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.
Accepted:
Published online:
Alfredo Bermúdez 1; L. Hervella-Nieto 2; A. Prieto 1; R. Rodríguez 3
@article{CRMATH_2004__339_11_803_0, author = {Alfredo Berm\'udez and L. Hervella-Nieto and A. Prieto and R. Rodr{\'\i}guez}, title = {An exact bounded {PML} for the {Helmholtz} equation}, journal = {Comptes Rendus. Math\'ematique}, pages = {803--808}, publisher = {Elsevier}, volume = {339}, number = {11}, year = {2004}, doi = {10.1016/j.crma.2004.10.006}, language = {en}, }
TY - JOUR AU - Alfredo Bermúdez AU - L. Hervella-Nieto AU - A. Prieto AU - R. Rodríguez TI - An exact bounded PML for the Helmholtz equation JO - Comptes Rendus. Mathématique PY - 2004 SP - 803 EP - 808 VL - 339 IS - 11 PB - Elsevier DO - 10.1016/j.crma.2004.10.006 LA - en ID - CRMATH_2004__339_11_803_0 ER -
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] A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., Volume 114 (1994), pp. 185-200
[2] 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] The perfectly matched layer in curvilinear coordinates, SIAM J. Sci. Comput., Volume 19 (1998), pp. 2061-2090
[5] Integral Equation Methods in Scattering Theory, Wiley, New York, 1983
[6] Numerical solution for exterior problems, Numer. Math., Volume 51 (1987), pp. 87-101
Cited by Sources:
Comments - Policy