Since the program did not really deliver the goal we had originally intended
for (the computation of the minimal energy of finite element spaces), the
graphical output is also not very exciting. Here are plots of five of the
-first 10 solutions (clicking on a picture gives the unscaled version of the
-image):
+first 10 solutions:
@image html step-15.solution-1.png
As one would hope for, the x- (left) and y-displacements (right) shown here
closely match what we already saw in step-8. What may be more interesting,
-though, is to look at the mesh and partition at this step (to see the picture
-in its original size, simply click on it):
+though, is to look at the mesh and partition at this step:
@image html step-17.12-grid.png
The last step, going up to 1.5 million unknowns, takes about 55 minutes with
16 processes on 8 dual-processor machines. The graphical output generated by
this job is rather large (cycle 5 already prints around 82 MB of GMV data), so
-we contend ourselves with showing output from cycle 4 (again, clicking on the
-picture gives a version in original size):
+we contend ourselves with showing output from cycle 4:
@image html step-17.4-3d-partition.png
If we visualize these files with GMV, we get to see the full picture
-of the disaster our forced compression wreaks on the cylinder (click
-on the images for a larger version; colors in the images encode the
-norm of the stress in the material):
+of the disaster our forced compression wreaks on the cylinder (colors in the
+images encode the norm of the stress in the material):
<table width="100%">
similar, but quantitatively definitely different. The previous computation was
therefore certainly not converged, though we can't say for sure anything about
the present one. One would need an even finer computation to find out. However,
-the point may be moot: looking at the last picture in detail (click on it to
-see it in larger), it is pretty obvious that not only is the linear small
+the point may be moot: looking at the last picture in detail, it is pretty
+obvious that not only is the linear small
deformation model we chose completely inadequate, but for a realistic
simulation we would also need to make sure that the body does not intersects
itself during deformation. Without such a formulation we cannot expect anything
The fact that the number of iterations is so small, of course, is due to good
(but expensive!) preconditioner we have developed. To get confidence in the
solution, let us take a look at it. The following three images show (from left
-to right) the x-velocity, the y-velocity, and the pressure (click on the images
-for larger versions):
+to right) the x-velocity, the y-velocity, and the pressure:
@image html step-20.u.png
@image html step-20.v.png