3 papers
math.NA2025
Preconditioning of GMRES for Helmholtz problems with quasimodes
Victorita Dolean, Pierre Marchand, Axel Modave +1
Finite element methods are effective for Helmholtz problems involving complex geometries and heterogeneous media. However, the resulting linear systems are often large, indefinite,…
math.NA2025
Convergence analysis of GMRES applied to Helmholtz problems near resonances
Victorita Dolean, Pierre Marchand, Axel Modave +1
The finite element solution of Helmholtz problems near resonant or quasi-resonant frequencies poses significant challenges, as iterative solvers typically suffer from severely degr…
math.AP2021
High-frequency estimates on boundary integral operators for the Helmholtz exterior Neumann problem
Jeffrey Galkowski, Pierre Marchand, Euan A. Spence
We study a commonly-used second-kind boundary-integral equation for solving the Helmholtz exterior Neumann problem at high frequency, where, writing for the boundary of the obs…