Electrostatic solution for three-dimensional arbitrarily shaped conducting bodies using finite element and measured equation of invariance

Differential equation techniques such as finite element (FE) and finite difference (FD) have the advantage of sparse system matrices that have relatively small memory requirements for storage and relatively short central processing unit (CPU) time requirements for solving. However, these techniques do not lend themselves as readily for use in open-region problems as the method of moments (MoM) because they require the discretization of the space surrounding the object where MoM only requires discretization of the surface of the object. In this work, a relatively new mesh truncation method known as the measured equation of invariance (MEI) is investigated augmenting the FE method for the solution of electrostatic problems involving three-dimensional (3-D) arbitrarily shaped conducting objects. This technique allows truncation of the mesh as close as two node layers from the object. MEI views sparse-matrix numerical techniques as methods of determining weighting coefficients between neighboring nodes and finds those weights for nodes on the boundary of the mesh by assuming viable charge distributions on the surface of the object and using Green's function to measure the potentials at the nodes. Problems in the implementation of FE/MEI are discussed and the method is compared against MoM for a cube and a sphere.