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An open problem that arises when using modern iterative linear solvers, suchas the preconditioned conjugate gradient (PCG) method or Generalized MinimumRESidual method (GMRES) is how to choose the residual tolerance in the linearsolver to be consistent with the tolerance on the solution error. This problemis especially acute for integrated groundwater models which are implicitlycoupled to another model, such as surface water models, and resolve bothmultiple scales of flow and temporal interaction terms, giving rise to linearsystems with variable scaling.  This article uses the theory of 'forward error bound estimation' to show howrescaling the linear system affects the correspondence between the residualerror in the preconditioned linear system and the solution error. Usingexamples of linear systems from models developed using the USGS GSFLOW packageand the California State Department of Water Resources' Integrated Water FlowModel (IWFM), we observe that this error bound guides the choice of a practicalmeasure for controlling the error in rescaled linear systems. It is found thatforward error can be controlled in preconditioned GMRES by rescaling the linearsystem and normalizing the stopping tolerance. We implemented a preconditionedGMRES algorithm and benchmarked it against the Successive-Over-Relaxation (SOR)method. Improved error control reduces redundant iterations in the GMRESalgorithm and results in overall simulation speedups as large as 7.7x. Thisresearch is expected to broadly impact groundwater modelers through thedemonstration of a practical approach for setting the residual tolerance inline with the solution error tolerance.

Error Control of Iterative Linear Solvers for Integrated Groundwater Models