Application of proper generalized decomposition to multigroup neutron diffusion eigenvalue calculations

Abstract

In this paper, proper generalized decomposition (PGD) is utilized to reduce the computational burden of evaluating multigroup neutron diffusion eigenvalue problems. PGD is a reduced order modeling technique that seeks a separated representation to a multi-dimensional variable. In this application, each multigroup flux is sought as a finite sum of separable one-dimensional functions. This representation can significantly reduce the burden of evaluating multi-dimensional linear systems. Therefore, we use PGD to evaluate the linear systems within the power iteration process of the eigenvalue problem. In this paper, we discuss our implementation of PGD to these eigenvalue systems including a derivation of PGD operators for multigroup neutron diffusion problems with standard power iteration and power iteration accelerated with adaptive Wielandt shift. To illustrate PGD’s effectiveness, we apply our implementation to eigenvalue problems ranging from homogeneous to highly heterogeneous geometries with one-,two-, and four-group material properties. With comparison to full-order model evaluation with MOOSE, we find that the effectiveness of PGD is problem dependent. PGD always out performs the full-order model with close to homogeneous problems, but performs more poorly with more realistic reactor problems.