From: bangerth Date: Sat, 29 Oct 2011 11:08:55 +0000 (+0000) Subject: Minor adjustments. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=84afbd5ccf2be68ff0aefb43922ebfbe3fd98553;p=dealii-svn.git Minor adjustments. git-svn-id: https://svn.dealii.org/trunk@24686 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/doc/doxygen/headers/main.h b/deal.II/doc/doxygen/headers/main.h index d72b164db2..8bed63010d 100644 --- a/deal.II/doc/doxygen/headers/main.h +++ b/deal.II/doc/doxygen/headers/main.h @@ -22,17 +22,18 @@ * href="../tutorial/index.html">tutorial programs on the use of this * library. * - * Many of the classes in the deal.II library can be grouped into - * modules (see the Modules page or the - * corresponding entry in the menu at the top of this page). These - * modules follow roughly the following collaboration diagram that - * finite element programs follow: + * Many of the classes in the deal.II library can be grouped into modules (see + * the Modules page or the corresponding entry in + * the menu at the top of this page). These modules form around the building + * blocks of any finite element program. An outline of how the primary groups + * of classes in deal.II interact is given by the following clickable graph, + * with a more detailed description below: * * @dot digraph G { graph[rankdir="TB",bgcolor="transparent"]; - + edge [fontname="FreeSans",fontsize=15,labelfontname="FreeSans",labelfontsize=10]; node [fontname="FreeSans",fontsize=15, shape=record,height=0.2,width=0.4, @@ -44,8 +45,8 @@ Quadrature [label="Quadrature",URL="\ref Quadrature"]; Mapping [label="Mapping",URL="\ref mapping"]; FEValues [label="FEValues",URL="\ref feaccess"]; - Linear [label="Discrete System",URL="\ref LAC"]; - LinearSolver [label="Solver",URL="\ref Solvers"]; + Linear [label="Linear Systems",URL="\ref LAC"]; + LinearSolver [label="Linear Solvers",URL="\ref Solvers"]; Output [label="Output",URL="\ref output"]; Tria -> DoFHandler [color="black",fontsize=10,style="solid",fontname="FreeSans"]; @@ -122,8 +123,16 @@ * each vertex, line, or cell of the triangulation has the correct * number of them. It also gives them a global numbering. * + * A different viewpoint is this: While the mesh and finite element + * describe abstract properties of the the finite dimensional space + * $V_h$ in which we seek the discrete solution, the %DoFHandler + * classes enumerate a concrete basis of this space so that we can + * represent the discrete solution as $u_h(\mathbf x)= + * \sum_j U_j \varphi_i(\mathbf x)$ by an ordered set of coefficients + * $U_j$. + * * Just as with triangulation objects, most operations on - * DoFHandlers is done by looping over all cells and doing something + * DoFHandlers are done by looping over all cells and doing something * on each or a subset of them. The interfaces of the two classes are * therefore rather similar: they allow to get iterators to the * first and last cell (or face, or line, etc) and offer information @@ -143,7 +152,8 @@ * functions that correspond to the degrees of freedom it manages: * all it knows is that there are, for example, 2 degrees of freedom * for each vertex and 4 per cell interior. Nothing about their - * specifics is relevant to the DoFHandler class. + * specifics is relevant to the DoFHandler class with the exception of + * the fact that they exist. * * The DoFHandler class and its associates are described in the @ref * dofs module. In addition, there are specialized versions that can @@ -198,7 +208,7 @@ * module. * * - *
  • Linear System: If one knows how to evaluate the + *
  • Linear Systems: If one knows how to evaluate the * values and gradients of shape functions on individual cells using * FEValues and friends, and knows how to get the global numbers of * the degrees of freedom on a cell using the DoFHandler iterators, @@ -214,7 +224,7 @@ * to this end can be found in the @ref LAC module. * * - *
  • Linear %Solver: In order to determine the solution of + *
  • Linear Solvers: In order to determine the solution of * a finite-dimensional, linear system of equations, one needs * linear solvers. In finite element applications, they are * frequently iterative, but sometimes one may also want to use @@ -225,7 +235,7 @@ *
  • Output: Finally, once one has obtained a solution of * a finite element problem on a given triangulation, one will often * want to postprocess it using a visualization program. This - * library doesn't do that by itself, but rather generates output + * library doesn't do the visualization by itself, but rather generates output * files in a variety of graphics formats understood by widely * available visualization tools. * @@ -241,5 +251,6 @@ * finite element programs, but appear there as well. These classes * are all listed in the Classes and Namespaces views reachable from * the menu bar at the top of this page, and are also grouped into - * modules of their own (see the Modules view also in the menu bar). + * modules of their own (see the Modules linke + * at the top of this page). */