From: Martin Kronbichler Date: Wed, 18 Sep 2013 07:07:32 +0000 (+0000) Subject: Improve documentation of positive entries for constrained entries. X-Git-Tag: v8.1.0~783 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=e4e62eb131eede2b2a44f8fec610f168c944fb20;p=dealii.git Improve documentation of positive entries for constrained entries. git-svn-id: https://svn.dealii.org/trunk@30784 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/doc/doxygen/headers/constraints.h b/deal.II/doc/doxygen/headers/constraints.h index 999a97659e..0925516053 100644 --- a/deal.II/doc/doxygen/headers/constraints.h +++ b/deal.II/doc/doxygen/headers/constraints.h @@ -26,7 +26,7 @@ * Constraints typically come from several sources, for example: * - If you have Dirichlet-type boundary conditions, $u|_{\partial\Omega}=g$, * one usually enforces - * them by requiring that that degrees of freedom on the boundary have + * them by requiring that degrees of freedom on the boundary have * particular values, for example $x_{12}=42$ if the boundary condition * $g(\mathbf x)$ requires that the finite element solution $u(\mathbf x)$ * at the location of degree @@ -113,6 +113,13 @@ * below. The resulting linear systems are equivalent to those one gets after * calling the ConstraintMatrix::condense() functions. * + * @note Both ways of applying constraints set the value of the matrix + * diagonals to constrained entries to a positive entry of the same + * magnitude as the other entries in the matrix. As a consequence, you need to + * set up your problem such that the weak form describing the main matrix + * contribution is not negative definite. Otherwise, iterative solvers + * such as CG will break down or be considerably slower as GMRES. + * * @note While these two ways are equivalent, i.e., the solution of * linear systems computed via either approach is the same, the linear * systems themselves do not necessarily have the same matrix and right @@ -121,7 +128,6 @@ * as a result of the way in which we compute them; they are, however, always * chosen in such a way that the solution to the linear system is the same. * - * *

Condensing matrices and sparsity patterns

* * As mentioned above, the first way of using constraints is to build linear