CST2013: Tetrahedral Mesh

CST software uses the Finite Integration Method (FI-Method) on hexahedral and tetrahedral meshes and surface meshes for the integral equation solver (see Which Mesh to Use). The following topics will try to explain how a tetrahedral mesh influences the simulation and what requirements should be fulfilled to obtain good results on tetrahedral meshes. For an overview on hexahedral and surface meshing, see Mesh Generation Overview (Hexahedral) and Mesh Generation Overview (Surface), respectively.

Mesh and simulation

The mesh influences the accuracy and the simulation time of the solver. Please mind that tetrahedral meshes combined with first order elements need a higher resolution to gain the same accuracy as when higher order elements are used.

Viewing the mesh

The mesh can be displayed in the Mesh View.

Automatic mesh generation

A tetrahedral mesh is generated by an automatic mesh generator. If a solver will be started with a tetrahedral method, the mesh generator will be started automatically, unless a valid tetrahedral mesh already exists.

Alternatively, you may run the mesh generation to view the mesh before you start a specific solver by selecting Mesh: Mesh ControlUpdate in the Mesh View. Previewing the mesh is not necessary, but is recommended to get obtain insight as to whether  the defined problem is sufficiently resolved by the mesh, particularly if you do not use the adaptive mesh refinement.

Mesh and structure approximation - surface and volume mesh

Shape boundaries and sheets are discretized by the surface mesh consisting of triangles. A fine surface mesh will result in a good approximation of the structure geometry. Each triangle of the surface mesh is a side of one or two adjacent tetrahedrons. Consequently, each tetrahedron is part of a unique volume structure element (shape). This means that tetrahedral meshes always resolve material jumps and domain boundaries.

The set of tetrahedrons is called the volume mesh.

Controlling the mesh globally

The behavior of the automatic mesh generation can be changed by adjusting its parameters. These parameters can be accessed from the global mesh properties dialog box (Mesh: Mesh ControlGlobal Properties, ) and the corresponding specials sub dialog box. (Mesh: Mesh ControlGlobal PropertiesSpecials).

Controlling the mesh locally for specific structure elements

It is possible to set specific mesh control values for single structure elements. This can be carried out by selecting the corresponding shape and choosing either Mesh: Mesh ControlLocal Properties or Local Mesh Properties from the context menu.

Note that by multi-selection (holding down the CTRL key while selecting a shape) it is possible to simultaneously set the mesh property for several shapes.

Setting a locally finer mesh may be recommended for

• structure elements of high importance for the simulation,

• shapes with a too coarse geometry representation in the mesh (e.g. a cylinder, for which the mesh representation does not look smooth enough).

Adaptive mesh refinement

An optional adaptive mesh refinement ensures an accurate numerical solution in combination with a short simulation time. An adaptive solver run simulates the structure several times and locally improves the mesh from run to run. This results in optimal meshes, i.e. the computational power is concentrated to places where it is necessary. A good strategy is to start with a relatively coarse mesh and to use adaptive refinement to improve the results.

Adaptive refinement can be switched on and off in the respective solver dialog.