Fem-DDM With an Efficient Second-Order Transmission Condition in Both High-Frequency and Low-Frequency Applications

Abstract

Abstract-In this paper, a novel second-order transmission condition is developed in the framework of non-conformal finite element domain decomposition method to meet the challenges brought by complex and large-scale electromagnetic modeling. First, it is implemented efficiently on the non-conformal interface via a Gauss integral scheme. Then, the eigenvalue analysis of the DDM system show a more clustered eigenvalue distribution of this transmission condition compared with several existing transmission conditions. After that, it is applied to large-scale complex problems such as S-type waveguides in the high frequency band and dielectric well-logging applications in the low frequency band. The final numerical results demonstrate that this transmission condition has high efficiency and huge capability for modeling large-scale problems with multi-resolution in any frequency band.

Volume Integral Equation Method Solution for Spheroidal Inclusion Problem

“…It should be noted that, in order to investigate three-dimensional stress problems with multiple inclusions, in addition to parallelization and optimization of the sequential three-dimensional VIEM code, a domain decomposition method (DDM) was applied to the parallel three-dimensional VIEM code, with support from the Korea Institute of Science and Technology Information (KISTI). The domain decomposition method allows decomposition of large-sized problem solutions to solutions of several smaller-sized problems [23]. Therefore, the parallel volume integral equation method (PVIEM) using the domain decomposition method enables us to investigate more complicated multiple inclusion problems elastostatically or elastodynamically.…”

A Rigorous Code Verification Process of the Domain Decomposition Method in a Finite Element Method for Electromagnetics

“…Regarding discretization, we have used three different shapes with higher-order (up to fourth-order) basis functions, in contrast to the usual second-order tetrahedra present in the literature. Finally, we study in Section IV-B the effect on the approximation of the electric field if we provide the theoretically expected values of the vector ancillary variable and if we use a lower approximation order for the scalar ancillary variable, as suggested in [43], [44], [29], [31]. As far as the authors know, this study is not reported in the literature and is a clear illustration of the features that MMS provides to this formulation.…”