Inverse power method for source term inversion in neutron transport equation

Considering the inversion of the source term for neutron transport in such as fission reaction, the numerical solution of the effective multiplication factor related to k-eigenvalue problem is investigated. Based on the spherical harmonic functions expansion and finite difference for discretization of transport equation, an inverse power scheme is presented for calculation of the k-eigenvalue problem. This scheme can obviously speed up convergence rate under the proper initial value condition. The numerical results show that the error of the inverse power method gets only 0.045 45% at 3rd iterative step while the error of the standard power method is still reaching to 0.109% after 20 iterative steps, therefore the inverse power algorithm is endowed with higher computing rate and accuracy than the standard power method if an available estimate of the effective multiplication factor is pre-provided.