A fast and robust solver for the scattering from a layered periodic structure containing multi-particle inclusions

JOURNAL OF COMPUTATIONAL PHYSICS

卷:298

Article

Lai, Jun¹  Kobayashi, Motoki¹  Barnett, Alex² 

[1] NYU, Courant Inst Math Sci, New York, NY 10012 USA

[2] Dartmouth Coll, Dept Math, Hanover, NH 03755 USA

关键词: Fast solver;    Periodic scattering;    Multi-particle scattering;    Layered medium;    Diffraction;   

DOI  :  10.1016/j.jcp.2015.06.005

来源: Elsevier

【 摘 要 】

We present a solver for plane wave scattering from a periodic dielectric grating with a large number M of inclusions lying in each period of its middle layer. Such composite material geometries have a growing role in modern photonic devices and solar cells. The high-order scheme is based on boundary integral equations, and achieves many digits of accuracy with ease. The usual way to periodize the integral equation-via the quasi-periodic Green's function-fails at Wood's anomalies. We instead use the free-space Green's kernel for the near field, add auxiliary basis functions for the far field, and enforce periodicity in an expanded linear system; this is robust for all parameters. Inverting the periodic and layer unknowns, we are left with a square linear system involving only the inclusion scattering coefficients. Preconditioning by the single-inclusion scattering matrix, this is solved iteratively in O(M) time using a fast matrix-vector product. Numerical experiments show that a diffraction grating containing M = 1000 inclusions per period can be solved to 9-digit accuracy in under 5 minutes on a laptop. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free