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rAKA akantu
shape_igfem.hh
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/**
* @file shape_igfem.hh
*
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
*
*
* @brief shape functions for interface-enriched generalized FEM
*
*
* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
*/
/* -------------------------------------------------------------------------- */
#include "aka_array.hh"
#include "shape_functions.hh"
#ifndef AKANTU_SHAPE_IGFEM_HH_
#define AKANTU_SHAPE_IGFEM_HH_
namespace
akantu
{
/* -------------------------------------------------------------------------- */
template
<>
class
ShapeLagrange
<
_ek_igfem
>
:
public
ShapeFunctions
{
/* ------------------------------------------------------------------------ */
/* Constructors/Destructors */
/* ------------------------------------------------------------------------ */
public
:
ShapeLagrange
(
const
Mesh
&
mesh
,
const
ID
&
id
=
"shape_igfem"
,
const
MemoryID
&
memory_id
=
0
);
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
public
:
inline
void
initShapeFunctions
(
const
Array
<
Real
>
&
nodes
,
const
Matrix
<
Real
>
&
integration_points
,
const
Matrix
<
Real
>
&
integration_points_1
,
const
Matrix
<
Real
>
&
integration_points_2
,
ElementType
type
,
GhostType
ghost_type
);
inline
void
interpolateEnrichmentsAllTypes
(
const
Array
<
Real
>
&
src
,
Array
<
Real
>
&
dst
,
ElementType
type
,
GhostType
ghost_type
)
const
;
template
<
ElementType
type
>
inline
void
precomputeShapesOnEnrichedNodes
(
const
Array
<
Real
>
&
nodes
,
GhostType
ghost_type
);
template
<
ElementType
type
>
void
interpolateAtEnrichedNodes
(
const
Array
<
Real
>
&
src
,
Array
<
Real
>
&
dst
,
GhostType
ghost_type
)
const
;
/// pre compute all shapes on the element integration points from natural
/// coordinates
template
<
ElementType
type
>
void
precomputeShapesOnIntegrationPoints
(
const
Array
<
Real
>
&
nodes
,
GhostType
ghost_type
);
/// pre compute all shape derivatives on the element integration points from
/// natural coordinates
template
<
ElementType
type
>
void
precomputeShapeDerivativesOnIntegrationPoints
(
const
Array
<
Real
>
&
nodes
,
GhostType
ghost_type
);
/// interpolate nodal values on the integration points
template
<
ElementType
type
>
void
interpolateOnIntegrationPoints
(
const
Array
<
Real
>
&
u
,
Array
<
Real
>
&
uq
,
UInt
nb_degree_of_freedom
,
GhostType
ghost_type
=
_not_ghost
,
const
Array
<
UInt
>
&
filter_elements
=
empty_filter
)
const
;
/// interpolate on physical point
template
<
ElementType
type
>
void
interpolate
(
const
Vector
<
Real
>
&
real_coords
,
UInt
elem
,
const
Matrix
<
Real
>
&
nodal_values
,
Vector
<
Real
>
&
interpolated
,
GhostType
ghost_type
)
const
;
/// compute the gradient of u on the integration points
template
<
ElementType
type
>
void
gradientOnIntegrationPoints
(
const
Array
<
Real
>
&
u
,
Array
<
Real
>
&
nablauq
,
UInt
nb_degree_of_freedom
,
GhostType
ghost_type
=
_not_ghost
,
const
Array
<
UInt
>
&
filter_elements
=
empty_filter
)
const
;
/// multiply a field by shape functions @f$ fts_{ij} = f_i * \varphi_j @f$
template
<
ElementType
type
>
void
fieldTimesShapes
(
const
Array
<
Real
>
&
field
,
Array
<
Real
>
&
field_times_shapes
,
GhostType
ghost_type
)
const
;
/// find natural coords in parent element from real coords provided an element
template
<
ElementType
type
>
void
inverseMap
(
const
Vector
<
Real
>
&
real_coords
,
UInt
element
,
Vector
<
Real
>
&
natural_coords
,
GhostType
ghost_type
=
_not_ghost
)
const
;
/// find natural coords in sub-element from real coords provided an element
template
<
ElementType
type
>
void
inverseMap
(
const
Vector
<
Real
>
&
real_coords
,
UInt
element
,
Vector
<
Real
>
&
natural_coords
,
UInt
sub_element
,
GhostType
ghost_type
=
_not_ghost
)
const
;
/// return true if the coordinates provided are inside the element, false
/// otherwise
template
<
ElementType
type
>
bool
contains
(
const
Vector
<
Real
>
&
real_coords
,
UInt
elem
,
GhostType
ghost_type
)
const
;
/// compute the shape on a provided point
template
<
ElementType
type
>
void
computeShapes
(
const
Vector
<
Real
>
&
real_coords
,
UInt
elem
,
Vector
<
Real
>
&
shapes
,
GhostType
ghost_type
)
const
;
/// compute the shape derivatives on a provided point
template
<
ElementType
type
>
void
computeShapeDerivatives
(
const
Matrix
<
Real
>
&
real_coords
,
UInt
elem
,
Tensor3
<
Real
>
&
shapes
,
GhostType
ghost_type
)
const
;
/// interpolate a field on a given physical point
template
<
ElementType
type
>
void
interpolateOnPhysicalPoint
(
const
Vector
<
Real
>
&
real_coords
,
UInt
elem
,
const
Array
<
Real
>
&
field
,
Vector
<
Real
>
&
interpolated
,
GhostType
ghost_type
)
const
;
/// function to extract values at standard nodes and zero-out enriched values
/// of a nodal field
void
extractValuesAtStandardNodes
(
const
Array
<
Real
>
&
nodal_values
,
Array
<
Real
>
&
extracted_values
,
GhostType
ghost_type
)
const
;
/// function to print the containt of the class
virtual
void
printself
(
std
::
ostream
&
stream
,
int
indent
=
0
)
const
;
protected
:
/// compute the shape derivatives on integration points for a given element
template
<
ElementType
type
>
inline
void
computeShapeDerivativesOnCPointsByElement
(
const
Matrix
<
Real
>
&
node_coords
,
const
Matrix
<
Real
>
&
natural_coords
,
Tensor3
<
Real
>
&
shapesd
)
const
;
/* ------------------------------------------------------------------------ */
/* Accessors */
/* ------------------------------------------------------------------------ */
public
:
/// get a the shapes vector
inline
const
Array
<
Real
>
&
getShapes
(
ElementType
el_type
,
GhostType
ghost_type
=
_not_ghost
)
const
;
/// get a the shapes derivatives vector
inline
const
Array
<
Real
>
&
getShapesDerivatives
(
ElementType
el_type
,
GhostType
ghost_type
=
_not_ghost
)
const
;
/// get a the shapes vector
inline
const
Array
<
Real
>
&
getShapesAtEnrichedNodes
(
ElementType
el_type
,
GhostType
ghost_type
=
_not_ghost
)
const
;
/* ------------------------------------------------------------------------ */
/* Class Members */
/* ------------------------------------------------------------------------ */
protected
:
/// shape functions for all elements
ElementTypeMapArray
<
Real
,
InterpolationType
>
shapes
;
/// shape functions derivatives for all elements
ElementTypeMapArray
<
Real
,
InterpolationType
>
shapes_derivatives
;
/// additional integration points for the IGFEM formulation
ElementTypeMapArray
<
Real
>
igfem_integration_points
;
/// values of shape functions for all elements on the enriched nodes
ElementTypeMapArray
<
Real
,
InterpolationType
>
shapes_at_enrichments
;
};
}
// namespace akantu
/* -------------------------------------------------------------------------- */
/* inline functions */
/* -------------------------------------------------------------------------- */
#include "shape_igfem_inline_impl.hh"
/// standard output stream operator
// template <class ShapeFunction>
// inline std::ostream & operator <<(std::ostream & stream, const
// ShapeIGFEM<ShapeFunction> & _this)
// {
// _this.printself(stream);
// return stream;
// }
#endif
/* AKANTU_SHAPE_IGFEM_HH_ */
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