The next step is to convert this file or these files into whatever
format you like. The program that does this is the step-19 tutorial program:
-call it through
+for example, for the first time step, call it through
\begin{center}
- \texttt{../step-19/step-19 solution-0000.0000.*.d2 solution-0000-0000.gmv}
+ \texttt{../step-19/step-19 solution-0001.0000.*.d2 solution-0001.0000.gmv}
\end{center}
to merge all the intermediate format files into a single file in GMV
format. More details on the parameters of this program and what it can do for
\subsection*{Overall structure of the program}
+
+
\subsection*{Possible directions for extensions}
The program as is does not really solve an equation that has many applications
process a little more unpleasant.
-
-Make sure that cells are always well-formed
-
-Mention 3d in makefile.
+\paragraph*{Ensure mesh regularity.} At present, the program makes no attempt
+to make sure that a cell, after moving its vertices at the end of the time
+step, still has a valid geometry (i.e. that its Jacobian determinant is
+positive and bounded away from zero everywhere). It is, in fact, not very hard
+to set boundary values and forcing terms in such a way that one gets distorted
+and inverted cells rather quickly. Certainly, in some cases of large
+deformation, this is unavoidable with a mesh of finite mesh size, but in some
+other cases this should be preventable by appropriate mesh refinement and/or a
+reduction of the time step size. The program does not do that, but a more
+sophisticated version definitely should employ some sort of heuristic defining
+what amount of deformation of cells acceptable, and what isn't.
+
+
+\subsection*{Compiling the program}
+
+Finally, just to remind everyone: the program runs in 3d (see the definition
+of the \texttt{elastic\_problem} variable in \texttt{main()}, unlike almost all
+of the other example programs. While the compiler doesn't care what dimension
+it compiles for, the linker has to know which library to link with. And as
+explained in other places, this requires slight changes to the Makefile
+compared to the other tutorial programs. In particular, everywhere where the
+2d versions of libraries are mentioned, one needs to change this to
+3d. Conversely, if you want to run the program in 2d (after making the
+necessary changes to accomodate for a 2d geometry), you have to change the
+Makefile back to allow for 2d.
\end{document}