Solving Electrostatic Problems

with the effects of electric charges at rest. For modern electron and microelectromechanical systems (MEMS), an accurate electrostatic analysis is both essential and indispensable. We know that if we use the conventional boundary element method (BEM) for electrostatic problems that have singularity due to degenerate boundaries, the coincidence of the boundaries gives rise to a difficult, or ill-conditioned, problem. The coincidence is when different elements use the same nodes, but there is a free-edge between the elements. In a degenerate boundary problem, the spatial coincidence of the two sides of the degenerate boundary leads to the singular integral equation on one side being indistinguishable from that on the other, even though the potentials on the two sides differ.1 Our dual boundary element method (DBEM) uses a dual integral formulation with a hypersingular integral to solve boundary value problems in which singularity arises from degenerate boundaries. To prove this, we analyzed an electrostatic problem to check the mathematical model’s validity; the analysis also showed that we could avoid deploying artificial boundaries and encountering the ill-conditioned problem of the conventional BEM and still get a more accurate and reasonable result. In this article, we compare results between finite-element method (FEM) and DBEM analyses to prove the DBEM’s superiority. Because model creation requires the most effort in electrical engineering practices, we strongly recommend the DBEM for industrial applications.