Abstract

We study the Helmholtz equation with a Sommerfeld radiation condition in an unbounded domain. We prove the existence of an exact bounded perfectly matched layer (PML) for this problem, in the sense that we recover the exact solution in the physical domain by choosing a singular PML function in a bounded domain. We approximate the solution for the PML problem using a standard finite element method and assess its performance through numerical tests. © 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved.