Non-conformal and parallel discontinuous Galerkin time domain method for Maxwell’s equations: EM analysis of IC packages

Abstract

In this article, we present an Interior Penalty discontinuous Galerkin Time Domain (IPDGTD) method on non-conformal meshes. The motivation for a non-conformal IPDGTD comes from the fact there are applications with very complicated geometries (for example, IC packages) where a conformal mesh may be very difficult to obtain. Therefore, the ability to handle non-conformal meshes really comes in handy. In the proposed approach, we first decompose the computational domain into non-overlapping subdomains. Afterward, each sub-domain is meshed independently resulting in non-conformal domain interfaces, but simultaneously providing great flexibility in the meshing process. The non-conformal triangulations at sub-domain interfaces can be naturally supported within the IPDGTD framework. Moreover, a MPI parallelization together with a local time-stepping strategy is applied to significantly increase the efficiency of the method. Furthermore, a general balancing strategy is described. Through a practical example with multi-scale features, it is shown that the proposed balancing strategy leads to better use of the available computational resources and reduces substantially the total simulation time. Finally, numerical results are included to validate the accuracy and demonstrate the flexibilities of the proposed non-conformal IPDGTD.