Non-reflecting boundary condition on ellipsoidal boundary
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 2, pp. 131-139.

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Modeling of wave propagation problems using finite element methods usually requires the truncation of the computation domain around the scatterer of interest. Absorbing boundary conditions are classically considered in order to avoid spurious reflections. In this paper, we investigate some properties of the Dirichlet to Neumann map posed on a spheroidal boundary in the context of the Helmholtz equation.
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H. Barucq; A.-G. Dupouy St-Guirons; S. Tordeux. Non-reflecting boundary condition on ellipsoidal boundary. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 2, pp. 131-139. http://geodesic.mathdoc.fr/item/SJVM_2012_15_2_a1/

[1] Abramowitz M., Stegun I. A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, ninth dover printing, tenth GPO printing edition, Dover, New York, 1964 | MR

[2] Barucq H., Djellouli R., Saint-Guirons A.-G., “Construction and performance assessment of new local DtN conditions for elongated obstacles”, Applied Numerical Mathematics, 59:7 (2009), 1467–1498 | DOI | MR | Zbl

[3] Claeys X., Analyse asymptotique et numérique de la diffraction d'ondes par des films minces, PhD thesis, Université de Versailles Saint-Quentin-en-Yvelines, December 2008

[4] Engquist B., Majda A., “Absorbing boundary conditions for the numerical simulation of waves”, Math. Comp., 31 (1977), 629–651 | DOI | MR | Zbl

[5] Engquist B., Majda A., “Radiation boundary conditions for acoustic and elastic wave calculations”, Comm. Pure Appl. Math., 32:3 (1979), 314–358 | DOI | MR

[6] Keller J. B., Givoli D., “Exact non-reflecting boundary conditions”, J. of Computational Physics, 82 (1989), 172–192 | DOI | MR | Zbl

[7] Kirby P., “Calculation of spheroidal wave function”, Computer Physics Communications, 175 (2006), 465–472 | DOI | Zbl

[8] Kirby P., “Calculation of radial prolate spheroidal wave functions of the second kind”, Computer Physic Communications, 181 (2010), 514–519 | DOI | MR | Zbl

[9] Lebedev N. N., Silverman R. A., Special Functions and their Applications, Dover, New York, 1972 | MR | Zbl

[10] Lenoir M., Tounsi A., “The localized finite element method and its application to the two-dimensional seakeeping problem”, SIAM J. Numer. Anal., 25 (1988), 729–752 | DOI | MR | Zbl

[11] Protter M. H., “Unique continuation for elliptic equations”, Trans AMS, 95 (1960), 81–91 | DOI | MR | Zbl

[12] Saint-Guirons A.-G., Construction et analyse de conditions absorbantes de type Dirichlet-to-Neumann pour des frontières ellipsoidales, PhD thesis, Université de Pau et des Pays de l'Adour, November 2008

[13] Wilcox C. H., Scattering Theory for Diffraction Gratings, Springer-Verlag, New York, 1984 | MR | Zbl