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Closed form optimized transmission conditions for complex diffusion with many subdomains
Victorita Dolean, Martin J. Gander, Alexandros Kyriakis
Optimized transmission conditions in domain decomposition methods have been the focus of intensive research efforts over the past decade. Traditionally, transmission conditions are…
Can DtN and GenEO coarse spaces be sufficiently robust for heterogeneous Helmholtz problems?
Niall Bootland, Victorita Dolean
Numerical solution of heterogeneous Helmholtz problems presents various computational challenges, with descriptive theory remaining out of reach for many popular approaches. Robust…
Optimizing transmission conditions for multiple subdomains in the Magnetotelluric Approximation of Maxwell's equations
Victorita Dolean, Martin J. Gander, Alexandros Kyriakis
Classically transmission conditions between subdomains are optimized for a simplified two subdomain decomposition to obtain optimized Schwarz methods for many subdomains. We invest…
Several ways to achieve robustness when solving wave propagation problems
Niall Bootland, Victorita Dolean, Pierre Jolivet +3
Wave propagation problems are notoriously difficult to solve. Time-harmonic problems are especially challenging in mid and high frequency regimes. The main reason is the oscillator…
Two-level DDM preconditioners for positive Maxwell equations
Niall Bootland, Victorita Dolean, Frédéric Nataf +1
In this paper we develop and analyse domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type eq…
A comparison of coarse spaces for Helmholtz problems in the high frequency regime
Niall Bootland, Victorita Dolean, Pierre Jolivet +1
Solving time-harmonic wave propagation problems in the frequency domain and within heterogeneous media brings many mathematical and computational challenges, especially in the high…