From 880f2ce3df77afdb0bc6498f5a5cd27d2545fd19 Mon Sep 17 00:00:00 2001 From: kanschat Date: Wed, 29 Sep 2010 15:22:27 +0000 Subject: [PATCH] Write a bit on multilevel matrices... to be continued git-svn-id: https://svn.dealii.org/trunk@22193 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/doc/doxygen/headers/mg.h | 41 +++++++++++++++++++++++++++++--- 1 file changed, 38 insertions(+), 3 deletions(-) diff --git a/deal.II/doc/doxygen/headers/mg.h b/deal.II/doc/doxygen/headers/mg.h index 071ad2eaa6..ab162e9d50 100644 --- a/deal.II/doc/doxygen/headers/mg.h +++ b/deal.II/doc/doxygen/headers/mg.h @@ -2,7 +2,7 @@ // $Id$ // Version: $Name$ // -// Copyright (C) 2003, 2005, 2006, 2009 by the deal.II authors +// Copyright (C) 2003, 2005, 2006, 2009, 2010 by the deal.II authors // // This file is subject to QPL and may not be distributed // without copyright and license information. Please refer @@ -37,9 +37,44 @@ * global vector and the level vectors. * * Finally, we have several auxiliary classes, namely MGLevelObject, - * which stores an object on each level + * which stores an object on each level* * - * See the step-16 example program on how to use this + * See the step-16 and step-39 example programs on how to use this * functionality. + + *

Multigrid and hanging nodes

+ * + * Using multigrid methods on adaptively refined meshes involves + * more infrastructure than with regular refinement. First, in order + * to keep the complexity optimal, we need to decide how to do the + * smoothing on each level. And to this end, we have to define what a + * level is in the sense of multilevel decomposition. + * + * First, we define that a level in the multigrid sense is constituted + * by all cells of a certain level in the mesh hierarchy. Thus, + * smoothing on a certain level is restricted to the subdomain which + * consists of cells of this level or finer. This is usually referred + * to as local smoothing. The advantage of this definition is, that + * level matrices for the multigrid scheme can be assembled easily by + * traversing to all cells of a certain level, and that these level + * matrices do not contain hanging nodes. + * + * The disadvantage of this decomposition is, that we need additional + * matrices to handle the issues that arise at refinement + * edges. Furthermore, the treatment is different, depending on + * whether the method is continuous (thus having degrees of freedom on + * the refinement edge) or discontinuous (employs flux matrices at the + * refinement edge). While these matrices are small, we have to + * assemble them and notify the multigrid method of them. */ +/** + * This namespace contains the reimplementation of multilevel support + * after we know what is needed in the context of local refinement and + * block systems. + * + * @ingroup mg + */ +namespace mg +{ +} -- 2.39.5