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

Hussam Al Daas | Zendy; Laura Grigori | Zendy; Pascal Hé | Zendy; Philippe Ricoux | Zendy

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

Author(s) -

Hussam Al Daas,

Laura Grigori,

Pascal Hé,

Philippe Ricoux

Publication year - 2021

Publication title -

acm transactions on mathematical software

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.767

H-Index - 87

eISSN - 1557-7295

pISSN - 0098-3500

DOI - 10.1145/3439746

Subject(s) - deflation , krylov subspace , linear subspace , sequence (biology) , subspace topology , singular value decomposition , mathematics , linear system , generalized minimal residual method , mathematical optimization , computer science , algorithm , mathematical analysis , pure mathematics , economics , monetary policy , biology , monetary economics , genetics

This article 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 Singular Value Decomposition based deflation technique. We consider the recycling in two contexts: recycling the Krylov subspace between the restart cycles and recycling a deflation subspace when the matrix changes in a sequence of linear systems. Numerical experiments on real-life reservoir simulation demonstrate the impact of our proposed strategy.

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