algebraic multigrid (AMG) can now no longer be used here because their
implementation requires knowledge of the elements of the system matrix.
-One solution is to use multigrid methods as shown in @ref step_16
-"step-16". They are known to be very fast, and they are suitable for our
+One solution is to use multigrid methods as shown in
+step-16. They are known to be very fast, and they are suitable for our
purpose since they can be designed based purely on matrix-vector products. All
one needs to do is to find a smoother that works with matrix-vector products
only (our choice requires knowledge of the diagonal entries of the matrix,
be parallelized by working on diagonal sub-blocks of the matrix, which
decreases efficiency.
-The implementation into the multigrid framework is then straightforward. We
-will only need some minor modifications compared to step-16.
+The implementation into the multigrid framework is then straightforward. This
+program is based on an earlier version of step-16 that demonstrated multigrid
+on uniformly refined grids. However, the present matrix-free techniques would
+obviously also apply to the adaptive meshes the current step-16 uses.
+
<h3>The test case</h3>