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Preconditioned conjugate gradient methods for large-scale fluid flow applications (1989)

Ewing, Richard E.

Springer

BIT 29 (1989), S. 850-866

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ISSN: 1572-9125

Keywords: 65F10 ; 65N20

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract The simulation of large-scale fluid flow applications often requires the efficient solution of extremely large nonsymmetric linear and nonlinear sparse systems of equations arising from the discretization of systems of partial differential equations. While preconditioned conjugate gradient methods work well for symmetric, positive-definite matrices, other methods are necessary to treat large, nonsymmetric matrices. The applications may also involve highly localized phenomena which can be addressed via local and adaptive grid refinement techniques. These local refinement methods usually cause non-standard grid connections which destroy the bandedness of the matrices and the associated ease of solution and vectorization of the algorithms. The use of preconditioned conjugate gradient or conjugate-gradient-like iterative methods in large-scale reservoir simulation applications is briefly surveyed. Then, some block preconditioning methods for adaptive grid refinement via domain decomposition techniques are presented and compared. These techniques are being used efficiently in existing large-scale simulation codes.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01932749

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Application of conjugate-gradient-like methods to a hyperbolic problem in porous-media flow (1987)

Obeysekare, Upul R. B. ; Allen, Myron B. ; Ewing, Richard E. ; [et al.]

Chichester : Wiley-Blackwell

International Journal for Numerical Methods in Fluids 7 (1987), S. 551-566

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ISSN: 0271-2091

Keywords: Generalized Conjugate Residual Method ; Nested Factorization ; Buckley-Leverett Equation ; Preconditioned Conjugate Gradients ; 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: This paper presents the application of a preconditioned conjugate-gradient-like method to a non-self-adjoint problem of interest in underground flow simulation. The method furnishes a reliable iterative solution scheme for the non-symmetric matrices arising at each iteration of the non-linear time-stepping scheme. The method employs a generalized conjugate residual scheme with nested factorization as a preconditioner. Model runs demonstrate significant computational savings over direct sparse matrix solvers.

Additional Material: 12 Ill.