Introduction to Numerical Electrostatics Using MATLAB

6 Triangles

6.1 Introduction to Triangular Cells

All of the examples and calculations presented thus far have been based on the use of rectangular cells in an X–Y plane. Rectangular cells in an X–Y plane are very useful for many practical problems, so this wasn’t a bad choice. However, rectangular cells are very awkward to work with in three-dimensional (3d) structures, especially when the surfaces involved are not planar. A good example of this problem is the surface of a sphere; there is simply no convenient way to approximate the surface of a (conducting) sphere using a collection of rectangular cells. Also, when a structure has regions where smaller cells are needed to resolve complex geometric features and/or accurate approximate regions where the electric field is changing rapidly but larger cells are satisfactory for much of the geometry, the programs presented in Chapters 1 and 3–5 seldom can do the job — they were written to be as simple as possible and used square cells. A much more useful choice is triangular cells of arbitrary size, location, and orientation. Also, and finally, readers by now must be wondering whether there isn't more to electrostatics than transmission line sections.

Restricting ourselves to uniform-size rectangular cells in X–Y planes let us develop basic method of moments (MoM) solution techniques for different situations (images, dielectric interfaces, rotated electrodes, etc.) and look at solutions without being distracted by complexities ...