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PRECONDITIONED CONJUGATE-GRADIENT 2 (PCG2), a computer program for solving ground-water flow equations

Water-Resources Investigations Report 90-4048
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https://doi.org/10.3133/wri904048

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Abstract

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 conditions may be simulated. PCG2 includes two reconditioning 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.

Suggested Citation

Hill, M.C., 1990, PRECONDITIONED CONJUGATE-GRADIENT 2 (PCG2), a computer program for solving ground-water flow equations: U.S. Geological Survey Water-Resources Investigations Report 90-4048, iii, 43 p. :ill. ;28 cm., https://doi.org/10.3133/wri904048.

Publication type Report
Publication Subtype USGS Numbered Series
Title PRECONDITIONED CONJUGATE-GRADIENT 2 (PCG2), a computer program for solving ground-water flow equations
Series title Water-Resources Investigations Report
Series number 90-4048
DOI 10.3133/wri904048
Year Published 1990
Language ENGLISH
Publisher U.S. Geological Survey ; Books and Open-File Reports Section,
Description iii, 43 p. :ill. ;28 cm.
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