<h3>Possibilities for extensions</h3>
Computing on surfaces only becomes interesting if the surface is more
-interesting than just 5/6th of a sphere. To achieve this, deal.II can read
+interesting than just a half sphere. To achieve this, deal.II can read
meshes that describe surfaces through the usual GridIn class. Or, in case you
have an analytic description, a simple mesh can sometimes be stretched and
bent into a shape we are interested in.
-Let us consider a relatively simple example: we take the 5/6th sphere we used
+Let us consider a relatively simple example: we take the half sphere we used
before, we stretch it by a factor of 10 in the z-direction, and then we jumble
the x- and y-coordinates a bit. Let's show the computational domain and the
solution first before we go into details of the implementation below:
@endcode
If we followed the <code>LaplaceBeltrami::make_grid_and_dofs</code> function, we would
-extract the 5/6th spherical surface mesh as before, warp it into the shape we
+extract the half spherical surface mesh as before, warp it into the shape we
want, and refine as often as necessary. This is not quite as simple as we'd
like here, though: refining requires that we have an appropriate manifold
object attached to the triangulation that describes where new vertices of the
transformation above (yielding the spherical surface again), finding the
location of a new point on the sphere, and then re-warping the result. But I'm
a lazy person, and since doing this is not really the point here, let's just
-make our lives a bit easier: we'll extract the 5/6th sphere, refine it as
+make our lives a bit easier: we'll extract the half sphere, refine it as
often as necessary, get rid of the object that describes the manifold since we
now no longer need it, and then finally warp the mesh. With the function
above, this would look as follows:
projects / dealii-svn.git / commitdiff