Iterative residual-based vector methods to accelerate fixed point iterations

摘要

Fixed point iterations are still the most common approach to dealing with a variety of numerical problems such as coupled problems (multi-physics, domain decomposition, ...) or nonlinear problems (electronic structure, heat transfer, nonlinear mechanics, ...). Methods to accelerate fixed point iteration convergence or more generally sequence convergence have been extensively studied since the 1960's. For scalar sequences, the most popular and efficient acceleration method remains the 42 of Aitken. Various vector acceleration algorithms are available in the literature, which often aim at being multidimensional generalizations of the Delta(2) method.