New applications of Orthomin(1) algorithm for K-eigenvalue problem in Reactor Physics

This paper presents some new investigations on the use of Orthomin(1) algorithm for the solution of K-eigenvalue problem in Nuclear Reactor Physics. The algorithm was first used by Suetomi and Sekimoto [Conjugate gradient like methods and their application to eigenvalue problems for neutron diffusion equations, Annals of Nuclear Energy, 18(4) (1991) 205-227.] to find fundamental mode solution of K-eigenvalue problem based on multi-group neutron diffusion theory. It was shown to be an efficient alternative to the conventional methods based on power iterations. The use of this algorithm needs software development to evaluate product of coefficient matrices with vectors. Here, it is shown that the algorithm can also be applied to the K-eigenvalue equation cast in terms of fission matrix. This opens up the possibility of using conventional well-established diffusion codes to implement Orthomin(1) so that new software is not needed. Apart from this, a remarkable feature of Orthomin(1) brought out in this paper is its utility to find higher mode solutions of the K-eigenvalue problem. This procedure is radically different from the methods commonly used for finding higher K-modes. It may also be of interest for finding higher mode eigensolutions in other scientific fields