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Error Control Of Iterative Linear Solvers For Integrated Groundwater Models, Matthew Dixon, Z Bai, C F. Brush, F I. Chung, E C. Dogrul, T M. Kadir

Business Analytics and Information Systems

An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient method or Generalized Minimum RESidual (GMRES) method, is how to choose the residual tolerance in the linear solver to be consistent with the tolerance on the solution error. This problem is especially acute for integrated groundwater models, which are implicitly coupled to another model, such as surface water models, and resolve both multiple scales of flow and temporal interaction terms, giving rise to linear systems with variable scaling. This article uses the theory of “forward error bound estimation” to explain the correspondence between …