From: bangerth Date: Fri, 5 Feb 2010 17:59:20 +0000 (+0000) Subject: Some more words. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=d652b4e017d992e99eeaf49632bbc94a11472a06;p=dealii-svn.git Some more words. git-svn-id: https://svn.dealii.org/trunk@20516 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-16/doc/intro.dox b/deal.II/examples/step-16/doc/intro.dox index e86be0b0b6..f09995f383 100644 --- a/deal.II/examples/step-16/doc/intro.dox +++ b/deal.II/examples/step-16/doc/intro.dox @@ -12,32 +12,43 @@ multigrid algorithms on adaptively refined meshes. This example shows the basic usage of the multilevel functions in -deal.II. It solves the Poisson equation with Dirichlet boundary -conditions similar to @ref step_5 "step-5". - - - In order to allow sufficient flexibility in conjunction with systems of +deal.II. It solves the same problem as used in @ref step_6 "step-6", +but demonstrating the things one has to provide when using multigrid +as a preconditioner. In particular, this requires that we define a +hierarchy of levels, provide transfer operators from one level to the +next and back, and provide representations of the Laplace operator on +each level. + +In order to allow sufficient flexibility in conjunction with systems of differential equations and block preconditioners, quite a few different objects -have to be created before starting the multilevel method. These are +have to be created before starting the multilevel method, although +most of what needs to be done is provided by deal.II itself. These are +Most of these objects will only be needed inside the function that +actually solves the linear system. There, these objects are combined +in an object of type Multigrid, containing the implementation of the +V-cycle, which is in turn used by the preconditioner PreconditionMG, +ready for plug-in into a linear solver of the LAC library. +The multilevel method in deal.II follows in many respects the outlines +of the various publications by James Bramble, Joseph Pasciak and +Jinchao Xu (i.e. the "BPX" framework). In order to understand many of +the options, a rough familiarity with their work is quite helpful. +However, in comparison to this framework, the implementation in +deal.II has to take into account the fact that we want to solve linear +systems on adaptively refined meshes. This leads to the complication +that it isn't quite as clear any more what exactly a "level" in a +multilevel hierarchy of a mesh is. -These objects are combined in an object of type Multigrid, containing the -implementation of the V-cycle, which is in turn used by the preconditioner -PreconditionMG, ready for plug-in into a linear solver of the LAC library. - - - -The multilevel method in deal.II follows in many respects the outlines -of the various publications by James Bramble, Joseph Pasciak and Jinchao Xu. In -order to understand many of the options, a rough familiarity with their work is -quite helpful.