  Anderson Acceleration (AA) is a method to accelerate the convergence of fixed
point iterations for nonlinear, algebraic systems of equations. Due to the
requirement of solving a least squares problem at each iteration and a reliance
on modified Gram-Schmidt for updating the iteration space, AA requires extra
costly synchronization steps for global reductions. Moreover, the number of
reductions in each iteration depends on the size of the iteration space. In
this work, we introduce three low synchronization orthogonalization algorithms
into AA within SUNDIALS that reduce the total number of global reductions per
iteration to a constant of 2 or 3, independent of the size of the iteration
space. A performance study demonstrates the reduced time required by the new
algorithms at large processor counts with CPUs and demonstrates the predicted
performance on multi-GPU architectures. Most importantly, we provide
convergence and timing data for multiple numerical experiments to demonstrate
reliability of the algorithms within AA and improved performance at parallel
strong-scaling limits.
