From the resolved geometry the software is capable to create unstructured meshes in 2D, or 3D (in 1D it is trivial). Three algorithms are implemented, for different needs:

• MZXBowyerWatson: algorithm for generation of meshes with very high node count.
• Netgen: The mesher interface from Netgen project is implemented, it is an advancing front algorithm for high quality meshes.
• MZXAdvancingFront: Advancing front mesh generation, but only in 2D for triangular meshes (experimental, not reliable)

### MZXBowyerWatson

Tetrahedral, and triangular mesher, based on the Bowyer-Watson Delaunay triangulation algorithm. It simply generates points to the resolved geometry (edges, surfaces, volumes), and uses a constrained Delaunay triangulation to connect the points. Laplacian smoothing is not implemented yet, the resulted mesh is homogeneous. Usage from graphical interface:

• Generate a resolved geometry from the Cluster Builder tool, and the geometry automatically loaded in the mesher window.
• In the elements window the user could define the mesh size for each element, means for the spacing between the points in the generated pre-mesh.
• These values could be homogeneously set with the tool button “flash”, which asks for the number of points in the geometry should be created, than it calculates the volume of the geometry. The resulted mesh spacing is the following:

$$size= \sqrt[d]{\frac{\sum V_{cluster}}{N_{points}}}$$

In which the $d$ means the dimension of the geometry. With the build button, the mesh generator Application is called, and return the mesh for the specified parameters. When the meshing fails, the generated mesh is not updated. Examples for meshed geometries:

Simple circle, with $r = 1$ and the meshing size is $0.1$
ore different domains in one geometry. An intersecting circle with a rectangle results 3 disjoint domains

### Netgen Mesher

The Netgen mesher library can be found at http://www.hpfem.jku.at/netgen/ which is controlled though the MZXSim environment. It is based on the advancing front algorithm, which can create well shaped unstructured meshes. The algorithm creates high quality meshes with lower node count than the BowyerWatson mesher, but for a simple geometry high node count can be reached faster with the BowyerWatson mesher.

• mzxmeshbuilder.txt