Bérenger/Maxwell with Discontinous Absorptions : Existence, Perfection, and No Loss

Laurence Halpern[1]; Jeffrey Rauch[2]

  • [1] LAGA, UMR 7539 CNRS Université Paris 13 93430 Villetaneuse France
  • [2] Department of Mathematics University of Michigan Ann Arbor 48109 MI USA

Séminaire Laurent Schwartz — EDP et applications (2012-2013)

  • Volume: 2012-2013, page 1-20
  • ISSN: 2266-0607

Abstract

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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.

How to cite

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Halpern, Laurence, and Rauch, Jeffrey. "Bérenger/Maxwell with Discontinous Absorptions : Existence, Perfection, and No Loss." Séminaire Laurent Schwartz — EDP et applications 2012-2013 (2012-2013): 1-20. <http://eudml.org/doc/275742>.

@article{Halpern2012-2013,
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.},
affiliation = {LAGA, UMR 7539 CNRS Université Paris 13 93430 Villetaneuse France; Department of Mathematics University of Michigan Ann Arbor 48109 MI USA},
author = {Halpern, Laurence, Rauch, Jeffrey},
journal = {Séminaire Laurent Schwartz — EDP et applications},
keywords = {Maxwell equations; perfectly matched layers; well posedness; loss of derivatives; perfect matching},
language = {eng},
pages = {1-20},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Bérenger/Maxwell with Discontinous Absorptions : Existence, Perfection, and No Loss},
url = {http://eudml.org/doc/275742},
volume = {2012-2013},
year = {2012-2013},
}

TY - JOUR
AU - Halpern, Laurence
AU - Rauch, Jeffrey
TI - Bérenger/Maxwell with Discontinous Absorptions : Existence, Perfection, and No Loss
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2012-2013
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2012-2013
SP - 1
EP - 20
AB - 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.
LA - eng
KW - Maxwell equations; perfectly matched layers; well posedness; loss of derivatives; perfect matching
UR - http://eudml.org/doc/275742
ER -

References

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  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. Zbl1119.76046MR2221776
  10. L. Halpern, S. Petit-Bergez, and J. Rauch The analysis of matched layers, Confluentes Math., 3 no. 2, 159-236, 2011. Zbl1263.65088MR2807107
  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. Zbl0929.35031MR1711059
  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. Zbl0928.35176
  14. S. Petit-Bergez, Problèmes faiblement bien posés : discrétisation et applications, Thèse de l’Université Paris 13, 2006. 

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