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Recycling Krylov Subspaces and Truncating Deflation Subspaces for Solving Sequence of Linear Systems

Hussam Al Daas 1 Laura Grigori 1 Pascal Hénon 2 Philippe Ricoux 3
1 ALPINES - Algorithms and parallel tools for integrated numerical simulations
INSMI - Institut National des Sciences Mathématiques et de leurs Interactions, Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
Abstract : This paper presents deflation strategies related to recycling Krylov subspace methods for solving one or a sequence of linear systems of equations. Besides well-known strategies of deflation, Ritz- and harmonic Ritz-based deflation, we introduce an SVD-based deflation technique. We consider the recycling in two contexts, recycling the Krylov subspace between the cycles of restarts and recycling a deflation subspace when the matrix changes in a sequence of linear systems. Numerical experiments on real-life reservoir simulations demonstrate the impact of our proposed strategy.
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https://hal.inria.fr/hal-01886546
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Hussam Al Daas, Laura Grigori, Pascal Hénon, Philippe Ricoux. Recycling Krylov Subspaces and Truncating Deflation Subspaces for Solving Sequence of Linear Systems. [Research Report] RR-9206, Inria Paris. 2018. ⟨hal-01886546v2⟩

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