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manual-feengine.tex
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\chapter
{
FEEngine
\index
{
FEEngine
}}
\label
{
chap:feengine
}
The
\code
{
FEEngine
}
interface is dedicated to handle the
finite-element approximations and the numerical integration of the
weak form. As we will see in Chapter
\ref
{
sect:smm
}
,
\code
{
Model
}
creates its own
\code
{
FEEngine
}
object so the explicit creation of the
object is not required.
\section
{
Mathematical Operations
\label
{
sect:fe:mathop
}}
Using the
\code
{
FEEngine
}
object, one can compute a interpolation, an
integration or a gradient. A simple example is given below.
\begin
{
cpp
}
// having a FEEngine object
FEEngine *fem = new FEEngineTemplate<IntegratorGauss,ShapeLagrange>(my
_
mesh,
dim,
"my
_
fem");
// instead of this, a FEEngine object can be get using the model:
// model.getFEEngine()
//compute the gradient
Array<Real> u; //append the values you want
Array<Real> nablauq; //gradient array to be computed
// compute the gradient
fem->gradientOnIntegrationPoints(const Array<Real>
&
u,
Array<Real>
&
nablauq,
const UInt nb
_
degree
_
of
_
freedom,
ElementType type);
// interpolate
Array<Real> uq; //interpolated array to be computed
// compute the interpolation
fem->interpolateOnIntegrationPoints(const Array<Real>
&
u,
Array<Real>
&
uq,
UInt nb
_
degree
_
of
_
freedom,
ElementType type);
// interpolated function can be integrated over the elements
Array<Real> int
_
val
_
on
_
elem;
// integrate
fem->integrate(const Array<Real>
&
uq,
Array<Real>
&
int
_
uq,
UInt nb
_
degree
_
of
_
freedom,
ElementType type);
\end
{
cpp
}
Another example below shows how to integrate stress and strain fields
over elements assigned to a particular material.
\begin
{
cpp
}
UInt sp
_
dim = 3; //spatial dimension
UInt m = 1; //material index of interest
const ElementType type =
_
tetrahedron
_
4; //element type
// get the stress and strain arrays associated to the material index m
const Array<Real>
&
strain
_
vec = model.getMaterial(m).getGradU(type);
const Array<Real>
&
stress
_
vec = model.getMaterial(m).getStress(type);
// get the element filter for the material index
const Array<UInt>
&
elem
_
filter = model.getMaterial(m).getElementFilter(type);
// initialize the integrated stress and strain arrays
Array<Real> int
_
strain
_
vec(elem
_
filter.getSize(),
sp
_
dim*sp
_
dim, "int
_
of
_
strain");
Array<Real> int
_
stress
_
vec(elem
_
filter.getSize(),
sp
_
dim*sp
_
dim, "int
_
of
_
stress");
// integrate the fields
model.getFEEngine().integrate(strain
_
vec, int
_
strain
_
vec,
sp
_
dim*sp
_
dim, type,
_
not
_
ghost, elem
_
filter);
model.getFEEngine().integrate(stress
_
vec, int
_
stress
_
vec,
sp
_
dim*sp
_
dim, type,
_
not
_
ghost, elem
_
filter);
\end
{
cpp
}
\input
{
manual-elements
}
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