Anderson acceleration for nonlinear PDEs discretized by space–time spectral methods.

In this work, we consider Anderson acceleration for numerical solutions 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 Schrödinger 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 in solving 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. [ABSTRACT FROM AUTHOR]