ISSN:
0271-2091
Keywords:
Bi-conjugate gradient
;
Conjugate gradient
;
Conjugate gradient squared
;
Finite elements
;
Flow simulation
;
Preconditioning
;
Vector processor
;
Frontal solver
;
Navier-Stokes
;
Boussinesq approximation Newton method
;
Picard iteration
;
Galerkin method
;
Petrov-Galerkin
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
A series of numerical experiments on the Cray XMP/48 and on the Cray 2 investigate the robustness and economy of direct and unsymmetric conjugate gradient (CG) type methods for the solution of matrix systems arising from a 3D FEM discretization of fluid flow problems. Computations on a Boussinesq flow model problem with either ILU preconditioned or unpreconditioned unsymmetric CG methods are presented. Such experiments seem to indicate that the unpreconditioned BICG method is robust for moderately non-linear incompressible Navier-Stokes FEM discretizations and that the ILU preconditioned BICG method is very robust and more economic than an unsymmetric frontal solver when the generous memory of the Cray 2 is exploited to store both the matrix and its preconditioner. We cover some of the programming aspects of direct and iterative methods on a supercomputer and find that direct methods have advantages: the crucial CPU-consuming area of code is compact but overwhelming, and its percentage of total CPU usage is independent of the spectral properties of the matrix involved. An optimal implementation of the unsymmetric CG method is more difficult because its work is related to the spectral distribution of the matrix considered and because there is no single portion of the code that overwhelmingly dominates the CPU usuage.
Additional Material:
3 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/fld.1650100806
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