@article{hamilton_berrill_clarno_pawlowski_toth_kelley_evans_philip_2016, title={An assessment of coupling algorithms for nuclear reactor core physics simulations}, volume={311}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2016.02.012}, abstractNote={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 of JFNK and Anderson acceleration relative to standard Picard iteration are performed on a 3D model of a nuclear fuel assembly. Both criticality (k-eigenvalue) and critical boron search problems are considered.}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Hamilton, Steven and Berrill, Mark and Clarno, Kevin and Pawlowski, Roger and Toth, Alex and Kelley, C. T. and Evans, Thomas and Philip, Bobby}, year={2016}, month={Apr}, pages={241–257} }
@article{toth_kelley_2015, title={Convergence Analysis for Anderson Acceleration}, volume={53}, ISSN={0036-1429 1095-7170}, url={http://dx.doi.org/10.1137/130919398}, DOI={10.1137/130919398}, abstractNote={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. Without assumptions on the coefficients, we prove q-linear convergence of Anderson(1) and, in the case of linear problems, Anderson($m$). We observe that the optimization problem for the coefficients can be formulated and solved in nonstandard ways and report on numerical experiments which illustrate the ideas.}, number={2}, journal={SIAM Journal on Numerical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Toth, Alex and Kelley, C. T.}, year={2015}, month={Jan}, pages={805–819} }