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test_igfem_triangle_5.cc
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rAKA akantu
test_igfem_triangle_5.cc
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/**
* @file test_igfem_triangle_5.cc
*
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
*
*
* @brief patch tests with elements of type _igfem_triangle_5
*
*
* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
*/
/* -------------------------------------------------------------------------- */
#include "dumpable_inline_impl.hh"
#include "solid_mechanics_model_igfem.hh"
/* -------------------------------------------------------------------------- */
using
namespace
akantu
;
class
StraightInterfaceMatSelector
:
public
MeshDataMaterialSelector
<
std
::
string
>
{
public
:
StraightInterfaceMatSelector
(
const
ID
&
id
,
SolidMechanicsModelIGFEM
&
model
)
:
MeshDataMaterialSelector
<
std
::
string
>
(
id
,
model
)
{}
UInt
operator
()(
const
Element
&
elem
)
{
if
(
Mesh
::
getKind
(
elem
.
type
)
==
_ek_igfem
)
/// choose IGFEM material
return
2
;
return
MeshDataMaterialSelector
<
std
::
string
>::
operator
()(
elem
);
}
};
Real
computeL2Error
(
SolidMechanicsModelIGFEM
&
model
);
int
main
(
int
argc
,
char
*
argv
[])
{
initialize
(
"material.dat"
,
argc
,
argv
);
/// create a mesh and read the regular elements from the mesh file
/// mesh creation
const
UInt
spatial_dimension
=
2
;
Mesh
mesh
(
spatial_dimension
);
mesh
.
read
(
"plate.msh"
);
/// model creation
SolidMechanicsModelIGFEM
model
(
mesh
);
/// creation of material selector
MeshDataMaterialSelector
<
std
::
string
>
*
mat_selector
;
mat_selector
=
new
StraightInterfaceMatSelector
(
"physical_names"
,
model
);
model
.
setMaterialSelector
(
*
mat_selector
);
model
.
initFull
();
/// add fields that should be dumped
model
.
setBaseName
(
"regular_elements"
);
model
.
setBaseNameToDumper
(
"igfem elements"
,
"igfem elements"
);
model
.
addDumpField
(
"material_index"
);
model
.
addDumpFieldVector
(
"displacement"
);
model
.
addDumpField
(
"blocked_dofs"
);
model
.
addDumpField
(
"stress"
);
model
.
addDumpFieldToDumper
(
"igfem elements"
,
"lambda"
);
model
.
addDumpFieldVectorToDumper
(
"igfem elements"
,
"displacement"
);
model
.
addDumpFieldVectorToDumper
(
"igfem elements"
,
"real_displacement"
);
model
.
addDumpFieldToDumper
(
"igfem elements"
,
"blocked_dofs"
);
model
.
addDumpFieldToDumper
(
"igfem elements"
,
"material_index"
);
model
.
addDumpFieldToDumper
(
"igfem elements"
,
"stress"
);
/// dump mesh before the IGFEM interface is created
model
.
dump
();
model
.
dump
(
"igfem elements"
);
/// create the interace: the bi-material interface is a straight line
/// since the SMMIGFEM has only a sphere intersector we generate a large
/// sphere so that the intersection points with the mesh lie almost along
/// the straight line x = 0.25. We then move the interface nodes to correct
/// their position and make them lie exactly along the line. This is a
/// workaround to generate a straight line with the sphere intersector.
/// Ideally, there should be a new type of IGFEM enrichment implemented to
/// generate straight lines
std
::
list
<
SK
::
Sphere_3
>
sphere_list
;
SK
::
Sphere_3
sphere_1
(
SK
::
Point_3
(
6.57
,
0.
,
0.
),
6.32
*
6.32
);
sphere_list
.
push_back
(
sphere_1
);
model
.
registerGeometryObject
(
sphere_list
,
"inside"
);
UInt
nb_regular_nodes
=
mesh
.
getNbNodes
();
model
.
update
();
UInt
nb_igfem_nodes
=
mesh
.
getNbNodes
()
-
nb_regular_nodes
;
/// adjust the positions of the node to have an exact straight line
Array
<
Real
>
&
nodes
=
const_cast
<
Array
<
Real
>
&>
(
mesh
.
getNodes
());
Array
<
Real
>::
vector_iterator
nodes_it
=
nodes
.
begin
(
spatial_dimension
);
nodes_it
+=
nb_regular_nodes
;
for
(
UInt
i
=
0
;
i
<
nb_igfem_nodes
;
++
i
,
++
nodes_it
)
{
Vector
<
Real
>
&
node_coords
=
*
nodes_it
;
node_coords
(
0
)
=
0.25
;
Int
multiplier
=
std
::
round
(
node_coords
(
1
)
/
0.25
);
node_coords
(
1
)
=
0.25
*
multiplier
;
}
/// reinitialize the shape functions because node coordinates have changed
model
.
getFEEngine
(
"IGFEMFEEngine"
).
initShapeFunctions
(
_not_ghost
);
model
.
getFEEngine
(
"IGFEMFEEngine"
).
initShapeFunctions
(
_ghost
);
/// dump mesh after the IGFEM interface is created
model
.
dump
();
model
.
dump
(
"igfem elements"
);
/// apply the boundary conditions: left and bottom side on rollers
/// imposed displacement along right side
mesh
.
computeBoundingBox
();
const
Vector
<
Real
>
&
lower_bounds
=
mesh
.
getLowerBounds
();
const
Vector
<
Real
>
&
upper_bounds
=
mesh
.
getUpperBounds
();
Real
bottom
=
lower_bounds
(
1
);
Real
left
=
lower_bounds
(
0
);
Real
right
=
upper_bounds
(
0
);
Real
eps
=
std
::
abs
((
right
-
left
)
*
1e-6
);
const
Array
<
Real
>
&
pos
=
mesh
.
getNodes
();
Array
<
Real
>
&
disp
=
model
.
getDisplacement
();
Array
<
bool
>
&
boun
=
model
.
getBlockedDOFs
();
for
(
UInt
i
=
0
;
i
<
mesh
.
getNbNodes
();
++
i
)
{
if
(
std
::
abs
(
pos
(
i
,
1
)
-
bottom
)
<
eps
)
{
boun
(
i
,
1
)
=
true
;
disp
(
i
,
1
)
=
0.0
;
}
if
(
std
::
abs
(
pos
(
i
,
0
)
-
left
)
<
eps
)
{
boun
(
i
,
0
)
=
true
;
disp
(
i
,
0
)
=
0.0
;
}
if
(
std
::
abs
(
pos
(
i
,
0
)
-
right
)
<
eps
)
{
boun
(
i
,
0
)
=
true
;
disp
(
i
,
0
)
=
1.0
;
}
}
/// compute the volume of the mesh
Real
int_volume
=
0.
;
std
::
map
<
ElementKind
,
FEEngine
*>
fe_engines
=
model
.
getFEEnginesPerKind
();
std
::
map
<
ElementKind
,
FEEngine
*>::
const_iterator
fe_it
=
fe_engines
.
begin
();
for
(;
fe_it
!=
fe_engines
.
end
();
++
fe_it
)
{
ElementKind
kind
=
fe_it
->
first
;
FEEngine
&
fe_engine
=
*
(
fe_it
->
second
);
Mesh
::
type_iterator
it
=
mesh
.
firstType
(
spatial_dimension
,
_not_ghost
,
kind
);
Mesh
::
type_iterator
last_type
=
mesh
.
lastType
(
spatial_dimension
,
_not_ghost
,
kind
);
for
(;
it
!=
last_type
;
++
it
)
{
ElementType
type
=
*
it
;
Array
<
Real
>
Volume
(
mesh
.
getNbElement
(
type
)
*
fe_engine
.
getNbIntegrationPoints
(
type
),
1
,
1.
);
int_volume
+=
fe_engine
.
integrate
(
Volume
,
type
);
}
}
if
(
!
Math
::
are_float_equal
(
int_volume
,
4
))
{
std
::
cout
<<
"Error in area computation of the 2D mesh"
<<
std
::
endl
;
return
EXIT_FAILURE
;
}
std
::
cout
<<
"the area of the mesh is: "
<<
int_volume
<<
std
::
endl
;
/// solve the system
model
.
assembleStiffnessMatrix
();
Real
error
=
0
;
bool
converged
=
false
;
bool
factorize
=
false
;
converged
=
model
.
solveStep
<
_scm_newton_raphson_tangent
,
SolveConvergenceCriteria
::
_increment
>
(
1e-12
,
error
,
2
,
factorize
);
if
(
!
converged
)
{
std
::
cout
<<
"The solver did not converge!!! The error is: "
<<
error
<<
std
::
endl
;
finalize
();
return
EXIT_FAILURE
;
}
/// dump the deformed mesh
model
.
dump
();
model
.
dump
(
"igfem elements"
);
Real
L2_error
=
computeL2Error
(
model
);
std
::
cout
<<
"Error: "
<<
L2_error
<<
std
::
endl
;
if
(
L2_error
>
1e-12
)
{
finalize
();
std
::
cout
<<
"The patch test did not pass!!!!"
<<
std
::
endl
;
return
EXIT_FAILURE
;
}
finalize
();
return
EXIT_SUCCESS
;
}
/* -------------------------------------------------------------------------- */
Real
computeL2Error
(
SolidMechanicsModelIGFEM
&
model
)
{
/// store the error on each element for visualization
ElementTypeMapReal
error_per_element
(
"error_per_element"
);
Real
error
=
0
;
Real
normalization
=
0
;
/// Young's moduli for the two materials
Real
E_1
=
10.
;
Real
E_2
=
1.
;
Mesh
&
mesh
=
model
.
getMesh
();
UInt
spatial_dimension
=
mesh
.
getSpatialDimension
();
mesh
.
addDumpFieldExternal
(
"error_per_element"
,
error_per_element
,
spatial_dimension
,
_not_ghost
,
_ek_regular
);
mesh
.
addDumpFieldExternalToDumper
(
"igfem elements"
,
"error_per_element"
,
error_per_element
,
spatial_dimension
,
_not_ghost
,
_ek_igfem
);
ElementTypeMapReal
quad_coords
(
"quad_coords"
);
GhostType
ghost_type
=
_not_ghost
;
const
std
::
map
<
ElementKind
,
FEEngine
*>
&
fe_engines
=
model
.
getFEEnginesPerKind
();
std
::
map
<
ElementKind
,
FEEngine
*>::
const_iterator
fe_it
=
fe_engines
.
begin
();
for
(;
fe_it
!=
fe_engines
.
end
();
++
fe_it
)
{
ElementKind
kind
=
fe_it
->
first
;
FEEngine
&
fe_engine
=
*
(
fe_it
->
second
);
mesh
.
initElementTypeMapArray
(
quad_coords
,
spatial_dimension
,
spatial_dimension
,
false
,
kind
,
true
);
mesh
.
initElementTypeMapArray
(
error_per_element
,
1
,
spatial_dimension
,
false
,
kind
,
true
);
fe_engine
.
computeIntegrationPointsCoordinates
(
quad_coords
);
Mesh
::
type_iterator
it
=
mesh
.
firstType
(
spatial_dimension
,
ghost_type
,
kind
);
Mesh
::
type_iterator
last_type
=
mesh
.
lastType
(
spatial_dimension
,
ghost_type
,
kind
);
for
(;
it
!=
last_type
;
++
it
)
{
ElementType
type
=
*
it
;
UInt
nb_elements
=
mesh
.
getNbElement
(
type
,
ghost_type
);
UInt
nb_quads
=
fe_engine
.
getNbIntegrationPoints
(
type
);
/// interpolate the displacement at the quadrature points
Array
<
Real
>
displ_on_quads
(
nb_quads
*
nb_elements
,
spatial_dimension
,
"displ_on_quads"
);
Array
<
Real
>
quad_coords
(
nb_quads
*
nb_elements
,
spatial_dimension
,
"quad_coords"
);
fe_engine
.
interpolateOnIntegrationPoints
(
model
.
getDisplacement
(),
displ_on_quads
,
spatial_dimension
,
type
);
fe_engine
.
computeIntegrationPointsCoordinates
(
quad_coords
,
type
,
ghost_type
);
Array
<
Real
>
&
el_error
=
error_per_element
(
type
,
ghost_type
);
Array
<
Real
>::
const_vector_iterator
displ_it
=
displ_on_quads
.
begin
(
spatial_dimension
);
Array
<
Real
>::
const_vector_iterator
coord_it
=
quad_coords
.
begin
(
spatial_dimension
);
Vector
<
Real
>
error_vec
(
spatial_dimension
);
for
(
UInt
e
=
0
;
e
<
nb_elements
;
++
e
)
{
Vector
<
Real
>
error_per_quad
(
nb_quads
);
Vector
<
Real
>
normalization_per_quad
(
nb_quads
);
for
(
UInt
q
=
0
;
q
<
nb_quads
;
++
q
,
++
displ_it
,
++
coord_it
)
{
Real
exact
=
0.
;
Real
x
=
(
*
coord_it
)(
0
);
if
(
x
<
0.25
)
exact
=
(
4.
*
x
*
E_2
)
/
(
3.
*
E_1
+
5.
*
E_2
)
+
(
4.
*
E_2
)
/
(
3.
*
E_1
+
5.
*
E_2
);
else
exact
=
4.
*
x
*
E_1
/
(
3.
*
E_1
+
5.
*
E_2
)
-
(
E_1
-
5.
*
E_2
)
/
(
3.
*
E_1
+
5.
*
E_2
);
error_vec
=
*
displ_it
;
error_vec
(
0
)
-=
exact
;
error_per_quad
(
q
)
=
error_vec
.
dot
(
error_vec
);
normalization_per_quad
(
q
)
=
std
::
abs
(
exact
)
*
std
::
abs
(
exact
);
std
::
cout
<<
error_vec
<<
std
::
endl
;
}
/// integrate the error in the element and the corresponding
/// normalization
Real
int_error
=
fe_engine
.
integrate
(
error_per_quad
,
type
,
e
,
ghost_type
);
error
+=
int_error
;
el_error
(
e
)
=
std
::
sqrt
(
int_error
);
normalization
+=
fe_engine
.
integrate
(
normalization_per_quad
,
type
,
e
,
ghost_type
);
}
}
}
model
.
dump
();
model
.
dump
(
"igfem elements"
);
return
(
std
::
sqrt
(
error
)
/
std
::
sqrt
(
normalization
));
}
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