| 130 |
method!FEM}). The basic idea is to fill the domain with a |
method!FEM}). The basic idea is to fill the domain with a |
| 131 |
set of points called nodes. The solution is approximated by its |
set of points called nodes. The solution is approximated by its |
| 132 |
values on the nodes\index{finite element |
values on the nodes\index{finite element |
| 133 |
method!nodes}. Moreover, the domain is subdivided into small, |
method!nodes}. Moreover, the domain is subdivided into smaller |
| 134 |
sub-domain called elements \index{finite element |
sub-domains called elements \index{finite element |
| 135 |
method!element}. On each element the solution is |
method!element}. On each element the solution is |
| 136 |
represented by a polynomial of a certain degree through its values at |
represented by a polynomial of a certain degree through its values at |
| 137 |
the nodes located in the element. The nodes and its connection through |
the nodes located in the element. The nodes and its connection through |
| 181 |
we need to construct a function \var{gammaD} which is positive for the cases $x\hackscore{0}=0$ or $x\hackscore{1}=0$. To get |
we need to construct a function \var{gammaD} which is positive for the cases $x\hackscore{0}=0$ or $x\hackscore{1}=0$. To get |
| 182 |
an object \var{x} which represents locations in the domain one uses |
an object \var{x} which represents locations in the domain one uses |
| 183 |
\begin{python} |
\begin{python} |
| 184 |
x=mydomain.getX() \;. |
x=mydomain.getX() |
| 185 |
\end{python} |
\end{python} |
| 186 |
In fact \var{x} is a \Data object which we will learn more about in Chapter~\ref{X}. At this stage we only have to know |
In fact \var{x} is a \Data object which we will learn more about in Chapter~\ref{X}. At this stage we only have to know |
| 187 |
that \var{x} has a |
that \var{x} has a |
| 226 |
\end{python} |
\end{python} |
| 227 |
We can now construct the function \var{gammaD} by |
We can now construct the function \var{gammaD} by |
| 228 |
\begin{python} |
\begin{python} |
| 229 |
|
from esys.escript import whereZero |
| 230 |
gammaD=whereZero(x[0])+whereZero(x[1]) |
gammaD=whereZero(x[0])+whereZero(x[1]) |
| 231 |
\end{python} |
\end{python} |
| 232 |
where |
where |
| 253 |
x = mydomain.getX() |
x = mydomain.getX() |
| 254 |
gammaD = whereZero(x[0])+whereZero(x[1]) |
gammaD = whereZero(x[0])+whereZero(x[1]) |
| 255 |
mypde = Poisson(domain=mydomain) |
mypde = Poisson(domain=mydomain) |
| 256 |
mypde = setValue(f=1,q=gammaD) |
mypde.setValue(f=1,q=gammaD) |
| 257 |
\end{python} |
\end{python} |
| 258 |
The first statement imports the \Poisson class definition form the \linearPDEs module \escript package. |
The first statement imports the \Poisson class definition from the \linearPDEs module \escript package. |
| 259 |
To get the solution of the Poisson equation defined by \var{mypde} we just have to call its |
To get the solution of the Poisson equation defined by \var{mypde} we just have to call its |
| 260 |
\method{getSolution}. |
\method{getSolution}. |
| 261 |
|
|
| 281 |
The last statement writes the solution tagged with the name "sol" to the external file \file{u.xml} in |
The last statement writes the solution tagged with the name "sol" to the external file \file{u.xml} in |
| 282 |
\VTK file format. \VTK is a software library |
\VTK file format. \VTK is a software library |
| 283 |
for the visualization of scientific, engineering and analytical data and is freely available |
for the visualization of scientific, engineering and analytical data and is freely available |
| 284 |
from \url{http://www.vtk.org}. There are a variaty of graphical user interfaces |
from \url{http://www.vtk.org}. There are a variety of graphical user interfaces |
| 285 |
for \VTK available, for instance \mayavi which can be downloaded from \url{http://mayavi.sourceforge.net/} but is also available on most |
for \VTK available, for instance \mayavi which can be downloaded from \url{http://mayavi.sourceforge.net/} but is also available on most |
| 286 |
\LINUX distributions. |
\LINUX distributions. |
| 287 |
|
|
| 288 |
\begin{figure} |
\begin{figure} |
| 289 |
\centerline{\includegraphics[width=\figwidth]{FirstStepResult.eps}} |
\centerline{\includegraphics[width=\figwidth]{FirstStepResult.eps}} |
| 290 |
\caption{Visualization of the Possion Equation Solution for $f=1$} |
\caption{Visualization of the Poisson Equation Solution for $f=1$} |
| 291 |
\label{fig:FirstSteps.3} |
\label{fig:FirstSteps.3} |
| 292 |
\end{figure} |
\end{figure} |
| 293 |
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