From: Krishnakumar Gopalakrishnan Date: Mon, 13 Jan 2020 13:38:57 +0000 (+0000) Subject: In step 6 results doc, move the header file inclusion sentence to reflect that we... X-Git-Tag: v9.2.0-rc1~671^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=52733132452f730aa33defdf67c46c200a9b9eaf;p=dealii.git In step 6 results doc, move the header file inclusion sentence to reflect that we need it for Sparse_ILU and not Jacobi preconditioner Addresses reviewers comments for the PR --- diff --git a/examples/step-6/doc/results.dox b/examples/step-6/doc/results.dox index e6156f6cc7..d7c2c6a789 100644 --- a/examples/step-6/doc/results.dox +++ b/examples/step-6/doc/results.dox @@ -142,8 +142,6 @@ into preconditioner.initialize(system_matrix, 1.0); @endcode we can try out different relaxation parameters for SSOR. By using -(you have to also add the header file lac/sparse_ilu.h to -the include list at the top of the file) @code PreconditionJacobi<> preconditioner; preconditioner.initialize(system_matrix); @@ -153,8 +151,10 @@ we can use Jacobi as a preconditioner. And by using SparseILU preconditioner; preconditioner.initialize(system_matrix); @endcode -we can use a simple incomplete LU decomposition without any -thresholding or strengthening of the diagonal. +we can use a simple incomplete LU decomposition without any thresholding or +strengthening of the diagonal (to use this preconditioner, you have to also +add the header file deal.II/lac/sparse_ilu.h to the include list +at the top of the file). Using these various different preconditioners, we can compare the number of CG iterations needed (available through the @@ -504,12 +504,12 @@ methods because the mesh will have to resolve the singularity that causes the solution to not be in $W^{1,\infty}$ any more. The typical example one uses for this is called the Kellogg problem -(referring to @cite Kel74), which in the commonly used form has a coefficient -$a(\mathbf x)$ that has different values in the four quadrants of the plane -(or eight different values in the octants of ${\mathbb R}^3$). The exact degree -of regularity (the $s$ in the index of the Sobolev space above) depends on the -values of $a(\mathbf x)$ coming together at the origin, and by choosing the -jumps large enough, the regularity of the solution can be made as close as +(referring to @cite Kel74), which in the commonly used form has a coefficient +$a(\mathbf x)$ that has different values in the four quadrants of the plane +(or eight different values in the octants of ${\mathbb R}^3$). The exact degree +of regularity (the $s$ in the index of the Sobolev space above) depends on the +values of $a(\mathbf x)$ coming together at the origin, and by choosing the +jumps large enough, the regularity of the solution can be made as close as desired to $H^1$. To implement something like this, one could replace the coefficient