Proceedings of the 45th annual Design Automation Conference
Preconditioner updates applied to CFD model problems
Applied Numerical Mathematics
Fast and robust solvers for pressure-correction in bubbly flow problems
Journal of Computational Physics
Reuse, Recycle, Reduce (3R) -- strategies for the calculation of transient magnetic fields
Applied Numerical Mathematics
A capacitance solver for incremental variation-aware extraction
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
Journal of Scientific Computing
Improving Triangular Preconditioner Updates for Nonsymmetric Linear Systems
Large-Scale Scientific Computing
Minimizing communication in sparse matrix solvers
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
Incremental large-scale electrostatic analysis
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Variation-aware interconnect extraction using statistical moment preserving model order reduction
Proceedings of the Conference on Design, Automation and Test in Europe
The Lanczos Method for Parameterized Symmetric Linear Systems with Multiple Right-Hand Sides
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
Flexible GMRES with Deflated Restarting
SIAM Journal on Scientific Computing
Accelerating the LSTRS Algorithm
SIAM Journal on Scientific Computing
Nonsymmetric Preconditioner Updates in Newton-Krylov Methods for Nonlinear Systems
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Supporting dynamic parameter sweep in adaptive and user-steered workflow
Proceedings of the 6th workshop on Workflows in support of large-scale science
SIAM Journal on Matrix Analysis and Applications
Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems
SIAM Journal on Matrix Analysis and Applications
Journal of Computational Physics
Accelerated GCRO-DR method for solving sequences of systems of linear equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Amesos2 and Belos: Direct and iterative solvers for large sparse linear systems
Scientific Programming
Sound transmission through a poroelastic layered panel
Computational Mechanics
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Many problems in science and engineering require the solution of a long sequence of slowly changing linear systems. We propose and analyze two methods that significantly reduce the total number of matrix-vector products required to solve all systems. We consider the general case where both the matrix and right-hand side change, and we make no assumptions regarding the change in the right-hand sides. Furthermore, we consider general nonsingular matrices, and we do not assume that all matrices are pairwise close or that the sequence of matrices converges to a particular matrix. Our methods work well under these general assumptions, and hence form a significant advancement with respect to related work in this area. We can reduce the cost of solving subsequent systems in the sequence by recycling selected subspaces generated for previous systems. We consider two approaches that allow for the continuous improvement of the recycled subspace at low cost. We consider both Hermitian and non-Hermitian problems, and we analyze our algorithms both theoretically and numerically to illustrate the effects of subspace recycling. We also demonstrate the effectiveness of our algorithms for a range of applications from computational mechanics, materials science, and computational physics.