Abstract
This paper introduces the application of asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is designed, whose asynchronous convergence is established under classical spectral radius conditions. For the usual case where local Schur complement matrices are not constructed, suitable splittings based only on explicitly generated matrices are provided. Numerical experiments are conducted on a supercomputer for both Poisson’s and linear elasticity problems. The asynchronous Schur solver outperformed the classical conjugate-gradient-based one in case of computing node failures.
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The research has been supported by the RUDN University Program 5-100, the French national program LEFE/INSU, the project ADOM (Méthodes de décomposition de domaine asynchrones) of the French National Research Agency (ANR), and using HPC resources from the Mésocentre computing center of CentraleSupélec and École Normale Supérieure Paris-Saclay supported by CNRS and Région Île-de-France.
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Gbikpi-Benissan, G., Magoulès, F. Resilient asynchronous primal Schur method. Appl Math 67, 679–704 (2022). https://doi.org/10.21136/AM.2022.0146-21
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DOI: https://doi.org/10.21136/AM.2022.0146-21