Memory-efficient recycling of large Krylov-subspaces for sequences of Hermitian linear systems
This work addresses the need for efficient iterative solvers in large-scale simulations involving time-dependent PDEs, where sequences of linear systems arise.
The paper introduces a new short-recurrence residual-optimal Krylov subspace recycling method for sequences of Hermitian linear systems with a fixed matrix and changing right-hand sides, achieving lower computational overhead and storage requirements compared to existing methods like R-MINRES.
We present a new short-recurrence reaidual-optimal Krylov subspace recycling method for sequences of Hermitian systems of linear equations with a fixed system matrix and changing right-hand sides. Such sequences of linear systems occur while solving, e.g., discretized time-dependent partial differential equations. With this new method it is possible to recycle large-dimensional Krylov-subspaces with smaller computational overhead and storage requirements compared to current Krylov subspace recycling methods as e.g. R-MINRES. In this paper we derive the method from the residual-optimal preconditioned conjugate residual method and duscuss implementation issues. Numerical experiments illustrate the efficiency of our method.