Operator Factorization for Multiple-Scattering Problems and an Application to Periodic Media
J. Coatleven 1*, P. Joly 11 POems Project Team, UMR ENSTA/CNRS/INRIA, Inria Rocquencourt, 78153 Le Chesnay Cedex, France.
Received 23 November 2009; Accepted (in revised version) 9 July 2010
Available online 24 October 2011
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.AMS subject classifications: 35C15, 35J05, 35Q60, 74J20
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Key words: Multiple-scattering, harmonic wave equation, exact boundary conditions, periodic media.
Email: firstname.lastname@example.org (J. Coatleven), email@example.com (P. Joly)