A Least-Squares FEM for the Direct and Inverse Rectangular Cavity Scattering Problem. (3rd March 2015)

• Record Type: Journal Article
• Authors: Zheng, Enxi; Ma, Fuming; Wang, Yujie
• Other Names: Lenci Stefano Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2015(2015)
• Publication Date: 2015-03-03
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2015/524345
• Languages: English
• ISSNs: 1024-123X

Abstract

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.