Subregion Iteration of Finite Element Method for Large‐Field Problems of Ground‐Water Solute Transport

Abstract

To compute groundwater solute transport, the CPU memory requirement can be drastically reduced by using the subregion iteration of the orthogonal-upstream weighting finite element method. The use of an orthogonal-upstream weighting function results in an irreducible and diagonally dominant coefficient matrix. These properties provide sufficient conditions for the convergence of block iteration methods. Computer runs for a test problem were carried out for 10 × 10, 30 × 30, and 50 × 50 grid systems with 2, 3, and 4 subregions. The CPU memory and CPU time were monitored during each run. The number of iterations required for the convergent solution in each time step was also recorded. The results are useful for determining the number of subregions required for a given computer memory capacity, and for estimating the CPU time when using the subregion iteration method.