Computer Programs Mary C. Hill Preconditioned Conjugate Gradient 2 (PCG2), A Computer Program for Solving Ground-Water Flow Equations 1990, U.S. Geological Survey Water-Resources Investigations Report 90-4048 Mary C. Hill This report documents PCG2: a numerical code to be used with the U.S. Geological Survey modular, three-dimensional, finite-difference, ground-water flow model. PCG2 uses the preconditioned conjugate-gradient method to solve the equations produced by the model for hydraulic head. Linear or nonlinear flow equations may be simulated. PCG2 includes two preconditioning options: modified incomplete Cholesky preconditioning, which is efficient on scalar computers; and polynomial preconditioning, which requires less computer storage and, with modifications that depend on the computer used, is most efficient on vector computers. Convergence of the solver is determined using both head-change and residual criteria. Nonlinear problems are solved using Picard iterations. This documentation provides a description of the preconditioned conjugate-gradient method and the two preconditioners, detailed instructions for linking PCG2 to the modular model, sample data inputs, a brief description of PCG2, and a FORTRAN listing. Common problem: The convergence criteria discussed on page 12 of the documentation are dimensional. Given units of feet and seconds, the values of HCLOSE and RCLOSE are often similar in value. Given units of feet and days, however, RCLOSE generally would be much larger, in fact, 60 seconds/minute x 60 minutes/hour x 24hours/day = 86,400 seconds/day larger! Program change since release: A new value called DAMP has been added to the input file, and can be useful when PCG2 does not converge. A value of DAMP less than 1.0, but larger than 0.0, reduces the amount the hydraulic heads are changed each solver iteration. The solver will take longer to converge, but will approach the solution more smoothly, which aids convergence in some circumstances. This is often helpful, for example, when layers are confined and convertible, and cells vacillating between being wet and dry are prohibiting solver convergence. An electronic version of the documentation is not available. It can be ordered from: U.S. Geological Survey Books and Open File Services Box 25425 Federal Center Denver, CO 80225-0425 The program is distributed with MODFLOW and MODFLOWP. mchill@usgs.gov Last Modified: March 17, 1999