An alternating iterative method for solving the Cauchy problem for the Helmholtz equation in interior multiply connected domain

Abstract

This paper is concerned with the Cauchy problem for the Helmholtz equation in interior multiply connected domain. We propose an alternating iterative method to solve the Cauchy problem and prove the convergence of the iterative procedure by using fixed point theory. To solve the two well-posed auxiliary problems in each iteration, we employ the boundary integral equation method. The effectiveness of our iterative method is demonstrated by some numerical tests.