An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems
Abstract
In this paper we try to achieve hindependent convergence with preconditioned GMRES and BiCGSTAB for 2D singular perturbed equations. Three recently developed multigrid methods are adopted as a preconditioner. They are also used as solution methods in order to compare the performance of the methods as solvers and as preconditioners. Two of the multigrid methods differ only in the transfer operators. One uses standard matrix dependent prolongation operators from. The second uses {open_quotes}upwind{close_quotes} prolongation operators, developed. Both employ the Galerkin coarse grid approximation and an alternating zebra line GaussSeidel smoother. The third method is based on the block LU decomposition of a matrix and on an approximate Schur complement. This multigrid variant is presented in. All three multigrid algorithms are algebraic methods.
 Authors:

 Inst. for Algorithms and Scientific Computing, Sankt Augustin (Germany)
 C&C Research Lab., Sankt Augustin (Germany)
 Publication Date:
 Research Org.:
 Front Range Scientific Computations, Inc., Lakewood, CO (United States)
 OSTI Identifier:
 433348
 Report Number(s):
 CONF9604167Vol.1
ON: DE96015306; TRN: 97:0007200021
 Resource Type:
 Conference
 Resource Relation:
 Conference: Copper Mountain conference on iterative methods, Copper Mountain, CO (United States), 913 Apr 1996; Other Information: PBD: [1996]; Related Information: Is Part Of Copper Mountain conference on iterative methods: Proceedings: Volume 1; PB: 422 p.
 Country of Publication:
 United States
 Language:
 English
 Subject:
 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; PARALLEL PROCESSING; EFFICIENCY; ALGORITHMS; CONVERGENCE; ITERATIVE METHODS; EIGENVALUES
Citation Formats
Oosterlee, C W, and Washio, T. An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems. United States: N. p., 1996.
Web.
Oosterlee, C W, & Washio, T. An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems. United States.
Oosterlee, C W, and Washio, T. 1996.
"An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems". United States. https://www.osti.gov/servlets/purl/433348.
@article{osti_433348,
title = {An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems},
author = {Oosterlee, C W and Washio, T},
abstractNote = {In this paper we try to achieve hindependent convergence with preconditioned GMRES and BiCGSTAB for 2D singular perturbed equations. Three recently developed multigrid methods are adopted as a preconditioner. They are also used as solution methods in order to compare the performance of the methods as solvers and as preconditioners. Two of the multigrid methods differ only in the transfer operators. One uses standard matrix dependent prolongation operators from. The second uses {open_quotes}upwind{close_quotes} prolongation operators, developed. Both employ the Galerkin coarse grid approximation and an alternating zebra line GaussSeidel smoother. The third method is based on the block LU decomposition of a matrix and on an approximate Schur complement. This multigrid variant is presented in. All three multigrid algorithms are algebraic methods.},
doi = {},
url = {https://www.osti.gov/biblio/433348},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1996},
month = {12}
}