GCROT swMATH ID: 8876 Software Authors: Hicken, Jason E.; Zingg, David W. Description: 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. Homepage: http://epubs.siam.org/doi/abs/10.1137/090754674 Keywords: nonsymmetric sparse linear systems; Krylov subspace; iterative methods; truncation; flexible iterations; { t GMRES}; { t LGMRES}; { t GCROT}; numerical examples; preconditioning; finite volume method; generalized conjugate residual; orthogonalization; numerical experiments; aerodynamics Related Software: SparseMatrix; Spalart-Allmaras; LAPACK; LYAPACK; TensorToolbox; TAU; GenIDLEST; BiCGstab; Adjoint; MatrixMarket; P-SPARSLIB Cited in: 10 Publications all top 5 Cited by 21 Authors 4 Hicken, Jason E. 4 Zingg, David W. 1 Ahuja, Kapil 1 Amritkar, Amit 1 Brown, David A. 1 Castonguay, Patrice 1 Chen, Chih-Hao 1 de Sturler, Eric 1 Elbouyahyaoui, Lakhdar 1 Heyouni, Mohammed 1 Li, Houbiao 1 Meng, Jing 1 Nadarajah, Siva K. 1 Osusky, Michal 1 Saberi Movahed, Farid 1 Świrydowicz, Katarzyna 1 Tafti, Danesh K. 1 Tajaddini, Azita 1 Timme, Sebastian 1 Xu, Shenren 1 Zhu, Peiyong Cited in 5 Serials 3 Journal of Computational Physics 2 Computers and Fluids 2 Journal of Computational and Applied Mathematics 1 Applied Numerical Mathematics 1 SIAM Journal on Scientific Computing all top 5 Cited in 6 Fields 10 Numerical analysis (65-XX) 6 Fluid mechanics (76-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Partial differential equations (35-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of deformable solids (74-XX) Citations by Year