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Some special purpose preconditioners for conjugate gradient‐like methods applied to CFD
Author(s) -
Strigberger J.,
Baruzzi G.,
Habashi W.,
Fortin M.
Publication year - 1993
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650160703
Subject(s) - transonic , preconditioner , conjugate gradient method , inviscid flow , domain decomposition methods , mathematics , computation , finite element method , euler equations , incomplete lu factorization , mathematical optimization , iterative method , matrix decomposition , mathematical analysis , aerodynamics , algorithm , mechanics , physics , eigenvalues and eigenvectors , quantum mechanics , thermodynamics
Standard preconditioners such as incomplete LU decomposition perform well when used with conjugate gradient‐like iterative solvers such as GMRES for the solution of elliptic problems. However, efficient computation of convection‐dominated problems requires, in general, the use of preconditioners tuned to the particular class of fluid‐flow problems at hand. This paper presents three such preconditioners. The first is applied to the finite element computation of inviscid (Euler equations) transonic and supersonic flows with shocks and uses incomplete LU decomposition applied to a matrix with extra artificial dissipation. The second preconditioner is applied to the finite difference computation of unsteady incompressible viscous flow; it uses incomplete LU decomposition applied to a matrix to which a pseudo‐compressible term has been added. The third method and application are similar to the second, only the LU decomposition is replaced by Beam‐warming approximate factorization. In all cases, the results are in very good agreement with other published results and the new algorithms are found to be competitive with others; it is anticipated that the efficiency and robustness of conjugate‐gradient‐like methods will render them the method of choice as the difficulty of the problems that they are applied to is increased.