Inexact Subdomain Solves Using Deflated GMRES for Helmholtz Problems
N. Bootland (University of Strathclyde)
V. Dwarka (TU Delft - Numerical Analysis)
P. Jolivet (ENSIACET)
V. Dolean (Université Côte d'Azur, University of Strathclyde)
C. Vuik (TU Delft - Delft Institute of Applied Mathematics)
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Abstract
In recent years, domain decomposition based preconditioners have become popular tools to solve the Helmholtz equation. Notorious for causing a variety of convergence issues, the Helmholtz equation remains a challenging PDE to solve numerically. Even for simple model problems, the resulting linear system after discretisation becomes indefinite and tailored iterative solvers are required to obtain the numerical solution efficiently. At the same time, the mesh must be kept fine enough in order to prevent numerical dispersion ‘polluting’ the solution [4]. This leads to very large linear systems, further amplifying the need to develop economical solver methodologies.
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