Memory-efficient recycling of large Krylov-subspaces for sequences of Hermitian linear systems

TL;DR

This paper introduces a memory-efficient Krylov subspace recycling method for sequences of Hermitian linear systems, reducing computational and storage costs while maintaining effectiveness in solving time-dependent PDE discretizations.

Contribution

A novel short-recurrence residual-optimal recycling method derived from the preconditioned conjugate residual approach, optimized for large Krylov subspaces with lower overhead.

Findings

Method reduces storage and computational costs compared to R-MINRES.

Numerical experiments demonstrate improved efficiency.

Applicable to sequences of Hermitian systems in PDE contexts.

Abstract

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.