Using Spectral Coarse Spaces of the H-Geneo Type for Efficient Solutions of the Helmholtz Equation

06.05.2025 14:00 – 15:00

The Helmholtz equation is a widely used model in wave propagation and scattering problems. However, its numerical solution can be computationally expensive in high-frequency regime due to the oscillatory solution and the potential contrasts in coefficients. Parallel domain decomposition methods have been identified as promising solvers for such problems, but they often require a suitable coarse space to achieve robust behaviour. In this talk, we present the H-GenEO coarse space, which constructs an effective coarse space using localized eigenvectors of the Helmholtz operator. Since the GenEO coarse space is designed for symmetric positive definite problems, the theory cannot be extended directly to the H-GenEO coarse space due to the indefinite nature of the underlying problem. During this talk it will be shown that the H-GenEO coarse space is capable of providing the required robust behaviour when used with a suitable domain decomposition method. Numerical experiments for increasing wave numbers demonstrate the efficiency of the method in solving complex Helmholtz problems, with potential applications in various scientific and engineering domains.

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

entrée libre