AN EFFICIENT TRANSMISSION OPERATOR FOR COMPUTING WAVE PROPAGATION BY DOMAIN DECOMPOSITION

For large size problems, domain decompositions can be used to solve wave propagation problems such as the Helmholtz equation. Generally, this leads to an iterative process where data are exchanged at the boundary between subdomains. Depending on the quality of this exchange the number of iterations is more or less. Moreover, this number of iterations can depend on the frequency and on the number of domains. Here, we propose transmission operators approximating the Dirichlet to Neumann (DtN) operator which is known to be near optimal. We show this can be done using only the solution of problems involving sparse matrices and so keeping the computational time at an acceptable level. When this is combined with the double sweep preconditioner and that the computational domain is decomposed into a sequel of slices this results in an algorithm with a low number of iterations. Different examples are presented to support the precedent analysis.