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Related Experiment Video

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Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure

Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure

Published on: April 25, 2025

Error control of iterative linear solvers for integrated groundwater models.

Matthew F Dixon¹, Zhaojun Bai, Charles F Brush

¹Department of Mathematics, One Shields Avenue, University of California, Davis, CA 95616, USA. mfdixon@ucdavis.edu

|February 1, 2011

Summary

Choosing the right residual tolerance for iterative linear solvers is crucial for accurate groundwater modeling. This study demonstrates how forward error bounds improve solver performance and enable significant speedups in simulations.

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Area of Science:

Environmental Science
Computational Science
Applied Mathematics

Background:

Modern iterative linear solvers require careful selection of residual tolerance for accurate results.
Integrated groundwater models present challenges due to variable scaling in linear systems.

Purpose of the Study:

To establish a correspondence between residual error and solution error in linear systems.
To provide a practical method for setting residual tolerance in groundwater models.

Main Methods:

Utilizing forward error bound estimation theory.
Implementing and benchmarking a preconditioned Generalized Minimum Residual (GMRES) algorithm.
Comparing GMRES against the Successive Over-Relaxation (SOR) method.

Main Results:

Forward error bounds effectively guide the control of linear system errors.
Preconditioned GMRES with forward error control achieved speedups up to 7.74× compared to SOR.
GMRES offers a viable replacement for SOR in legacy groundwater modeling software.

Conclusions:

A practical and general approach for setting residual tolerance in line with solution error tolerance is demonstrated.
GMRES with forward error control can enhance the efficiency of groundwater simulations.
This research impacts groundwater modelers by improving solver tolerance selection and simulation speed.