A Fast AWE-Augmented Wideband Discontinuous Galerkin Frequency-Domain Method in Solving Electromagnetic Wave Equations

In this research, a discontinuous Galerkin frequency-domain (DGFD) method is proposed to solve the electromagnetic wave equations. Different to the explicit time-domain analysis, the electric-field and magnetic-field in frequency-domain wave equations are coupled together implicitly, thus the established matrix equation is globally coupled, which is computational expensive if solving it directly. To address this issue, a Block-diagonal preconditioner and a restriction operator are applied to the matrix equation, which splits the global matrix into a number of small local matrix systems pertinent to each subdomain. Then, a direct solver can be employed to solve them with a FETI-like procedure. Besides, to further speed up the wideband analysis, the asymptotic waveform evaluation (AWE) is implemented into the DGFD solver, which only needs to calculate a few frequency points in a broadband. To benchmark the proposed algorithm, a SIW filter is investigated.