Self Surface Charge Method for Static Field Simulation Compatible With Non-Conformal Meshes

Abstract

Numerical analysis of static field problems is often encountered in science and engineering. The boundary element methods based on integral equations are popular due to small number of unknowns and high computational efficiency. Conventional boundary element methods require conformal meshes on the interface between two contact dielectric objects, which are more complicated to generate than non-conformal meshes. This paper presents a boundary element integral equation method compatible with non-conformal meshes on the interface between contacting objects. In this method, surface polarization charges on a homogeneous dielectric object are the unknowns, and the relationship between the electric field and surface polarization charges are employed to establish the integral equations. The discretization of such an integral equation and the treatment for singularity integration are discussed. Since the proposed method is compatible with non-conformal meshes, it reduces the meshing complexity for dielectric objects in contact, while the number of unknowns of the proposed method is intermediate compared with conventional methods. The proposed method is general for electrostatic field, magnetostatic field and stationary current field simulations. To demonstrate the feasibility, accuracy and efficiency of this approach, numerical tests and comparison with conventional methods are presented in this paper.