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.

  1. Y. Boubendir, X. Antoine and C. Geuzaine, A Quasi-Optimal Non-Overlapping Domain Decomposition Algorithm for the Helmholtz Equation. Journal of Computational Physics 231 (2), (2012), pp.262-280 ↩︎

Bertrand Thierry
Bertrand Thierry

Permanent researcher at CNRS, working in numerical simulation for wave propagation.