Recycling BiCGSTAB with an application to parametric model order reduction / Kapil Ahuja, Eric de Sturler, Lihong Feng, Peter Benner

Abstract

Abstract: Krylov subspace recycling is a process for accelerating the convergence of sequences of linear systems. Based on this technique we have recently developed the recycling BiCG algorithm. We now generalize and extend this recycling theory to BiCGSTAB. Recycling BiCG focuses on efficiently solving sequences of dual linear systems, while the focus here is on efficiently solving sequences of single linear systems (assuming non-symmetric matrices for both recycling BiCG and recycling BiCGSTAB). As compared to other methods for solving sequences of single linear systems with non-symmetric matrices (e.g., recycling variants of GMRES), BiCG based recycling algorithms, like recycling BiCGSTAB, have the advantage that they involve a short-term recurrence, and hence, do not suffer from storage issues and are also cheaper with respect to the orthogonalizations. We modify the BiCGSTAB algorithm to use a recycle space, which is built from left and right approximate eigenvectors. Using our algorithm for parametric model order reduction examples gives good results. We show about 40% reduction in iteration count when using recycling BiCGSTAB as compared to the one without recycling.