Discuss the reason why we even use such a complicated solver.

This seems to perpetually unsettle my students as they think that one
can only solve coupled systems using block solvers (step-20 is the
first coupled problem they encounter). But this is not true -- one
can just use a direct solver, for example.

diff --git a/examples/step-20/doc/intro.dox b/examples/step-20/doc/intro.dox
index dbea94c6031c66a5894d3346e94a0dca67302e4c..b1e3ba846dbe1ae6b2094463b2ca0cb26a9b5717 100644 (file)
--- a/examples/step-20/doc/intro.dox
+++ b/examples/step-20/doc/intro.dox
@@ -351,7 +351,14 @@ the next problem immediately surfaces: due to the zero block, there are zeros
 on the diagonal and none of the usual preconditioners (Jacobi, SSOR) will work
 as they require division by diagonal elements.
 
-In the following, we will introduce some techniques that can be used in cases
+For the matrix sizes we expect to run with this program, the by far simplest
+approach would be to just use a direct solver (in particular, the 
+SparseDirectUMFPACK class that is bundled with deal.II). step-29 goes this
+route and shows that solving <i>any</i> linear system can be done in just
+3 or 4 lines of code. 
+
+But then, this is a tutorial: we teach how to do things. Consequently,
+in the following, we will introduce some techniques that can be used in cases
 like these. Namely, we will consider the linear system as not consisting of one
 large matrix and vectors, but we will want to decompose matrices into vectors
 into <i>blocks</i> that correspond to the individual operators that appear in