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

Differential equation techniques such as finite element (FE) and finite dif ference (FD) have the advantage of sparse system matrices that have relativ ely small memory requirements for storage and relatively short central proc essing unit (CPU) time requirements for solving. However, these techniques do not lend themselves as readily for use in open-region problems as the me thod of moments (MoM) because they require the discretization of the space surrounding the object where MoM only requires discretization of the surfac e of the object. In this work, a relatively new mesh truncation method know n as the measured equation of invariance (MEI) is investigated augmenting t he FE method for the solution of electrostatic problems involving three-dim ensional (3-D) arbitrarily shaped conducting objects. This technique allows truncation of the mesh as close as two node layers from the object. MEI vi ews 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 su rface 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.