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Anderson Acceleration (AA) is a method to accelerate the convergence of fixedpoint iterations for nonlinear, algebraic systems of equations. Due to therequirement of solving a least squares problem at each iteration and a relianceon modified Gram-Schmidt for updating the iteration space, AA requires extracostly synchronization steps for global reductions. Moreover, the number ofreductions in each iteration depends on the size of the iteration space. Inthis work, we introduce three low synchronization orthogonalization algorithmsinto AA within SUNDIALS that reduce the total number of global reductions periteration to a constant of 2 or 3, independent of the size of the iterationspace. A performance study demonstrates the reduced time required by the newalgorithms at large processor counts with CPUs and demonstrates the predictedperformance on multi-GPU architectures. Most importantly, we provideconvergence and timing data for multiple numerical experiments to demonstratereliability of the algorithms within AA and improved performance at parallelstrong-scaling limits.

Performance of Low Synchronization Orthogonalization Methods in Anderson Accelerated Fixed Point Solvers