Improved Domain Decomposition Method for the Helmholtz Equation

In this talk we will present recent improvements to the quasi-optimal 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 Dirichlet-to-Neumann operator which leads to a new transmission operator between sub-domains. We will show that this local approximation, based on complex Pad approximants, is well-suited 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 quasi-optimal in the sense that the convergence rate of the iterative solver depends only slightly on both the frequency and the mesh refinement.