* href="../tutorial/index.html">tutorial programs on the use of this
* library</a>.
*
- * Many of the classes in the deal.II library can be grouped into
- * modules (see the <a href="modules.html">Modules page</a> 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 <a href="modules.html">Modules page</a> 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,
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"];
* 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
* 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
* module.
*
*
- * <li> <b>Linear System</b>: If one knows how to evaluate the
+ * <li> <b>Linear Systems</b>: 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,
* to this end can be found in the @ref LAC module.
*
*
- * <li> <b>Linear %Solver</b>: In order to determine the solution of
+ * <li> <b>Linear Solvers</b>: 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
* <li> <b>Output</b>: 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.
*
* 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 <a href="modules.html">Modules linke</a>
+ * at the top of this page).
*/