Richardson's iteration with dynamic parameters and the SIP incomplete factorization for the solution of linear systems of equations

Journal Article · Tue Dec 01 04:00:00 EST 1981 · SPEJ, Soc. Pet. Eng. J.; (United States)

DOI:https://doi.org/10.2118/7686-PA· OSTI ID:5378767

Saylor, P E

Reservoir simulation yields a system of linear algebraic equations, Ap.q, that may be solved by Richardson's iterative method, p/sup (k+1)/.p/sup (k)/+t/sub k/r/sup (k)/, where r/sup (k)/.q - Ap/sup (k)/ is the residual and t/sub 0/,...t/sub k/ are acceleration parameters. The incomplete factorization, K/sub //alpha/, of the strongly implicit procedure (SIP) yields an improvement of Richardson's method, p/sup (k+1)/.p/sup (k)/+t/sub k/K/sub //alpha//sup -1/r/sup (k)/. Parameter /alpha/ originates from SIP. The product of the L and U factors produced by SIP gives K/sub //alpha/.LU. The best values of the t/sub k/ acceleration parameters may be computed dynamically by an efficient algorithm; the best value of /alpha/ must be found by trial and error, which is not hard for only one value. The advantages of the method are presented. 15 refs.

• Research Organization: Univ of Ill
• OSTI ID: 5378767
• Journal Information: SPEJ, Soc. Pet. Eng. J.; (United States), Journal Name: SPEJ, Soc. Pet. Eng. J.; (United States) Vol. 21:6; ISSN SSPJD
• Country of Publication: United States
• Language: English

Related Subjects

02 PETROLEUM
020300* -- Petroleum-- Drilling & Production
ALGORITHMS
COMPUTERIZED SIMULATION
ENGINEERING
ITERATIVE METHODS
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
OIL WELLS
RESERVOIR ENGINEERING
SIMULATION
WELLS