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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 524345, 10 pages
Research Article

A Least-Squares FEM for the Direct and Inverse Rectangular Cavity Scattering Problem

1Department of Mathematics, Dalian Maritime University, Dalian 116026, China
2School of Mathematics, Jilin University, Changchun 130012, China

Received 29 September 2014; Revised 14 February 2015; Accepted 14 February 2015

Academic Editor: Stefano Lenci

Copyright © 2015 Enxi Zheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the scattering problem of a rectangular cavity. We solve this problem by a least-squares nonpolynomial finite element method. In the method, we use Fourier-Bessel functions to capture the behaviors of the total field around corners. And the scattered field towards infinity is represented by a combination of half-space Green functions. Then we analyze the convergence and give an error estimate of the method. By coupling the least-squares nonpolynomial finite element method and the Newton method, we proposed an algorithm for the inverse scattering problem. Numerical experiments are presented to show the effectiveness of our method.