Optimized Eigenvalue Solvers for the Neutron Transport Equation A. Vidal-Ferr` andiz 1[0000−0001−5449−7356] , S.Gonz´alez-Pintor 2[0000−0003−2470−2085] , D. Ginestar 3[0000−0003−1243−6648] , A. Carre˜ no 1[0000−0003−2302−1157] , and G. Verd´ u 1[0000−0001−5098−080X] 1 Instituto Universitario de Seguridad Industrial, Radiof´ ısica y Medioambiental Universitat Polit` ecnica de Val` encia, Val` encia, Spain, anvifer2@upv.es, amcarsan@iqn.upv.es, gverdu@iqn.upv.es 2 Zenuity, Lindholmspiren 2, 41756, G¨ oteborg Sweden, segonpin@gmail.com 3 Instituto Universitario de Matem´ atica Multidisciplinar, Universitat Polit` ecnica de Val` encia, Val` encia, Spain, dginesta@mat.upv.es Abstract. A discrete ordinates method has been developed to approxi- mate the neutron transport equation for the computation of the lambda modes of a given configuration of a nuclear reactor core. This method is based on discrete ordinates method for the angular discretization, re- sulting in a very large and sparse algebraic generalized eigenvalue prob- lem. The computation of the dominant eigenvalue of this problem and its corresponding eigenfunction has been done with a matrix-free imple- mentation using both, the power iteration method and the Krylov-Schur method. The performance of these methods has been compared solving different benchmark problems with different dominant ratios. Keywords: Neutron Transport, Discrete Ordinates, Eigenvalues. 1 Introduction Neutron transport simulations of nuclear systems are an important goal to ensure the efficient and safe operation of nuclear reactors. The steady-state neutron transport equation [4] predicts the quantity of neutrons in every region of the reactor and thus, the number of fissions and nuclear reactions. The neutron transport equation for three-dimensional problems is an equation defined in a support space of dimension 7, and this makes that high-fidelity simulations using this equation can only be done using super computers. Different approximations have been successfully used for deterministic neu- tron transport. They eliminate the energy dependence of the equations by means of the a multi-group approximation and use a special treatment to eliminate the dependence on the direction of flight of the incident neutrons. The angular discretization of the neutron transport equation chosen in this work has been the Discrete Ordinates method (S N ), which is a collocation method based on a ICCS Camera Ready Version 2018 To cite this paper please use the final published version: DOI: 10.1007/978-3-319-93701-4_65