A Vectorized Polynomial Preconditioned Conjugate Gradient Solver Package for the Usgs 3-d Ground-water Model Solution Algorithms the Coeecient Matrix Resulting from a Nite Diierence Discretization of the Governing

A vectorized polynomial preconditioned conjugate gradient (PPCG) numerical algorithm is presented as an additional solver package interfaced with the Modular Three-Dimensional Finite Diierence GroundWater Flow Model 1] (hereafter called the USGS model). The USGS model with its existing strongly implicit procedure (SIP) and slice-successive overrelaxation (SSOR) solution packages and with the new PPCG package is applied to the solution of three successively more complex 3-D groundwater modeling problems on the CDC CYBER 205. The USGS model determines the head distribution for all nodes in each of the three problems. The purpose of this paper is to compare the eeciency of the three algorithms for varying problem sizes. PROGRAM DESCRIPTION The rst problem considered is taken from reference 1]. It involves a groundwater system of 22.8 square kilometer areal extent consisting of three aquifers (two connned and one water-table) modeled with 675 nite diierence nodes on a 31515 grid. The aquifers are isotropic. Flow into the system is from precipitation recharge and from an adjacent lake which provides a constant-head boundary condition. Buried drain tubes and fteen discharging wells provide outtow from the system. The second problem, consisting of 16,875 nodes on a 3 75 75 grid, incorporates all of the features of the smallest problem with the addition of unsteady ow with seventeen time steps. Finally, the third and largest problem consists of 62,500 nodes on a 4 125 125 grid with anisotropic transmissivities and randomly introduced relatively impermeable zones.