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

Abstract EN

This paper is concerned with the scattering problem of a rectangular cavity.

We solve thisproblem 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.