Anderson(m) is a method for acceleration of fixed point iteration which stores m + 1 prior evaluations of the fixed point map and computes the new iteration as a linear combination of those evaluations. Anderson(0) is fixed point iteration. In this paper we show that Anderson(m) is locally r-linearly convergent if the fixed point map is a contraction and the coefficients in the linear combination remain bounded. We prove q-linear convergence of the residuals for linear problems for Anderson(1) without the assumption of boundedness of the coefficients. We observe that the optimization problem for the coefficients can be formulated and solved in non-standard ways and report on numerical experiments which illustrate the ideas.

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This paper evaluates the performance of multiphysics coupling algorithms applied to a light water nuclear reactor core simulation. The simulation couples the k-eigenvalue form of the neutron transport equation with heat conduction and subchannel flow equations. We compare Picard iteration (block Gauss-Seidel) to Anderson acceleration and multiple variants of preconditioned Jacobian-free Newton-Krylov (JFNK). The performance of the methods are evaluated over a range of energy group structures and core power levels. A novel physics-based approximation to a Jacobian-vector product has been developed to mitigate the impact of expensive on-line cross section processing steps. Numerical simulations demonstrating the efficiency

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We investigate the effects of the δ 2 transform on the partial sums of Fourier series for functions with a finite number of jumps, which in general, converge slowly. Although the δ 2 process is known to accelerate convergence for many sequences, we prove that in this case, the transformed series will usually fail to converge to the original function.