* such a way that the bandwidth of associated matrices is minimized. Finally,
* the DoFTools namespace offers a variety of algorithms around handling
* degrees of freedom.
+ *
+ * In the grand scheme of things, the pieces of this module interact
+ * with a variety of other parts of the library:
+ * @dot
+ digraph G
+{
+ graph[rankdir="TB",bgcolor="transparent"];
+
+ node [fontname="FreeSans",fontsize=15,
+ shape=record,height=0.2,width=0.4,
+ color="black", fillcolor="white", style="filled"];
+ edge [color="black", weight=10];
+
+ tria [label="Triangulation", URL="\ref grid"];
+ fe [label="Finite elements", URL="\ref feall"];
+ mapping [label="Mapping", URL="\ref mapping"];
+ quadrature [label="Quadrature", URL="\ref Quadrature"];
+ dh [label="DoFHandler", URL="\ref dofs", fillcolor="deepskyblue"];
+ fevalues [label="FEValues", URL="\ref feaccess"];
+ systems [label="Linear systems", URL="\ref LAC"];
+ solvers [label="Linear solvers", URL="\ref Solvers"];
+ output [label="Graphical output", URL="\ref output"];
+ manifold [label="Manifold", URL="\ref manifold"];
+
+ tria -> dh [color="black",style="solid"];
+ fe -> dh [color="black",style="solid"];
+ fe -> fevalues [color="black",style="solid"];
+ mapping -> fevalues [color="black",style="solid"];
+ quadrature -> fevalues [color="black",style="solid"];
+ dh -> systems [color="black",style="solid"];
+ fevalues -> systems [color="black",style="solid"];
+ systems -> solvers [color="black",style="solid"];
+ solvers -> output [color="black",style="solid"];
+ manifold -> tria [color="black",style="solid"];
+ manifold -> mapping [color="black",style="solid"];
+
+
+
+ node [fontname="FreeSans",fontsize=12,
+ shape=record,height=0.2,width=0.4,
+ color="gray55", fontcolor="gray55", fillcolor="white", style="filled"];
+ edge [color="gray55", weight=1];
+
+ opencascade [label="OpenCASCADE"];
+ opencascade -> manifold [dir="none"];
+
+
+ node [fontname="FreeSans",fontsize=12,
+ shape=ellipse,height=0.2,width=0.4,
+ color="gray55", fontcolor="gray55", fillcolor="white", style="filled"];
+ edge [color="gray55", weight=1];
+
+ gmsh [label="gmsh", URL="\ref Gmsh"];
+ gmsh -> tria [dir="none"];
+}
+ * @enddot
*/
* are discussed in their respective sub-modules listed above. In addition,
* the FETools class provides functions that provide information on finite
* elements, transformations between elements, etc.
+ *
+ * In the grand scheme of things, the pieces of this module interact
+ * with a variety of other parts of the library:
+ * @dot
+ digraph G
+{
+ graph[rankdir="TB",bgcolor="transparent"];
+
+ node [fontname="FreeSans",fontsize=15,
+ shape=record,height=0.2,width=0.4,
+ color="black", fillcolor="white", style="filled"];
+ edge [color="black", weight=10];
+
+ tria [label="Triangulation", URL="\ref grid"];
+ fe [label="Finite elements", URL="\ref feall", fillcolor="deepskyblue"];
+ mapping [label="Mapping", URL="\ref mapping"];
+ quadrature [label="Quadrature", URL="\ref Quadrature"];
+ dh [label="DoFHandler", URL="\ref dofs"];
+ fevalues [label="FEValues", URL="\ref feaccess"];
+ systems [label="Linear systems", URL="\ref LAC"];
+ solvers [label="Linear solvers", URL="\ref Solvers"];
+ output [label="Graphical output", URL="\ref output"];
+ manifold [label="Manifold", URL="\ref manifold"];
+
+ tria -> dh [color="black",style="solid"];
+ fe -> dh [color="black",style="solid"];
+ fe -> fevalues [color="black",style="solid"];
+ mapping -> fevalues [color="black",style="solid"];
+ quadrature -> fevalues [color="black",style="solid"];
+ dh -> systems [color="black",style="solid"];
+ fevalues -> systems [color="black",style="solid"];
+ systems -> solvers [color="black",style="solid"];
+ solvers -> output [color="black",style="solid"];
+ manifold -> tria [color="black",style="solid"];
+ manifold -> mapping [color="black",style="solid"];
+
+
+
+ node [fontname="FreeSans",fontsize=12,
+ shape=record,height=0.2,width=0.4,
+ color="gray55", fontcolor="gray55", fillcolor="white", style="filled"];
+ edge [color="gray55", weight=1];
+
+ opencascade [label="OpenCASCADE"];
+ opencascade -> manifold [dir="none"];
+
+
+ node [fontname="FreeSans",fontsize=12,
+ shape=ellipse,height=0.2,width=0.4,
+ color="gray55", fontcolor="gray55", fillcolor="white", style="filled"];
+ edge [color="gray55", weight=1];
+
+ gmsh [label="gmsh", URL="\ref Gmsh"];
+ gmsh -> tria [dir="none"];
+}
+ * @enddot
*/
* @ref UpdateFlags
* attempts to give an overview of how this works.
*
+ * In the grand scheme of things, the pieces of this module interact
+ * with a variety of other parts of the library:
+ * @dot
+ digraph G
+{
+ graph[rankdir="TB",bgcolor="transparent"];
+
+ node [fontname="FreeSans",fontsize=15,
+ shape=record,height=0.2,width=0.4,
+ color="black", fillcolor="white", style="filled"];
+ edge [color="black", weight=10];
+
+ tria [label="Triangulation", URL="\ref grid"];
+ fe [label="Finite elements", URL="\ref feall"];
+ mapping [label="Mapping", URL="\ref mapping"];
+ quadrature [label="Quadrature", URL="\ref Quadrature"];
+ dh [label="DoFHandler", URL="\ref dofs"];
+ fevalues [label="FEValues", URL="\ref feaccess", fillcolor="deepskyblue"];
+ systems [label="Linear systems", URL="\ref LAC"];
+ solvers [label="Linear solvers", URL="\ref Solvers"];
+ output [label="Graphical output", URL="\ref output"];
+ manifold [label="Manifold", URL="\ref manifold"];
+
+ tria -> dh [color="black",style="solid"];
+ fe -> dh [color="black",style="solid"];
+ fe -> fevalues [color="black",style="solid"];
+ mapping -> fevalues [color="black",style="solid"];
+ quadrature -> fevalues [color="black",style="solid"];
+ dh -> systems [color="black",style="solid"];
+ fevalues -> systems [color="black",style="solid"];
+ systems -> solvers [color="black",style="solid"];
+ solvers -> output [color="black",style="solid"];
+ manifold -> tria [color="black",style="solid"];
+ manifold -> mapping [color="black",style="solid"];
+
+
+
+ node [fontname="FreeSans",fontsize=12,
+ shape=record,height=0.2,width=0.4,
+ color="gray55", fontcolor="gray55", fillcolor="white", style="filled"];
+ edge [color="gray55", weight=1];
+
+ opencascade [label="OpenCASCADE"];
+ opencascade -> manifold [dir="none"];
+
+
+ node [fontname="FreeSans",fontsize=12,
+ shape=ellipse,height=0.2,width=0.4,
+ color="gray55", fontcolor="gray55", fillcolor="white", style="filled"];
+ edge [color="gray55", weight=1];
+
+ gmsh [label="gmsh", URL="\ref Gmsh"];
+ gmsh -> tria [dir="none"];
+}
+ * @enddot
+ *
* @ingroup feall
*/
* Finally, the MappingCartesian class is an optimization for elements that
* are brick-shaped and with edges parallel to the coordinate axes.
*
+ * In the grand scheme of things, the pieces of this module interact
+ * with a variety of other parts of the library:
+ * @dot
+ digraph G
+{
+ graph[rankdir="TB",bgcolor="transparent"];
+
+ node [fontname="FreeSans",fontsize=15,
+ shape=record,height=0.2,width=0.4,
+ color="black", fillcolor="white", style="filled"];
+ edge [color="black", weight=10];
+
+ tria [label="Triangulation", URL="\ref grid"];
+ fe [label="Finite elements", URL="\ref feall"];
+ mapping [label="Mapping", URL="\ref mapping", fillcolor="deepskyblue"];
+ quadrature [label="Quadrature", URL="\ref Quadrature"];
+ dh [label="DoFHandler", URL="\ref dofs"];
+ fevalues [label="FEValues", URL="\ref feaccess"];
+ systems [label="Linear systems", URL="\ref LAC"];
+ solvers [label="Linear solvers", URL="\ref Solvers"];
+ output [label="Graphical output", URL="\ref output"];
+ manifold [label="Manifold", URL="\ref manifold"];
+
+ tria -> dh [color="black",style="solid"];
+ fe -> dh [color="black",style="solid"];
+ fe -> fevalues [color="black",style="solid"];
+ mapping -> fevalues [color="black",style="solid"];
+ quadrature -> fevalues [color="black",style="solid"];
+ dh -> systems [color="black",style="solid"];
+ fevalues -> systems [color="black",style="solid"];
+ systems -> solvers [color="black",style="solid"];
+ solvers -> output [color="black",style="solid"];
+ manifold -> tria [color="black",style="solid"];
+ manifold -> mapping [color="black",style="solid"];
+
+
+
+ node [fontname="FreeSans",fontsize=12,
+ shape=record,height=0.2,width=0.4,
+ color="gray55", fontcolor="gray55", fillcolor="white", style="filled"];
+ edge [color="gray55", weight=1];
+
+ opencascade [label="OpenCASCADE"];
+ opencascade -> manifold [dir="none"];
+
+
+ node [fontname="FreeSans",fontsize=12,
+ shape=ellipse,height=0.2,width=0.4,
+ color="gray55", fontcolor="gray55", fillcolor="white", style="filled"];
+ edge [color="gray55", weight=1];
+
+ gmsh [label="gmsh", URL="\ref Gmsh"];
+ gmsh -> tria [dir="none"];
+}
+ * @enddot
+ *
* @ingroup feall
*/
* @defgroup grid Grid classes
*
* This module groups classes that have to do with the topology and
- * geometry of meshes. A mesh can be thought of a collection of cells;
+ * geometry of meshes. A mesh can be thought of as a collection of cells;
* if the mesh has been refined (possibly in an adaptive way), then
* this collection is grouped into a hierarchy of refinement
* levels. In addition to cells, the geometric objects that make up a
* triangulations made up of linear, quadrilateral, and hexahedral
* cells; triangles and tetrahedra are not supported.
*
- * This collection of cells is managed by the Triangulation class. It holds
- * the relevant data in memory and offers interfaces to query it. Most things
- * you want to do on cells are performed in loops over all cells. For this
- * purpose, the Triangulation class offers the concept of iterators (see @ref
- * Iterators): although implemented differently, they behave like pointers to
- * cells or faces and can be queried for the geometric properties of cells as
- * well as information like neighboring cells or faces of a cell.
+ * This collection of cells is managed by the Triangulation class and
+ * derived classes such as parallel::distributed::Triangulation and
+ * parallel::shared::Triangulation. It holds the relevant data in
+ * memory and offers interfaces to query it. Most things you want to
+ * do on cells are performed in loops over all cells. For this
+ * purpose, the Triangulation class offers the concept of iterators
+ * (see @ref Iterators): although implemented differently, they behave
+ * like pointers to cells or faces and can be queried for the
+ * geometric properties of cells as well as information like
+ * neighboring cells or faces of a cell.
*
* It is worth noting that the Triangulation class only stores geometry
* (i.e. the location of vertices and cells) and topology of a mesh
* (i.e. which cells are neighbors of which other cells, etc). It has nothing
* to do with finite elements or degrees of freedom that might be defined on a
- * mesh. These functions are performed by the DoFHandler class (see the @ref
- * dofs module) that gets a description of the finite element space and the
+ * mesh. These functions are performed by the DoFHandler class (see the
+ * @ref dofs module) that gets a description of the finite element space and the
* allocates and manages degrees of freedom on vertices, faces, or cells, as
* described by the finite element class. This separation makes it possible to
* have multiple DoFHandler classes work on the same mesh at the same time.
*
+ * In the grand scheme of things, triangulations in deal.II interact
+ * with a variety of other parts of the library:
+ * @dot
+ digraph G
+{
+ graph[rankdir="TB",bgcolor="transparent"];
+
+ node [fontname="FreeSans",fontsize=15,
+ shape=record,height=0.2,width=0.4,
+ color="black", fillcolor="white", style="filled"];
+ edge [color="black", weight=10];
+
+ tria [label="Triangulation", URL="\ref grid", fillcolor="deepskyblue"];
+ fe [label="Finite elements", URL="\ref feall"];
+ mapping [label="Mapping", URL="\ref mapping"];
+ quadrature [label="Quadrature", URL="\ref Quadrature"];
+ dh [label="DoFHandler", URL="\ref dofs"];
+ fevalues [label="FEValues", URL="\ref feaccess"];
+ systems [label="Linear systems", URL="\ref LAC"];
+ solvers [label="Linear solvers", URL="\ref Solvers"];
+ output [label="Graphical output", URL="\ref output"];
+ manifold [label="Manifold", URL="\ref manifold"];
+
+ tria -> dh [color="black",style="solid"];
+ fe -> dh [color="black",style="solid"];
+ fe -> fevalues [color="black",style="solid"];
+ mapping -> fevalues [color="black",style="solid"];
+ quadrature -> fevalues [color="black",style="solid"];
+ dh -> systems [color="black",style="solid"];
+ fevalues -> systems [color="black",style="solid"];
+ systems -> solvers [color="black",style="solid"];
+ solvers -> output [color="black",style="solid"];
+ manifold -> tria [color="black",style="solid"];
+ manifold -> mapping [color="black",style="solid"];
+
+
+
+ node [fontname="FreeSans",fontsize=12,
+ shape=record,height=0.2,width=0.4,
+ color="gray55", fontcolor="gray55", fillcolor="white", style="filled"];
+ edge [color="gray55", weight=1];
+
+ opencascade [label="OpenCASCADE"];
+ opencascade -> manifold [dir="none"];
+
+
+ node [fontname="FreeSans",fontsize=12,
+ shape=ellipse,height=0.2,width=0.4,
+ color="gray55", fontcolor="gray55", fillcolor="white", style="filled"];
+ edge [color="gray55", weight=1];
+
+ gmsh [label="gmsh", URL="\ref Gmsh"];
+ gmsh -> tria [dir="none"];
+}
+ * @enddot
*
* <h3>Grid generation</h3>
*
color="black", fillcolor="white", style="filled"];
edge [color="black", weight=10];
- tria [label="Triangulation", URL="\ref grid", ];
+ tria [label="Triangulation", URL="\ref grid"];
fe [label="Finite elements", URL="\ref feall"];
mapping [label="Mapping", URL="\ref mapping"];
quadrature [label="Quadrature", URL="\ref Quadrature"];
* reasonable implementations. More complicated examples can be described
* using the techniques shown in step-53 and step-54.
*
+ * In the grand scheme of things, the classes of this module interact
+ * with a variety of other parts of the library:
+ * @dot
+ digraph G
+{
+ graph[rankdir="TB",bgcolor="transparent"];
+
+ node [fontname="FreeSans",fontsize=15,
+ shape=record,height=0.2,width=0.4,
+ color="black", fillcolor="white", style="filled"];
+ edge [color="black", weight=10];
+
+ tria [label="Triangulation", URL="\ref grid"];
+ fe [label="Finite elements", URL="\ref feall"];
+ mapping [label="Mapping", URL="\ref mapping"];
+ quadrature [label="Quadrature", URL="\ref Quadrature"];
+ dh [label="DoFHandler", URL="\ref dofs"];
+ fevalues [label="FEValues", URL="\ref feaccess"];
+ systems [label="Linear systems", URL="\ref LAC"];
+ solvers [label="Linear solvers", URL="\ref Solvers"];
+ output [label="Graphical output", URL="\ref output"];
+ manifold [label="Manifold", URL="\ref manifold", fillcolor="deepskyblue"];
+
+ tria -> dh [color="black",style="solid"];
+ fe -> dh [color="black",style="solid"];
+ fe -> fevalues [color="black",style="solid"];
+ mapping -> fevalues [color="black",style="solid"];
+ quadrature -> fevalues [color="black",style="solid"];
+ dh -> systems [color="black",style="solid"];
+ fevalues -> systems [color="black",style="solid"];
+ systems -> solvers [color="black",style="solid"];
+ solvers -> output [color="black",style="solid"];
+ manifold -> tria [color="black",style="solid"];
+ manifold -> mapping [color="black",style="solid"];
+
+
+
+ node [fontname="FreeSans",fontsize=12,
+ shape=record,height=0.2,width=0.4,
+ color="gray55", fontcolor="gray55", fillcolor="white", style="filled"];
+ edge [color="gray55", weight=1];
+
+ opencascade [label="OpenCASCADE"];
+ opencascade -> manifold [dir="none"];
+
+
+ node [fontname="FreeSans",fontsize=12,
+ shape=ellipse,height=0.2,width=0.4,
+ color="gray55", fontcolor="gray55", fillcolor="white", style="filled"];
+ edge [color="gray55", weight=1];
+
+ gmsh [label="gmsh", URL="\ref Gmsh"];
+ gmsh -> tria [dir="none"];
+}
+ * @enddot
+ *
+ *
* <h3>An example</h3>
*
* A simple example why dealing with curved geometries is already provided by
edge [color="black", weight=10];
subgraph base {
rank="same";
- tria [label="Triangulation", URL="\ref grid", ];
+ tria [label="Triangulation", URL="\ref grid"];
fe [label="FiniteElement", URL="\ref feall"];
mapping [label="Mapping", URL="\ref mapping"];
quadrature [label="Quadrature", URL="\ref Quadrature"];
* coordinate direction than in another) through the QAnisotropic class, as
* well as the definition of quadrature formulas that are not tensor products.
*
+ * In the grand scheme of things, the classes of this module interact
+ * with a variety of other parts of the library:
+ * @dot
+ digraph G
+{
+ graph[rankdir="TB",bgcolor="transparent"];
+
+ node [fontname="FreeSans",fontsize=15,
+ shape=record,height=0.2,width=0.4,
+ color="black", fillcolor="white", style="filled"];
+ edge [color="black", weight=10];
+
+ tria [label="Triangulation", URL="\ref grid"];
+ fe [label="Finite elements", URL="\ref feall"];
+ mapping [label="Mapping", URL="\ref mapping"];
+ quadrature [label="Quadrature", URL="\ref Quadrature", fillcolor="deepskyblue"];
+ dh [label="DoFHandler", URL="\ref dofs"];
+ fevalues [label="FEValues", URL="\ref feaccess"];
+ systems [label="Linear systems", URL="\ref LAC"];
+ solvers [label="Linear solvers", URL="\ref Solvers"];
+ output [label="Graphical output", URL="\ref output"];
+ manifold [label="Manifold", URL="\ref manifold"];
+
+ tria -> dh [color="black",style="solid"];
+ fe -> dh [color="black",style="solid"];
+ fe -> fevalues [color="black",style="solid"];
+ mapping -> fevalues [color="black",style="solid"];
+ quadrature -> fevalues [color="black",style="solid"];
+ dh -> systems [color="black",style="solid"];
+ fevalues -> systems [color="black",style="solid"];
+ systems -> solvers [color="black",style="solid"];
+ solvers -> output [color="black",style="solid"];
+ manifold -> tria [color="black",style="solid"];
+ manifold -> mapping [color="black",style="solid"];
+
+
+
+ node [fontname="FreeSans",fontsize=12,
+ shape=record,height=0.2,width=0.4,
+ color="gray55", fontcolor="gray55", fillcolor="white", style="filled"];
+ edge [color="gray55", weight=1];
+
+ opencascade [label="OpenCASCADE"];
+ opencascade -> manifold [dir="none"];
+
+
+ node [fontname="FreeSans",fontsize=12,
+ shape=ellipse,height=0.2,width=0.4,
+ color="gray55", fontcolor="gray55", fillcolor="white", style="filled"];
+ edge [color="gray55", weight=1];
+
+ gmsh [label="gmsh", URL="\ref Gmsh"];
+ gmsh -> tria [dir="none"];
+}
+ * @enddot
+ *
*
* <h3>Use</h3>
*
projects / dealii.git / commitdiff