Anderson Acceleration for Nonlinear Finite Volume Scheme for Advection-Diffusion Problems

We consider the solution of systems of nonlinear algebraic equations that appear in a positivity preserving finite volume scheme for steady-state advection-diffusion equations. We propose and analyze numerically an efficient strategy for accelerating the Picard method when it is applied to these systems. The strategy is based on the Anderson acceleration and the adaptive inexact solution of linear systems. We demonstrate its numerical robustness for three black-box preconditioners.

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