GCROT
A simplified and flexible variant of GCROT for solving nonsymmetric linear systems. There is a need for flexible iterative solvers that can solve large-scale (>10 6 unknowns) nonsymmetric sparse linear systems to a small tolerance. Among flexible solvers, flexible GMRES (FGMRES) is attractive because it minimizes the residual norm over a particular subspace. In practice, FGMRES is often restarted periodically to keep memory and work requirements reasonable; however, like restarted GMRES, restarted FGMRES can suffer from stagnation. This has led us to develop a flexible variant of the Krylov linear solver GCROT (generalized conjugate residual with inner orthogonalization and outer truncation). Unlike the original GCROT algorithm, the proposed GCROT variant uses a simplified truncation strategy similar to loose GMRES (LGMRES). This modification is motivated by numerical experiments that suggest the specific subspace retained in the outer iteration of GCROT is less important than its size. The flexible GCROT variant appears to be well suited for advection-dominated problems. In particular, when applied to an adjoint problem from computational aerodynamics, the proposed GCROT variant is robust and efficient compared with several popular truncated Krylov subspace methods. Finally, a flexible version of LGMRES is easily constructed by recognizing algorithmic similarities to GCROT.
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References in zbMATH (referenced in 10 articles )
Showing results 1 to 10 of 10.
Sorted by year (- Saberi-Movahed, Farid; Tajaddini, Azita; Heyouni, Mohammed; Elbouyahyaoui, Lakhdar: Some iterative approaches for Sylvester tensor equations. II: A tensor format of simpler variant of GCRO-based methods (2022)
- Chen, Chih-Hao; Nadarajah, Siva; Castonguay, Patrice: A dynamically deflated GMRES adjoint solver for aerodynamic shape optimization (2019)
- Xu, Shenren; Timme, Sebastian: Robust and efficient adjoint solver for complex flow conditions (2017)
- Brown, David A.; Zingg, David W.: Efficient numerical differentiation of implicitly-defined curves for sparse systems (2016)
- Amritkar, Amit; de Sturler, Eric; Ćwirydowicz, Katarzyna; Tafti, Danesh; Ahuja, Kapil: Recycling Krylov subspaces for CFD applications and a new hybrid recycling solver (2015)
- Hicken, J. E.; Zingg, D. W.: Dual consistency and functional accuracy: a finite-difference perspective (2014)
- Meng, Jing; Zhu, Pei-Yong; Li, Hou-Biao: A block (\mathrmGCROT(m, k)) method for linear systems with multiple right-hand sides (2014)
- Hicken, J. E.: Output error estimation for summation-by-parts finite-difference schemes (2012)
- Hicken, Jason E.; Osusky, Michal; Zingg, David W.: Comparison of parallel preconditioners for a Newton-Krylov flow solver (2011)
- Hicken, Jason E.; Zingg, David W.: A simplified and flexible variant of \textttGCROTfor solving nonsymmetric linear systems (2010)