Nonlocal optimized schwarz methods for time-harmonic electromagnetics

Abstract

We introduce a new domain decomposition strategy for time harmonic Maxwell’s equations that is valid in the case of automatically generated subdomain partitions with possible presence of cross-points. The convergence of the algorithm is guaranteed and we present a complete analysis of the matrix form of the method. The method involves transmission matrices responsible for imposing coupling between subdomains. We discuss the choice of such matrices, their construction and the impact of this choice on the convergence of the domain decomposition algorithm. Numerical results and algorithms are provided.

Non-local optimized Schwarz method with physical boundaries

“…The whole theory was confirmed by numerical results both in 2D and 3D. While the previous developments were concerned with scalar harmonic wave propagation, the case of Maxwell's equations was considered in [7,20].…”

“…As cartesian products, these spaces are equipped with norms and duality pairings given by (7). Apart from the boundary terms attached to H b (Γ), the space H(Ω) should be understood as functions defined over Ω, admitting potential jumps through interfaces.…”

“…In a series of articles [5,6,7,8], we proposed a variant of OSM where the usual local swapping exchange operator is replaced by an alternative a priori non-local operator that naturally accommodates the presence of cross-points. This new approach can cope with arbitrary subdomain partitions, with a possibly very complicated wire basket.…”