@article { author = {Abbasi, Mohammadreza}, title = {A fast Jacobian-Free Newton-Krylov iterative solver for eigenvalue search problems in the reactor physics}, journal = {Radiation Physics and Engineering}, volume = {1}, number = {3}, pages = {1-9}, year = {2020}, publisher = {K. N. Toosi University of Technology}, issn = {2645-6397}, eissn = {2645-5188}, doi = {10.22034/rpe.2020.89324}, abstract = {‎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.}, keywords = {‎JFNK method,‎Even-parity neutron transport equation,‎Eigenvalue search,‎Nonlinear systems‎}, url = {https://rpe.kntu.ac.ir/article_89324.html}, eprint = {https://rpe.kntu.ac.ir/article_89324_7e3d4462f9b3f73668d6ee37d10c443e.pdf} }