Optimized Schwarz Methods for Heterogeneous Helmholtz and Maxwell's Equations

摘要

We studied the performance of optimized Schwarz methods for Helmholtz and Maxwell's equations for heterogeneous media. Using Fourier analysis, we showed that the convergence factor of the optimized Schwarz methods for the Helmholtz equation and the Maxwell's equations are the same, and it suffices therefore to study the algorithms only for the Helmholtz equation. We then studied in detail the performance for three different choices of the relationship between the wave number and the mesh size to control the pollution effect, and showed that increasing the resolution improves the performance of the optimized Schwarz methods. It was not possible to show all the proofs in detail in this short manuscript, but more information can be found in the PhD thesis (Veneros 2015).