Introduction to Numerical Electrostatics Using MATLAB

14A Zoning System and Some Examples

14.1 General Introduction

The program fem_2d_1.m presented in Chapter 13 is a general two-dimensional (2d) FEM program. It can handle sophisticated geometries. On the other hand, starting with a structure description and creating the zoning (also called the meshing or the tessellation), which generates the input files for this program, is a complex problem in its own right. Although generating an unstructured grid for a complex geometry by hand is not literally impossible, it is so difficult and the results would probably be so erroneous, that it would be a pointless quest. Computer-aided mesh generation is necessary.

Fortunately, for both academic and commercial purposes, many software packages have been developed. Some relatively simple packages were presented in the MoM unstructured grid discussed earlier. As was also discussed earlier, an in depth analysis or development of one of these programs is outside the scope of this book. On the other hand, we can't proceed with FEM examples or study the electrostatic properties of structures that FEM modeling would enable without a meshing system.

In this chapter we'll introduce the gmsh package; gmsh is a free three-dimensional (3d) FEM grid generator that may be downloaded along with very extensive documentation and tutorials (hhtp://geuz.org/gmsh/).¹ It is distributed under the GNU General Public License.² In the introduction to gmsh that follows, only a very small subset of gmsh capabilities ...