5 papers
A Guided Tour of Modern Domain Decomposition: From Schwarz Iterations to Robust Preconditioners and HPC Implementations
Victorita Dolean, Pierre Jolivet, Frédéric Nataf +1
Domain decomposition methods (DDMs) provide a unifying framework for the scalable numerical solution of partial differential equations. Originating from Schwarz's alternating metho…
Coarse spaces using extended generalized eigenproblems for heterogeneous Helmholtz problems
Emile Parolin, Frédéric Nataf
An abstract construction of coarse spaces for non-Hermitian problems and non-Hermitian domain decomposition preconditioners based on extended generalized eigenproblems was proposed…
Coarse spaces for non-symmetric two-level preconditioners based on local extended generalized eigenproblems
Frédéric Nataf, Emile Parolin
Domain decomposition (DD) methods are a natural way to take advantage of parallel computers when solving large scale linear systems. Their scalability depends on the design of the…
A robust and adaptive GenEO-type domain decomposition preconditioner for problems in three-dimensional general topologies
Niall Bootland, Victorita Dolean, Frédéric Nataf +1
In this paper we design, analyse and test domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-ty…
A GenEO Domain Decomposition method for Saddle Point problems
Frédéric Nataf, Pierre-Henri Tournier
We introduce an adaptive element-based domain decomposition (DD) method for solving saddle point problems defined as a block two by two matrix. The algorithm does not require any k…