Anderson Acceleration Using the H^-s Norm

02/10/2020

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by   Yunan Yang, et al.

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Anderson acceleration (AA) is a technique for accelerating the convergence of fixed-point iterations. In this paper, we apply AA to a sequence of functions and modify the norm in its internal optimization problem to the H^-s norm, for some integer s, to bias it towards low-frequency spectral content in the residual. We analyze the convergence of AA by quantifying its improvement over Picard iteration. We find that AA based on the H^-2 norm is well-suited to solve fixed-point operators derived from second-order elliptic differential operators and a Helmholtz recovery problem.