There are six different domains available for the magnetization problem (cf. figure 3). In addition it is possible to manipulate domains of any shape, if a tetrahedral finite element mesh is available. As their boundary is covered by triangles this general type of domain is called triabnd. It is even possible to refine and coarsen elements of disconnected meshes. This is useful if a finite element mesh of two distinct objects, which have no element and no vertex in common, is used. However, the projection of boundary midnodes to curved surfaces is not possible, since this would require an analytical description.
The cube is one of the standard domains provided by AGM 3D. A detailed description can be found in [Bey94] in section 2.4.4 on page 28.
The hexahedron has a quadratic base and an aspect ratio (height:base) of 2:1. It has been implemented for testing purposes. In order to manipulate the mesh of a general hexahedron it is advisable to project the vertices of a hexahedron onto a unit cube and use that domain within AGM 3D.
The pentahedron was created to test the algorithms of AGM 3D for compatibility with segments (surface planes) of triangular shape.
The sphere is another standard domain provided by AGM 3D. Its description can be found in [Bey94] in section 2.4.4 on page 28.
The s-shaped pipe is another standard domain provided by AGM 3D. It has been introduced in version 1.2 of AGM 3D for which no updated documentation is available, yet.
The cylindrical tube is another standard domain provided by AGM 3D. It has been introduced in version 1.2 of AGM 3D for which no updated documentation is available, yet.
The magnetization problem also provides commands to import domains of any shape and manipulate them. The domain has to be defined in a GeomView OFF file which consists of the boundary nodes and the boundary triangles of the tetrahedral mesh. The inner vertices can be imported using impivertex and the elements using impelements. There is also a converter (util/out2off) for neutral files (as exported by Patran), which generates the GeomView file, a file of the inner vertices and a file of the elements. See the description of impdomain in section 2.6 for further details.
![\begin{figure}
\centering
\subfigure[Cube]{
\includegraphics[scale=0.5]{cubenr...
...figure[Arbitrary domain]{
\includegraphics[scale=0.3]{arbit.eps}
}\end{figure}](img6.gif)