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test_gradient.cc
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rAKA akantu
test_gradient.cc
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/**
* @file test_gradient.cc
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Fri Jun 17 2011
* @date last modification: Thu Jun 05 2014
*
* @brief test of the fem class
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014 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/>.
*
* @section DESCRIPTION
*
* This code is computing the gradient of a linear field and check that it gives
* a constant result. It also compute the gradient the coordinates of the mesh
* and check that it gives the identity
*
*/
/* -------------------------------------------------------------------------- */
#include "aka_common.hh"
#include "fe_engine.hh"
#include "mesh.hh"
#include "mesh_io.hh"
#include "mesh_io_msh.hh"
#include "shape_lagrange.hh"
#include "integrator_gauss.hh"
/* -------------------------------------------------------------------------- */
#include <cstdlib>
#include <fstream>
#include <iostream>
/* -------------------------------------------------------------------------- */
using
namespace
akantu
;
int
main
(
int
argc
,
char
*
argv
[])
{
akantu
::
initialize
(
argc
,
argv
);
debug
::
setDebugLevel
(
dblTest
);
const
ElementType
type
=
TYPE
;
UInt
dim
=
ElementClass
<
type
>::
getSpatialDimension
();
Real
eps
=
1e-12
;
std
::
cout
<<
"Epsilon : "
<<
eps
<<
std
::
endl
;
MeshIOMSH
mesh_io
;
Mesh
my_mesh
(
dim
);
std
::
stringstream
meshfilename
;
meshfilename
<<
type
<<
".msh"
;
mesh_io
.
read
(
meshfilename
.
str
(),
my_mesh
);
FEEngine
*
fem
=
new
FEEngineTemplate
<
IntegratorGauss
,
ShapeLagrange
>
(
my_mesh
,
dim
,
"my_fem"
);
std
::
stringstream
outfilename
;
outfilename
<<
"out_grad"
<<
type
<<
".txt"
;
std
::
ofstream
my_file
(
outfilename
.
str
().
c_str
());
fem
->
initShapeFunctions
();
std
::
cout
<<
*
fem
<<
std
::
endl
;
Real
alpha
[
2
][
3
]
=
{{
13
,
23
,
31
},
{
11
,
7
,
5
}};
/// create the 2 component field
const
Array
<
Real
>
&
position
=
fem
->
getMesh
().
getNodes
();
Array
<
Real
>
const_val
(
fem
->
getMesh
().
getNbNodes
(),
2
,
"const_val"
);
UInt
nb_element
=
my_mesh
.
getNbElement
(
type
);
UInt
nb_quadrature_points
=
fem
->
getNbQuadraturePoints
(
type
)
*
nb_element
;
Array
<
Real
>
grad_on_quad
(
nb_quadrature_points
,
2
*
dim
,
"grad_on_quad"
);
for
(
UInt
i
=
0
;
i
<
const_val
.
getSize
();
++
i
)
{
const_val
(
i
,
0
)
=
0
;
const_val
(
i
,
1
)
=
0
;
for
(
UInt
d
=
0
;
d
<
dim
;
++
d
)
{
const_val
(
i
,
0
)
+=
alpha
[
0
][
d
]
*
position
(
i
,
d
);
const_val
(
i
,
1
)
+=
alpha
[
1
][
d
]
*
position
(
i
,
d
);
}
}
/// compute the gradient
fem
->
gradientOnQuadraturePoints
(
const_val
,
grad_on_quad
,
2
,
type
);
my_file
<<
const_val
<<
std
::
endl
;
my_file
<<
grad_on_quad
<<
std
::
endl
;
std
::
cout
<<
grad_on_quad
<<
std
::
endl
;
/// check the results
Array
<
Real
>::
matrix_iterator
it
=
grad_on_quad
.
begin
(
2
,
dim
);
Array
<
Real
>::
matrix_iterator
it_end
=
grad_on_quad
.
end
(
2
,
dim
);
for
(;
it
!=
it_end
;
++
it
)
{
for
(
UInt
d
=
0
;
d
<
dim
;
++
d
)
{
Matrix
<
Real
>
&
grad
=
*
it
;
if
(
!
(
std
::
abs
(
grad
(
0
,
d
)
-
alpha
[
0
][
d
])
<
eps
)
||
!
(
std
::
abs
(
grad
(
1
,
d
)
-
alpha
[
1
][
d
])
<
eps
))
{
std
::
cout
<<
"Error gradient is not correct "
<<
(
*
it
)(
0
,
d
)
<<
" "
<<
alpha
[
0
][
d
]
<<
" ("
<<
std
::
abs
((
*
it
)(
0
,
d
)
-
alpha
[
0
][
d
])
<<
")"
<<
" - "
<<
(
*
it
)(
1
,
d
)
<<
" "
<<
alpha
[
1
][
d
]
<<
" ("
<<
std
::
abs
((
*
it
)(
1
,
d
)
-
alpha
[
1
][
d
])
<<
")"
<<
" - "
<<
d
<<
std
::
endl
;
std
::
cout
<<
*
it
<<
std
::
endl
;
exit
(
EXIT_FAILURE
);
}
}
}
// compute gradient of coordinates
Array
<
Real
>
grad_coord_on_quad
(
nb_quadrature_points
,
dim
*
dim
,
"grad_coord_on_quad"
);
fem
->
gradientOnQuadraturePoints
(
my_mesh
.
getNodes
(),
grad_coord_on_quad
,
my_mesh
.
getSpatialDimension
(),
type
);
my_file
<<
my_mesh
.
getNodes
()
<<
std
::
endl
;
my_file
<<
grad_coord_on_quad
<<
std
::
endl
;
Array
<
Real
>::
matrix_iterator
itp
=
grad_coord_on_quad
.
begin
(
dim
,
dim
);
Array
<
Real
>::
matrix_iterator
itp_end
=
grad_coord_on_quad
.
end
(
dim
,
dim
);
for
(;
itp
!=
itp_end
;
++
itp
)
{
for
(
UInt
i
=
0
;
i
<
dim
;
++
i
)
{
for
(
UInt
j
=
0
;
j
<
dim
;
++
j
)
{
if
(
!
(
std
::
abs
((
*
itp
)(
i
,
j
)
-
(
i
==
j
))
<
eps
))
{
std
::
cout
<<
*
itp
<<
std
::
endl
;
exit
(
EXIT_FAILURE
);
}
}
}
}
delete
fem
;
finalize
();
return
EXIT_SUCCESS
;
}
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