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

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  • Enxi Zheng
  • Fuming Ma
  • Yujie Wang

Abstract

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.

Suggested Citation

  • Enxi Zheng & Fuming Ma & Yujie Wang, 2015. "A Least-Squares FEM for the Direct and Inverse Rectangular Cavity Scattering Problem," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-10, March.
    • Handle: RePEc:hin:jnlmpe:524345
    DOI: 10.1155/2015/524345
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