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Application of conjugate‐gradient‐like methods to a hyperbolic problem in porous‐media flow
Author(s) -
Obeysekare Upul R. B.,
Allen Myron B.,
Ewing Richard E.,
George John H.
Publication year - 1987
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.1650070603
Subject(s) - preconditioner , conjugate gradient method , conjugate residual method , mathematics , derivation of the conjugate gradient method , residual , iterative method , incomplete lu factorization , factorization , scheme (mathematics) , matrix (chemical analysis) , flow (mathematics) , linear system , mathematical optimization , algorithm , mathematical analysis , computer science , matrix decomposition , geometry , gradient descent , physics , eigenvalues and eigenvectors , materials science , quantum mechanics , machine learning , composite material , artificial neural network
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.