Non-overlapping domain decomposition algorithm based on modified transmission conditions for the Helmholtz equation

Abstract

A square-root based transmission conditions domain decomposition method was recently introduced for the Helmholtz equation. It produces an effective algorithm where the convergence is independent of the wavenumber and the mesh discretization. We modify here these conditions in order to guarantee well-posedness of local problems and further improve the efficiency of the whole method. Numerical results, in particular in the three dimensional case, show significant reduction of the computational time needed in the iterative procedure while preserving the iteration number when compared with the original algorithm.