Operator Factorization for Multiple-Scattering Problems and an Application to Periodic Media (Communications in Computational Physics, 2020)
This work concerns multiple-scattering problems for time-harmonic equations in a reference generic media. We consider scatterers that can be sources, obstaclesor 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 forthe interior problem. We show that one can always factorize the RtR map using onlyoperators defined using single-scatterer problems. This factorization is based on a decomposition of the diffracted field, on the whole domain where it is defined. Assumingthat there exists a good method for solving single-scatterer problems, it then gives aconvenient way to compute RtR maps for a random number of scatterers.