Some applications of substructuring and domain decomposition techniques to radiation and scattering of time-harmonic electromagnetic waves

After a quick review of the domain decomposition methods, and, more particularly on their application to large size problems relative to radiation and scattering of time-harmonic waves, we describe two contributions of the authors in this context. The two contributions are related to the scattering of a time-harmonic electromagnetic wave by a large perfectly conducting structure including a deep cavity. The first contribution is a substructuring technique. It is used to increase the speed of the convergence of the iterative algorithm in a Multi-Level Fast Multipol Method (MLFMM) solution. Numerical experiments illustrate the effectiveness of the approach since the number of iterations of the underlying Krylov iterative method remains almost constant while increasing a characteristic length in the problem. The second contribution proposes an adaptation of the overlapping domain decomposition techniques for a boundary integral formulation. It is used here to perform a hybridization of an exact formulation, used at the opening of the cavity, with an asymptotic high-frequency method employed for the rest of the exterior boundary of the structure. Numerical results demonstrate the reliability and the efficiency of the method. To cite this article: N. Balin et al., C. R. Physique 7 (2006).