A modified JFNK method for solving the fundamental eigenmode in k-eigenvalue problem

Abstract

JFNK method has been used to solve the k-eigenvalue fundamental eigenmode problem recently, due to excellent local convergence rate and its promising application in multi-physics coupling problems. However, JFNK method is usually sensitive to the choice of initial values and may converge to high-order eigenmode. To enable JFNK method converge to fundamental eigenmode within a wide range of initial values, a modified JFNK method is proposed in this work. Based on physical-based information, two simple but practical modifications are utilized on eigenvector and k-eigenvalue respectively, which could adjust intermediate iterative solution into convergence basin of fundamental eigenmode. Four well-known k-eigenvalue benchmarks, as well as a k-eigenvalue problem with temperature feedback, are utilized to evaluate the performance of this modified JFNK method. The results show that the performance of modified JFNK method is significantly prior to that of traditional JFNK method, which can converge to the fundamental eigenmode globally.