This item is non-discoverable
Loading...
Non-discoverable
Krylov subspace recycling for sequences of shifted linear systems
Soodhalter, KM Szyld, DB Xue, F
Soodhalter, KM
Szyld, DB
Xue, F
Citations
Altmetric:
Genre
Journal Article
Date
2014-01-01
Advisor
Committee member
Group
Department
Permanent link to this record
Collections
Research Projects
Organizational Units
Journal Issue
DOI
10.1016/j.apnum.2014.02.006
Abstract
We study the use of Krylov subspace recycling for the solution of a sequence of slowly-changing families of linear systems, where each family consists of shifted linear systems that differ in the coefficient matrix only by multiples of the identity. Our aim is to explore the simultaneous solution of each family of shifted systems within the framework of subspace recycling, using one augmented subspace to extract candidate solutions for all the shifted systems. The ideal method would use the same augmented subspace for all systems and have fixed storage requirements, independent of the number of shifted systems per family. We show that a method satisfying both requirements cannot exist in this framework. As an alternative, we introduce two schemes. One constructs a separate deflation space for each shifted system but solves each family of shifted systems simultaneously. The other builds only one recycled subspace and constructs approximate corrections to the solutions of the shifted systems at each cycle of the iterative linear solver while only minimizing the base system residual. At convergence of the base system solution, we apply the method recursively to the remaining unconverged systems. We present numerical examples involving systems arising in lattice quantum chromodynamics. © 2014 IMACS.
Description
Citation
Citation to related work
Elsevier BV
Has part
Applied Numerical Mathematics
ADA compliance
For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu