Recycling Krylov Subspaces and Truncating Deflation Subspaces for Solving Sequence of Linear Systems
Recycling Krylov Subspaces and Truncating Deflation Subspaces for Solving Sequence of Linear Systems
Hussam Al Daas,L. Grigori,P. Hénon,P. Ricoux
TLDR
An Singular Value Decomposition based deflation technique that considers 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.
Abstract
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.