Volume 11, Issue 2
Operator Factorization for Multiple-Scattering Problems and an Application to Periodic Media

J. Coatléven & P. Joly

Commun. Comput. Phys., 11 (2012), pp. 303-318.

Published online: 2012-12

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  • Abstract

This work concerns multiple-scattering problems for time-harmonic equations in a reference generic media. We consider scatterers that can be sources, obstacles or compact perturbations of the reference media. Our aim is to restrict the computational domain to small compact domains containing the scatterers. We use Robin-to-Robin (RtR) operators (in the most general case) to express boundary conditions for the interior problem. We show that one can always factorize the RtR map using only operators defined using single-scatterer problems. This factorization is based on a decomposition of the diffracted field, on the whole domain where it is defined. Assuming that there exists a good method for solving single-scatterer problems, it then gives a convenient way to compute RtR maps for a random number of scatterers.

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@Article{CiCP-11-303, author = {}, title = {Operator Factorization for Multiple-Scattering Problems and an Application to Periodic Media}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {2}, pages = {303--318}, abstract = {

This work concerns multiple-scattering problems for time-harmonic equations in a reference generic media. We consider scatterers that can be sources, obstacles or compact perturbations of the reference media. Our aim is to restrict the computational domain to small compact domains containing the scatterers. We use Robin-to-Robin (RtR) operators (in the most general case) to express boundary conditions for the interior problem. We show that one can always factorize the RtR map using only operators defined using single-scatterer problems. This factorization is based on a decomposition of the diffracted field, on the whole domain where it is defined. Assuming that there exists a good method for solving single-scatterer problems, it then gives a convenient way to compute RtR maps for a random number of scatterers.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.231109.090710s}, url = {http://global-sci.org/intro/article_detail/cicp/7363.html} }
TY - JOUR T1 - Operator Factorization for Multiple-Scattering Problems and an Application to Periodic Media JO - Communications in Computational Physics VL - 2 SP - 303 EP - 318 PY - 2012 DA - 2012/12 SN - 11 DO - http://dor.org/10.4208/cicp.231109.090710s UR - https://global-sci.org/intro/article_detail/cicp/7363.html KW - AB -

This work concerns multiple-scattering problems for time-harmonic equations in a reference generic media. We consider scatterers that can be sources, obstacles or compact perturbations of the reference media. Our aim is to restrict the computational domain to small compact domains containing the scatterers. We use Robin-to-Robin (RtR) operators (in the most general case) to express boundary conditions for the interior problem. We show that one can always factorize the RtR map using only operators defined using single-scatterer problems. This factorization is based on a decomposition of the diffracted field, on the whole domain where it is defined. Assuming that there exists a good method for solving single-scatterer problems, it then gives a convenient way to compute RtR maps for a random number of scatterers.

J. Coatléven & P. Joly. (2020). Operator Factorization for Multiple-Scattering Problems and an Application to Periodic Media. Communications in Computational Physics. 11 (2). 303-318. doi:10.4208/cicp.231109.090710s
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