IE-DDM with a novel multiple-grid p-FFT for analyzing multiscale structures in half space

Abstract

We present an integral equation domain decomposition method accelerated by a novel multiple-grid precorrected fast Fourier transform (MG-p-FFT) for the efficient analysis of multiscale structures in a half space. Based on the philosophy of DDM, the original computational domain is partitioned into several non-overlapping sub-domains. By employing non-conformal discretizations to each domain boundaries, combined field integral equation with half-space dyadic Green’s function is proposed for each individual sub-domain. Subsequently, the MG-p-FFT with auxiliary Cartesian grids with different size, order, location, and spacing, is adopted in each sub-domain independently to account for the self-interactions. Here, the proposed MG-p-FFT scheme outperforms the existing single-grid p-FFT scheme for multiscale problems by reducing the computational time and memory consumption. The proposed method can also be viewed as an effective preconditioning scheme for multiscale problems in a half space. The validity and advantages of the proposed method are illustrated by several representative numerical examples.

Keywords:

• Non-conformal domain decomposition
• half space
• multiple-grid p-FFT
• multiscale problems
• dyadic Green’s function

Notes

No potential conflict of interest was reported by theauthors.

This work is dedicated to the memory of Professor Joshua Le-Wei Li, a distinguished scholar and mentor in the area of EMs.

Additional information

Funding

This work is partially supported by Chang Jiang Scholar Project of MOE, and the National Science Foundation of China under [grant number 61271033], grant number 61231001]; National Excellent Youth Fund by NSFC [No. 61425010]; the Programme of Introducing Talents of Discipline to Universities under [grant number b07046].