European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2004 P. Neittaanm¨ aki, T. Rossi, S. Korotov, E. O˜ nate, J. P´eriaux, and D. Kn¨ orzer (eds.) Jyv¨ askyl¨ a, 24–28 July 2004 A FAMILY OF EXACT BOUNDED PML FOR THE HELMHOLTZ PROBLEM A. Berm´ udez ? , L. Hervella-Nieto ?? , A. Prieto ? and R. Rodr´ıguez † ? Departamento de Matem´ atica Aplicada. Universidad de Santiago de Compostela 15782 Santiago de Compostela, Spain e-mails: mabermud@usc.es , maprieto@usc.es ?? Departamento de Matem´ aticas. Universidad de A Coru˜ na 15071 A Coru˜ na, Spain e-mail: luisher@udc.es † GI 2 MA, Departamento de Ingenier´ıa Matem´ atica. Universidad de Concepci´ on Casilla 160-C, Concepci´ on, Chile. e-mail: rodolfo@ing-mat.udec.cl Key words: Helmholtz problem, unbounded domain, PML. Abstract. We study the Helmholtz equation with a Sommerfeld radiation condition in an unbounded domain. We introduce 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 compute the solution for the PML problem using a standard finite element method and assess its performance through numerical tests. 1