%0 Journal Article %T A fast Jacobian-Free Newton-Krylov iterative solver for eigenvalue search problems in the reactor physics %J Radiation Physics and Engineering %I K. N. Toosi University of Technology %Z 2645-6397 %A Abbasi, Mohammadreza %D 2020 %\ 08/01/2020 %V 1 %N 3 %P 1-9 %! A fast Jacobian-Free Newton-Krylov iterative solver for eigenvalue search problems in the reactor physics %K ‎JFNK method %K ‎Even-parity neutron transport equation %K ‎Eigenvalue search %K ‎Nonlinear systems‎ %R 10.22034/rpe.2020.89324 %X ‎The Jacobian-Free Newton-Krylov (JFNK) method has been widely used in solving nonlinear equations arising in many applications‎. ‎In this paper‎, ‎the JFNK solver is examined as an alternative to the traditional power iteration method for calculation of the fundamental eigenmode in reactor analysis based on even-parity neutron transport theory‎. ‎Since the Jacobian is not formed the only extra storage required is associated with the workspace of the Krylov solver used at every Newton step‎. ‎A new nonlinear function is developed for the even-parity neutron transport equation utilized to solve the eigenvalue problem using the JFNK‎. ‎This Newton-based method is compared with the standard iterative power method for a number of multi-groups‎, ‎one and two dimensional neutron transport benchmarks‎. ‎The results show that the proposed algorithm generally ends with fewer iterations and shorter run times than those of the traditional power method‎. %U https://rpe.kntu.ac.ir/article_89324_7e3d4462f9b3f73668d6ee37d10c443e.pdf