## An efficient hybrid method for scattering from arbitrary dielectric objects buried under a rough surface: TM case |

Optics Express, Vol. 22, Issue 6, pp. 6844-6858 (2014)

http://dx.doi.org/10.1364/OE.22.006844

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### Abstract

A hybrid method combining the finite element method (FEM) with the boundary integral equation (BIE) is presented in this paper to investigate two-dimensional (2D) electromagnetic scattering properties of multiple dielectric objects buried beneath a dielectric rough ground for TM case. In traditional FEM simulation, the artificial boundaries, such as perfectly matched layer (PML) and the absorbing boundary conditions (ABC), are usually adopted as truncated boundaries to enclose the whole model. However, the enclosed computational domain increases quickly in size for a rough surface with a large scale, especially for the scattering model of objects away from the rough surface. In the hybrid FEM-BIE method, one boundary integral equation is adopt to depict the scattering above the rough surface based on Green's function. Based on the domain decomposition technique, the computational region below the rough ground is divided into multiple isolated interior regions containing each object and the exterior region. Finite element formulations are only applied inside interior regions to derive a set of linear systems, and another boundary integral formula is developed below the rough surface which also acts as the boundary constraint of the FEM region. Compared with traditional FEM, the hybrid technique presented here is highly efficient in terms of computational memory, time, and versatility. Numerical simulations are carried out based on hybrid FEM-BIE to study the scattering from multiple dielectric objects buried beneath a rough ground.

© 2014 Optical Society of America

**OCIS Codes**

(290.5880) Scattering : Scattering, rough surfaces

(280.1350) Remote sensing and sensors : Backscattering

**ToC Category:**

Scattering

**History**

Original Manuscript: January 20, 2014

Revised Manuscript: February 22, 2014

Manuscript Accepted: March 6, 2014

Published: March 17, 2014

**Citation**

Run-Wen Xu and Li-Xin Guo, "An efficient hybrid method for scattering from arbitrary dielectric objects buried under a rough surface: TM case," Opt. Express **22**, 6844-6858 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-6-6844

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