Introduction to Numerical Electrostatics Using MATLAB

13Triangles and Two-Dimensional Unstructured Grids

13.1 Introduction

Because the finite element method (FEM) is capable of handling complex geometries and different boundary conditions, much of its development occurred in the mechanical engineering community.³ Electrostatic applications of FEM are rarely as demanding in either the structural complexity or the boundary condition arenas as are many mechanical (stress–strain) problems, so the full menu of capabilities of FEM analysis will not be considered in this book.

The flexibility of using unstructured triangular cells was demonstrated using the method of moments (MoM) technique discussed earlier. In this chapter the use of unstructured triangular cells for planar two-dimensional (2d) FEM models will be developed. For MoM models, there was a good argument for working with right triangles — the barycenter of every triangle was of particular interest, and using right triangles facilitated the analyses. In FEM analysis there is nothing special about a right triangle, so triangles of any shape will be allowed.

Unstructured FEM grids are bookkeeping intensive. The computer program needs three sets of information:

1. A List of Nodes. This list assigns a node number to each node and specifies its location.
2. A List of Elements. When the elements are triangles, the list specifies each triangle and the (three) nodes that are their vertices.
3. A List of Boundary Conditions. This list specifies which nodes are fixed or along planes of symmetry and, in ...