/// spatial dimension of the problem
UInt
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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