Comptes Rendus
Numerical Analysis
An exact bounded PML for the Helmholtz equation
Comptes Rendus. Mathématique, Volume 339 (2004) no. 11, pp. 803-808.

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.

Nous étudions l'équation de Helmholtz avec une condition de radiation de Sommerfeld dans un domaine non borné. Pour ce problème nous démontrons l'existence d'une couche bornée parfaitement adaptée et exacte, au sens où nous retrouvons la solution exacte dans le domaine physique. Nous approchons la solution du problème PML avec une méthode standard d'éléments finis et nous montrons ses bonnes propriétés sur des exemples test.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.10.006
Alfredo Bermúdez 1; L. Hervella-Nieto 2; A. Prieto 1; R. Rodríguez 3

1 Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain
2 Departamento de Matemáticas, Universidade da Coruña, 15707 A Coruña, Spain
3 GI
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     title = {An exact bounded {PML} for the {Helmholtz} equation},
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Alfredo Bermúdez; L. Hervella-Nieto; A. Prieto; R. Rodríguez. An exact bounded PML for the Helmholtz equation. Comptes Rendus. Mathématique, Volume 339 (2004) no. 11, pp. 803-808. doi : 10.1016/j.crma.2004.10.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.10.006/

[1] J.P. Bérenger A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., Volume 114 (1994), pp. 185-200

[2] J.P. Bérenger A perfectly matched layer for the FDTD solution of wave-structure interaction problems, IEEE T. Antennas and Propagation, Volume 44 (1996), pp. 110-117

[3] A. Bermúdez, L. Hervella-Nieto, A. Prieto, R. Rodríguez, An exact bounded perfectly matched layer for time-harmonic scattering problems, in preparation

[4] F. Collino; P. Monk The perfectly matched layer in curvilinear coordinates, SIAM J. Sci. Comput., Volume 19 (1998), pp. 2061-2090

[5] D. Colton; R. Kress Integral Equation Methods in Scattering Theory, Wiley, New York, 1983

[6] M. Masmoudi Numerical solution for exterior problems, Numer. Math., Volume 51 (1987), pp. 87-101

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