Parallel Double Sweep Preconditioner for the Optimized Schwarz Algorithm Applied to High Frequency Helmholtz and Maxwell Equations

Observing that the optimized Schwarz algorithm is equivalent to the solution of a linear system, we design a new preconditioner as an approximate inverse of the iteration operator, in the particular case of a layered decomposi- tion. We show that it can be rewritten as two independent sequences of subproblem solves (forward and back- ward), hence the name ‘double sweep’. The whole algorithm is implemented as a matrix-free GMRES iteration, that requires no more additional preprocessing than the original algorithm. Numerical experiments indicate that the convergence rate is independent of the wavenumber and number of subdomains when good approximations of the DtN maps are used, in both homogeneous and non-homogeneous cases.