Efficient techniques for BEM rank-deficiency electrostatic problems

For modern MEMS and electron devices, an accurate electrostatic analysis is essential and indispensable for engineers. The BEM is a widely used computational technique nowadays for MEMS and EM because of its superiority for unlimited exterior field. But for electrostatic problems with some specific geometry, the singularity caused by a degenerate scale will be encountered since the influence matrix is rank deficient, and numerical results become unstable. Therefore, the approach to correctly and efficiently solve the singularity arising from degenerate scale becomes a very essential and indispensable task for engineers. In this article, some efficient regularization BEM, RBM, CHIEF and hypersingular formulation, in conjunction with SVD technique, are employed to study and cope with the rank-deficiency problem numerically. These regularization techniques are successfully applied to overcome the degenerate scale and the error is suppressed in the numerical experiment.