Jemcov, Aleksandar; Maruszewski, Joseph P Nonlinear Flow Solver Acceleration by Reduced Rank Extrapolation Incollection 46th AIAA Aerospace Sciences Meeting and Exhibit, pp. 609, 2008. Abstract | Links | BibTeX | Tags: Acceleration, Algorithm, Extrapolation, GMRES, Nonlinear, RRE, SIMPLE, Solver @incollection{jemcov2008nonlinear,
title = {Nonlinear Flow Solver Acceleration by Reduced Rank Extrapolation},
author = { Aleksandar Jemcov and Joseph P Maruszewski},
url = {https://www.researchgate.net/profile/Aleksandar_Jemcov/publication/275275199_Nonlinear_Flow_Solver_Acceleration_by_Reduced_Rank_Extrapolation/links/5536ca190cf2058efdea9401.pdf?origin=publication_detail_rebranded&ev=pub_int_prw_xdl&msrp=mHcz4Kt3tcM0fKKvzoZAfJu5CZ7bJAZTebm7svkdI8HyTV2DqiloQBxWK3ZC9HHtc1VaKywIo53Gq4ACRkkbmQ%3D%3D_mZOVHfxww2SuKoJv0YEv1yJ19XXhbwqiKJ%2FuZ%2FsAeTe%2BZ2RdfWruA0KDkoFLyPO0ebx%2BKC9jrGwRj%2B%2F%2BKjsf7A%3D%3D},
year = {2008},
date = {2008-01-01},
booktitle = {46th AIAA Aerospace Sciences Meeting and Exhibit},
pages = {609},
abstract = {Convergence acceleration of nonlinear flow solvers through use of vector sequence ex-trapolation techniques is presented. In particular, suitability of the Reduced Rank Extrap-olation (RRE) algorithm for the use of convergence acceleration of nonlinear flow solvers is examined. In the RRE algorithm, the solution is obtained through a linear combination of Krylov vectors with weighting coefficients obtained by minimizing L2 norm of error in this space with properly chosen constraint conditions. This process effectively defines vector sequence extrapolation process in Krylov subspace that corresponds to the GMRES method applied to nonlinear problems. Moreover, when the RRE algorithm is used to solve nonlinear problems, the flow solver plays the role of the preconditioner for the non-linear GMRES method. Benefits of the application of the RRE algorithm include better convergence rates, removal of residual stalling and improved coupling between equations in numerical models. Proposed algorithm is independent of the type of flow solver and it is equally applicable to explicit, implicit, pressure and density based algorithms. Nomenclature Q Vector of conserved variables R Residual vector F c Vector of convective fluxes F v Vector of viscous fluxes S Source vector H Total enthalpy, J/m 3 p pressure, Pa τ ij viscous tensor ρ Density, Kg/m 3 u Velocity vector, m/s u X-component of velocity vector, m/s v Y-component of velocity vector, m/s w Z-component of velocity vector, m/s V Contravariant velocity, m/s f e,i Vector of external forces Φ Generic transport variable M Nonlinear preconditioning operator F Fixed-point function ∂ Q (·) Jacobian with respect to Q α ν Extrapolation coefficients c ν o t Time, s ∂Ω Boundary of computational domain Ω Computational domain},
keywords = {Acceleration, Algorithm, Extrapolation, GMRES, Nonlinear, RRE, SIMPLE, Solver},
pubstate = {published},
tppubtype = {incollection}
}
Convergence acceleration of nonlinear flow solvers through use of vector sequence ex-trapolation techniques is presented. In particular, suitability of the Reduced Rank Extrap-olation (RRE) algorithm for the use of convergence acceleration of nonlinear flow solvers is examined. In the RRE algorithm, the solution is obtained through a linear combination of Krylov vectors with weighting coefficients obtained by minimizing L2 norm of error in this space with properly chosen constraint conditions. This process effectively defines vector sequence extrapolation process in Krylov subspace that corresponds to the GMRES method applied to nonlinear problems. Moreover, when the RRE algorithm is used to solve nonlinear problems, the flow solver plays the role of the preconditioner for the non-linear GMRES method. Benefits of the application of the RRE algorithm include better convergence rates, removal of residual stalling and improved coupling between equations in numerical models. Proposed algorithm is independent of the type of flow solver and it is equally applicable to explicit, implicit, pressure and density based algorithms. Nomenclature Q Vector of conserved variables R Residual vector F c Vector of convective fluxes F v Vector of viscous fluxes S Source vector H Total enthalpy, J/m 3 p pressure, Pa τ ij viscous tensor ρ Density, Kg/m 3 u Velocity vector, m/s u X-component of velocity vector, m/s v Y-component of velocity vector, m/s w Z-component of velocity vector, m/s V Contravariant velocity, m/s f e,i Vector of external forces Φ Generic transport variable M Nonlinear preconditioning operator F Fixed-point function ∂ Q (·) Jacobian with respect to Q α ν Extrapolation coefficients c ν o t Time, s ∂Ω Boundary of computational domain Ω Computational domain |

Jemcov, Aleksandar; Maruszewski, Joseph P; Jasak, Hrvoje Performance improvement of algebraic multigrid solver by vector sequence extrapolation Conference CFD 2007 Conference, CFD Society of Canada, 2007. Abstract | Links | BibTeX | Tags: AMG, Extrapolation, Grid, MPE, Multigrid, PFE, RRE, Solver @conference{jemcov2007performance,
title = {Performance improvement of algebraic multigrid solver by vector sequence extrapolation},
author = { Aleksandar Jemcov and Joseph P Maruszewski and Hrvoje Jasak},
url = {https://www.researchgate.net/profile/Aleksandar_Jemcov/publication/255577657_Performance_Improvement_of_Algebraic_Multigrid_Solver_by_Vector_Sequence_Extrapolation/links/0deec530e01e9a1e91000000.pdf?origin=publication_detail_rebranded&ev=pub_int_prw_xdl&msrp=l%2FRqA1L7b0MsHj%2FU443TuP1z2sy1wGnZ36isKwJidqyfbvxfh1znfzdHGghuxvDZ1UsaTbrdodbLRM48tuw%2FSQ%3D%3D_0d7vGCwXITSmkPjwIoqTdFkhnJyIFX3cZPQVfLL9zoYt2B6bVpSn9PRtuwh7yMdk54t1LUp8kE3YNFzdQE15GA%3D%3D},
year = {2007},
date = {2007-01-01},
booktitle = {CFD 2007 Conference, CFD Society of Canada},
abstract = {Algebraic Multigrid Method (AMG) performance im- provement by vector sequence extrapolation is exam- ined. Projective Forward Extrapolation (PFE), Min- imal Polynomial Extrapolation (MPE) and Reduced Rank Extrapolation (RRE) are applied to the AMG resulting in a hybrid approach, vector extrapolated AMG. The impact of vector sequence extrapolation is shown to improve performance of the AMG in number of cycles and execution time, resulting in three new methods: PFE-AMG, MPE-AMG and RRE-AMG. Computational results of the application of vector ex- trapolated AMG to sparse matrices arising from dis- cretization of fluid flow equations are presented show- ing performance improvements compared to the tradi- tional AMG.},
keywords = {AMG, Extrapolation, Grid, MPE, Multigrid, PFE, RRE, Solver},
pubstate = {published},
tppubtype = {conference}
}
Algebraic Multigrid Method (AMG) performance im- provement by vector sequence extrapolation is exam- ined. Projective Forward Extrapolation (PFE), Min- imal Polynomial Extrapolation (MPE) and Reduced Rank Extrapolation (RRE) are applied to the AMG resulting in a hybrid approach, vector extrapolated AMG. The impact of vector sequence extrapolation is shown to improve performance of the AMG in number of cycles and execution time, resulting in three new methods: PFE-AMG, MPE-AMG and RRE-AMG. Computational results of the application of vector ex- trapolated AMG to sparse matrices arising from dis- cretization of fluid flow equations are presented show- ing performance improvements compared to the tradi- tional AMG. |