Improved Domain Decomposition Method for the Helmholtz Equation
In this talk we will present recent improvements to the quasioptimal domain decomposition method for the Helmholtz equation presented in ^{1}. The key point of the method is the construction of an accurate local approximation of the exact DirichlettoNeumann operator which leads to a new transmission operator between subdomains. We will show that this local approximation, based on complex Pad approximants, is wellsuited for large scale parallel finite element simulations of high frequency scattering problems, with either manual or automatic mesh partitioning. In particular, we will show that our algorithm is quasioptimal in the sense that the convergence rate of the iterative solver depends only slightly on both the frequency and the mesh refinement.

Y. Boubendir, X. Antoine and C. Geuzaine, A QuasiOptimal NonOverlapping Domain Decomposition Algorithm for the Helmholtz Equation. Journal of Computational Physics 231 (2), (2012), pp.262280 ↩︎