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U.S. GEOLOGICAL SURVEY
Water-Resources Open-File Report 2004-1261

125th Anniversary Logo

MODFLOW-2000, THE U.S. GEOLOGICAL SURVEY MODULAR GROUND-WATER MODEL -- GMG LINEAR EQUATION SOLVER PACKAGE DOCUMENTATION

By: J. D. Wilson, NRC Post-Doc, and R. L. Naff, U.S. Geological Survey


ABSTRACT

A geometric multigrid solver (GMG), based in the preconditioned conjugate gradient algorithm, has been developed for solving systems of equations resulting from applying the cell-centered finite difference algorithm to flow in porous media. This solver has been adapted to the U.S. Geological Survey ground-water flow model MODFLOW-2000. The documentation herein is a description of the solver and the adaptation to MODFLOW-2000.


TABLE OF CONTENTS

  • Abstract
  • Introduction
  • The GMG Solver and MF2K
    • Finite-Difference Matrix
    • Specified Heads and Inactive Cells
    • Linear Solution
    • Nonlinear Solution
    • Convergence Criteria
  • Multigrid
    • Smoothers
    • ILU Smoother
    • Coarse-Grid Correction
    • nu-Cycle
  • Comparison of GMG with AMG
  • Input Instructions for the GMG Solver
    • Adaptive Damping Example
    • Semi-Coarsening Example
    • ILU PCG Example
  • Description of GMG Interface
    • Module GMG1ALG
    • Module GMG1AP
  • Description of GMG Library
    • Vector Library
    • Solver Library
    • PCG Operator
    • MG Operator
    • CCFD Library
    • MF2KGMG Library

LIST OF FIGURES

  1. Smoothing the error
  2. Coarse-Grid Correction
  3. Grid Schedules
  4. Fractures with entrapped NAPL

LIST OF TABLES

  1. Computational differences between GMG and AMG

REDUCTION OF ERROR IN TWO-LEVEL MULTIGRID ALGORITHM


GMG Animation


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