An AWE-Enhanced Wideband Subdomain DG-RTC Algorithm in Solving Electromagnetic Problems

In this research, a Robin transmission condition enriched frequency-domain discontinuous Galerkin (DG-RTC) method is proposed to solve the electromagnetic problems. The proposed DG-RTC method directly discretizes the vector wave equation in each subdomain, and the numerical flux is used for the information communication of solutions between neighbor subdomains. Compared with the traditional Maxwell’s equations-based DG (ME-DG) method, the proposed DG-RTC method merely solves the E-field in the whole computational region, while the H-field is only present at the interfaces of adjacent subdomains, which thus significantly reduces the number of unknowns. Moreover, the finalized globally coupled matrix equation is split into a number of small local matrix equations pertinent to each subdomain, a finite-element tearing and interconnecting (FETI)-like procedure is developed. In this way, the direct solver PARDISO can be applied to solve them with trivial cost in a parallel way. In addition, for efficient wideband analysis, the asymptotic waveform evaluation (AWE) is incorporated into the subdomain DG-RTC solver, where merely a few points need to be evaluated in a broadband. Finally, to benchmark the accuracy and efficiency of the proposed algorithm, a microstrip transmission line and a SIW filter are investigated.

I. Introduction

As a natural domain decomposition method (DDM), discontinuous Galerkin (DG) method is extensively utilized in modeling complex electromagnetic problems due to its various valuable features such as the capability of irregular geometry modeling, the domain decomposition ability and flexibility in choosing the type and the order of basis functions [1][2], etc. However, in the conventional Maxwell’s equation-based DG (ME-DG) method, both Eand H-field need to be solved in the entire computational domain, which renders a great challenge to the computational performance.