From: Wolfgang Bangerth Date: Tue, 9 Feb 2010 23:45:58 +0000 (+0000) Subject: Write more. X-Git-Tag: v8.0.0~6522 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=61be64148d8738ebec397687fc6aacc135d49eb4;p=dealii.git Write more. git-svn-id: https://svn.dealii.org/trunk@20530 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 f09995f383..5be8845f81 100644 --- a/deal.II/examples/step-16/doc/intro.dox +++ b/deal.II/examples/step-16/doc/intro.dox @@ -49,6 +49,42 @@ 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. +multilevel hierarchy of a mesh is. The following image shows what we +consider to be a "level": +

+ @image html "hanging_nodes.png" "" +

+In other words, the fine level in this mesh consists only of the +degrees of freedom that are defined on the refined cells, but does not +extend to that part of the domain that is not refined. While this +guarantees that the overall effort grows as ${\cal O}(N)$ as necessary +for optimal multigrid complexity, it leads to problems when defining +where to smooth and what boundary conditions to pose for the operators +defined on individual levels if the level boundary is not an external +boundary. These questions are discussed in detail in the +@ref mg_paper "Multigrid paper by Janssen and Kanschat" that describes +the implementation in deal.II. + + + +

The testcase

+ +The problem we solve here is exactly the same as in +@ref step_6 "step-6", the only difference being the solver we use +here. You may want to look there for a definition of what we solve, +right hand side and boundary conditions. Obviously, the program would +also work if we changed the geometry and other pieces of data that +defines this particular problem. + +The things that are new are all those parts that concern the +multigrid. In particular, this includes the following members of the +main class: +- LaplaceProblem::mg_dof_handler +- LaplaceProblem::mg_sparsity +- LaplaceProblem::mg_matrices +- LaplaceProblem::mg_interface_matrices_up +- LaplaceProblem::assemble_multigrid () +- LaplaceProblem::solve () +Take a look at these functions.