A fast Jacobian-Free Newton-Krylov iterative solver for eigenvalue search problems in the reactor physics

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.