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8 papers · 1 filter
DFPI, A unified framework for deflated linear solvers: bridging the gap between Krylov subspace methods and Fixed-Point Iterations
Jeremy Kalfoun, Guillaume Pierrot, John Cagnol
Iterative algorithms are instrumental in modern numerical simulation for solving systems arising from the discretization of PDEs. They face however significant challenges in indust…
Asynchronous iterations of HSS method for non-Hermitian linear systems
Guillaume Gbikpi-Benissan, Qinmeng Zou, Frédéric Magoulès
A general asynchronous alternating iterative model is designed, for which convergence is theoretically ensured both under classical spectral radius bound and, then, for a classical…
Resilient asynchronous primal Schur method
Guillaume Gbikpi-Benissan, Frédéric Magoulès
This paper introduces the application of the asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is de…
Asynchronous multiplicative coarse-space correction
Guillaume Gbikpi-Benissan, Frédéric Magoulès
This paper introduces the multiplicative variant of the recently proposed asynchronous additive coarse-space correction method. Definition of an asynchronous extension of multiplic…
Uniform estimates for a fully discrete scheme integrating the linear heat equation on a bounded interval with pure Neumann boundary conditions
Guillaume Dujardin, Pauline Lafitte
This manuscript deals with the analysis of numerical methods for the full discretization (in time and space) of the linear heat equation with Neumann boundary conditions, and it pr…
Accurate Coarse Residual for Two-Level Asynchronous Domain Decomposition Methods
Guillaume Gbikpi-Benissan, Frédéric Magoulès
Recently, asynchronous coarse-space correction has been achieved within both the overlapping Schwarz and the primal Schur frameworks. Both additive and multiplicative corrections h…