Numerical solution of the k-eigenvalue problem
Solving the k-eigenvalue formulation of the Boltzmann radiation transport equation is a problem of significant interest in the design and analysis of nuclear reactors. Although considerable investigation into this problem has occurred over the last several decades, to date no truly satisfactory solution strategies exist. By appealing to the Davidson eigensolver framework, which has found favor in the computational chemistry community, we propose a new method that avoids many of the difficulties standard transport solvers encounter. In connection with the Davidson solver, we introduce a novel multigrid in energy preconditioner that efficiently approximates the inverse of the relevant transport operator. Numerical results demonstrating the effectiveness of the proposed strategy using the 2-D NEWT transport solver are presented. The role of this approach within the framework of large-scale multiphysics computations also will be briefly described.