A comparison of the incomplete cholesky‐conjugate gradient method with the strongly implicit method as applied to the solution of two‐dimensional groundwater flow equations

Abstract

This paper compares the efficiency of the strongly implicit procedure (SIP) and the incomplete Cholesky‐conjugate gradient method (ICCG) applied to the solution of the finite difference approximating equations for groundwater flow. Results for five isotropic two‐dimensional test problems are presented. Three are linear confined aquifer problems, and two are nonlinear water table aquifer problems; in all but one of the test problems the aquifer was considered to be nonhomogeneous. Both SIP and ICCG as applied to water table aquifer problems make use of iteration parameters. These were varied for each of the test problems to reduce the amount of computational work needed to find a solution. ICCG was usually substantially more efficient than SIP when applied to the confined aquifer test problems. For the water table aquifer test problems, SIP and ICCG performed equally well.

A Comparison of Iterative Methods as Applied to the Solution of the Nonlinear Three-Dimensional Groundwater Flow Equation

“…When e << Aij, (F') A so that an appropriate approximation for F' is the matrix A. With B A, (6) becomes: (7) x"+l=[A(x")]-lb, the method of Picard, an example of those methods whose basic structure is given by (6), where B F'. As with (5), (6) and (7) represent a variety of methods depending upon the method used to approximate x "+1.…”

“…Investigations of the performance of the many other methods for the solution of simultaneous nonlinear equations, applied to watertable aquifer simulations, are scarce in the literature. The author (Kuiper [6]) made a comparison of Picard iteration in conjunction with SIP (Picard-SIP), and Picard iteration in conjunction with the incomplete Cholesky conjugate gradient method (Picard-ICCG), applied to a two-dimensional watertable aquifer. Comments by Remson et al [9] praise a method called one-step point SOR-Newton by Ortega and Rheinboldt [7], whose naming and classification procedures will also be used in this work.…”

“…Depending upon the method used to approximate x "+ from(5), and also upon the number of inner iterations tn 1,2,..., M that might be used to arrive at this approximation,(5) represents a variety of Newton methods. The remainder of the methods in type 1 consist of those which have as their basic structure:(6) x "+' -x" -[B(x")]-'F(x") Downloaded 11/18/14 to 199.212.65.39. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php…”

Water-resources activities of the U.S. Geological Survey in South Dakota; fiscal year 1984

“…Project leader; Kathy D. Peter Project period;1981 Cooperators; South Dakota Department of Water and Natural Resources, Black HiJls Conservancy Sub-District.…”

Water-resources investigations of the U.S. Geological Survey in South Dakota, project status summary, July 1, 1983

“…Hamilton Project period;1981-1986 Cooperator; South Dakota Department of Water and Natural Resources.…”