Section: New Results

Recycling Krylov subspaces and reducing deflation subspaces for solving a sequence of linear systems

In [32] we present 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.