An Electrostatic Integral Equation Method Compatible with Non-conformal Meshes

Numerical analysis of electrostatic field problems is widely encountered in science and engineering. Boundary element methods based on integral equations are popular due to the high efficiencies. Conventional boundary element methods require conformal meshing on the interface between two contact dielectric objects, which is more complicated to generate than non-conformal meshing. This paper presents an 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 relation 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. To demonstrate the feasibility and accuracy of this approach, numerical tests and comparison with conventional methods are presented in this paper also.