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

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.

[1]  J. D. Bredehoeft,et al.  Digital Analysis of Areal Flow in Multiaquifer Groundwater Systems: A Quasi Three‐Dimensional Model , 1970 .

[2]  J. W. Watts.  A Method for Improving Line Successive Overrelaxation in Anisotropic Problems-A Theoretical Analysis , 1973 .

[3]  D. Kershaw.  The incomplete Cholesky—conjugate gradient method for the iterative solution of systems of linear equations , 1978 .

[4]  Khalid Aziz,et al.  A New Iterative Method For Solving Reservoir Simulation Equations , 1972 .

[5]  Magnus R. Hestenes,et al.  Conjugate Direction Methods in Optimization , 1980 .

[6]  R. D. Richtmyer,et al.  Difference methods for initial-value problems , 1959 .

[7]  J. Meijerink,et al.  An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix , 1977 .

[8]  P. C. Trescott,et al.  Comparison of iterative methods of solving two-dimensional groundwater flow equations , 1977 .

[9]  H. H. Rachford,et al.  The Numerical Solution of Parabolic and Elliptic Differential Equations , 1955 .

[10]  George M. Hornberger,et al.  Numerical Methods in Subsurface Hydrology , 1972, Soil Science Society of America Journal.

[11]  J. W. Watts.  An Iterative Matrix Solution Method Suitable for Anisotropic Problems , 1971 .

[12]  H. L. Stone.  ITERATIVE SOLUTION OF IMPLICIT APPROXIMATIONS OF MULTIDIMENSIONAL PARTIAL DIFFERENTIAL EQUATIONS , 1968 .

[13]  D. Young.  Iterative methods for solving partial difference equations of elliptic type , 1954 .