Center for diffusion of mathematic journals

 
 
 
 

Séminaire Laurent Schwartz — EDP et applications

Table of contents for this volume | Previous article | Next article
Laurence Halpern; Jeffrey Rauch
Bérenger/Maxwell with Discontinous Absorptions : Existence, Perfection, and No Loss
Séminaire Laurent Schwartz — EDP et applications (2012-2013), Exp. No. 10, 20 p., doi: 10.5802/slsedp.38
Article PDF

Résumé - Abstract

We analyse Bérenger’s split algorithm applied to the system version of the two dimensional wave equation with absorptions equal to Heaviside functions of $x_j$, $j=1,2$. The methods form the core of the analysis [11] for three dimensional Maxwell equations with absorptions not necessarily piecewise constant. The split problem is well posed, has no loss of derivatives (for divergence free data in the case of Maxwell), and is perfectly matched.

Bibliography

[1] S. Abarbanel, and D. Gottlieb, A mathematical analysis of the PML method, J. Comput. Phys., 134, 357-363, 1997.  MR 1458833 |  Zbl 0887.65122
[2] D. Appelo, T. Hagstrom, and G. Kreiss, Perfectly matched layers for hyperbolic systems: General formulation, well-posedness and stability , SIAM J. Appl. Math., 67, no. 1, 1–23, 2007.  MR 2272612 |  Zbl 1110.35042
[3] A. Bamberger, P. Joly, J.E. Roberts, Second order absorbing boundary conditions for the wave equation: a solution for the corner problem, INRIA Report RR-0644, 1987.  MR 902872 |  Zbl 0716.35036
[4] E. Bécache, S. Fauqueux, and P. Joly, Stability of perfectly matched layers, group velocities and anisotropic waves, J. Comput. Phys., 188, 399-433, 2003.  MR 1985305 |  Zbl 1127.74335
[5] E. Bécache. and P. Joly, On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations, M2AN Math. Model. Numer. Anal., 36, 87-119, 2002. Numdam |  MR 1916294 |  Zbl 0992.78032
[6] J.-P. Bérenger, A perfectly matched layer for the absorption of electromagnetic waves , J. Comput. Phys., 114, 185-200 , 1994.  MR 1294924 |  Zbl 0814.65129
[7] J.-P. Bérenger, Three-dimensional perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 127, 363-379, 1996.  MR 1412240 |  Zbl 0862.65080
[8] J.-P. Bérenger, Perfectly matched layers (PML) for computational electromagnetics, Synthesis lectures on computational electromagnetics, Morgan and Claypool, 2007.
[9] J. Diaz and P. Joly, A time domain analysis of PML models in acoustics, Computer Methods in Applied Mechanics and Engineering 195, 29-32, 3820-3853, 2006.  MR 2221776 |  Zbl 1119.76046
[10] L. Halpern, S. Petit-Bergez, and J. Rauch The analysis of matched layers, Confluentes Math., 3 no. 2, 159-236, 2011.  MR 2807107 |  Zbl pre05937819
[11] L. Halpern and J. Rauch, in preparation.
[12] P. Joly, S. Lohrengel, O. Vacus, Un résultat d’existence et d’unicité pour l’équation de Helmholtz avec conditions aux limites absorbantes d’ordre 2, C. R. Acad. Sci. Paris Sér. 1 Math. 329 (3) (1999) 193-198.  MR 1711059 |  Zbl 0929.35031
[13] J. Métral, and O. Vacus, Caractère bien posé du problème de Cauchy pour le système de Bérenger, C. R. Acad. Sci. Paris Sér. I Math., 10, 847–852, 1999.  Zbl 0928.35176
[14] S. Petit-Bergez, Problèmes faiblement bien posés : discrétisation et applications, Thèse de l’Université Paris 13, 2006.
Copyright Cellule MathDoc 2019 | Credit | Site Map