Multigrid Methods in GIS Grid-Cell–Based Modeling Environment

Abstract

Multigrid methods use a series of successively coarser grids to accelerate the solution of equations arising from the numerical solution of partial differential equations. A grid-cell–based geographic information system (GIS) with a map algebra language is capable of displaying and manipulating spatial data and attributes and handling the data arrays and results arising in ground-water simulation problems. To examine the efficacy of GIS to solve ground-water flow problems, we have performed ground-water modeling directly within a GIS without going outside the system for model solution. We have applied the multigrid method to solve steady ground-water flow problems in heterogeneous aquifers. Execution times for the GIS-multigrid approach using simple iterative techniques greatly exceed those of traditional ground-water simulation models due to the creation of temporary grids for intermediate calculations during the simulation. Efficient handling of boundary conditions is another difficult problem in GIS grid-cell–based modeling.