Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition
Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition
We prove sharp bounds on certain impedance-to-impedance maps (and their compositions) for the Helmholtz equation with large wavenumber (i.e., at high-frequency) using semiclassical defect measures.The paper [GGG + 22] recently showed that the behaviour of these impedance-to-impedance maps (and their compositions) dictates the convergence of the parallel overlapping Schwarz domain-decomposition …