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Anderson Acceleration for spectral methods for time dependent PDEs
In this talk, we consider Anderson acceleration for numerical solution of nonlinear time dependent partial differential equations discretized by space-time spectral methods, where classical fixed-point methods converge slowly or even diverge. Specifically, we apply Anderson acceleration with finite window size w to speed up fixed-point methods in solving nonlinear reaction diffusion, nonlinear Schrodinger and Navier Stokes equations. We focus on studying the influence of the window size w on the number of iterations to numerical convergence. Numerical results show the high efficiency of Anderson acceleration to solve a variety of nonlinear time dependent problems discretized by space-time spectral methods, and a small value of w is enough to achieve good performance. This is joint work with Dr. Yunhui He.