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6 papers · 2 filters
Balanced truncation and singular perturbation approximation model order reduction for stochastically controlled linear systems
Martin Redmann, Melina A. Freitag
When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used. Balanced truncation (BT) and singular perturbation approxima…
GMRES convergence bounds for eigenvalue problems
Melina Freitag, Patrick Kürschner, Jennifer Pestana
The convergence of GMRES for solving linear systems can be influenced heavily by the structure of the right hand side. Within the solution of eigenvalue problems via inverse iterat…
Unbiased `walk-on-spheres' Monte Carlo methods for the fractional Laplacian
Andreas E. Kyprianou, Ana Osojnik, Tony Shardlow
We consider Monte Carlo methods for simulating solutions to the analogue of the Dirichlet boundary-value problem in which the Laplacian is replaced by the fractional Laplacian and…
Recent Results on Domain Decomposition Preconditioning for the High-frequency Helmholtz Equation using Absorption
I. G. Graham, E. A. Spence, E. Vainikko
In this paper we present an overview of recent progress on the development and analysis of domain decomposition preconditioners for discretised Helmholtz problems, where the precon…
A regularized penalty-multiplier method for approximating cavitation solutions with prescribed cavity volume size
Pablo V. Negrón-Marrero, Jeyabal Sivaloganathan
Let be the region occupied by a body and let be a flaw point in . Let be an energy functional (defined on some appropriate admissibl…
Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation
Peter Benner, Sergey Dolgov, Venera Khoromskaia +1
In this paper, we study and implement the structural iterative eigensolvers for the large-scale eigenvalue problem in the Bethe-Salpeter equation (BSE) based on the reduced basis a…