A rapidly convergent hybrid domain decomposition method for the solution of large 3D scattering problems

Abstract

On account of the CT, this partitioning of D1 minimizes the dimension of the admittance matrices. Also, uniqueness is ensured at each step. Obviously, the bottleneck of this technique is the computation - and, if needed, the memory storage - of matrices Yi. However, we may replace one or several of them by approximate matrices, derived from the exact ones computed as indicated above, provided they satisfy (13) that ensures the uniqueness of the solutions in Omegai. Also, the fact that non diagonal blocks in Yi may be rank-deficient can be of interest to compress these matrices. Finally, the problem may be solved by employing a local DDM on the largest interface only, the subproblems in the subdomains located on each side of this interface being solved exactly via the technique presented.