Name
Abstract | ||
|---|---|---|
This work presents a new Krylov-subspace-recycling method for efficiently solving sequences of linear systems of equations characterized by varying right-hand sides and symmetric positive-definite matrices. As opposed to typical truncation strategies used in recycling such as deflation, we propose a truncation method inspired by goal-oriented proper orthogonal decomposition (POD) from model reduction. This idea is based on the observation that model reduction aims to compute a low-dimensional subspace that contains an accurate solution; as such, we expect the proposed method to generate a low-dimensional subspace that is well suited for computing solutions that can satisfy inexact tolerances. In particular, we propose specific goal-oriented POD "ingredients" that align the optimality properties of POD with the objective of Krylov-subspace recycling. To compute solutions in the resulting "augmented" POD subspace, we propose a hybrid direct/iterative three-stage method that leverages (1) the optimal ordering of POD basis vectors, and (2) well-conditioned reduced matrices. Numerical experiments performed on solid-mechanics problems highlight the benefits of the proposed method over existing approaches for Krylov-subspace recycling. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1137/16M1057693 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | DocType | Volume |
Krylov-subspace recycling,proper orthogonal decomposition,augmented Krylov methods,model reduction,conjugate-gradient method | Journal | 37 |
Issue | ISSN | Citations |
3 | 0895-4798 | 2 |
PageRank | References | Authors |
0.45 | 9 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kevin Carlberg | 1 | 93 | 10.20 |
| Virginia Forstall | 2 | 3 | 0.80 |
| Ray S. Tuminaro | 3 | 447 | 38.09 |