Boundary particle method for inverse cauchy problems of inhomogeneous helmholtz equations

Abstract

This paper investigates the boundary particle method (BPM) coupled with truncated singular value decomposition (TSVD) regularization technique on the solution of inverse Cauchy problems of inhomogeneous Helmholtz equations. Unlike the other boundary discretization methods, the BPM does not require any inner nodes to evaluate the particular solution, since the method uses the recursive composite multiple reciprocity technique to reduce an inhomogeneous problem to a series of higher-order homogeneous problems. The BPM is particular attractive to solve inverse problems thanks to its truly boundary-only meshless merit. In this study, numerical experiments demonstrate that the BPM in conjunction with the TSVD is highly accurate, computationally efficient and stable for inverse Cauchy problems.