Low precision preconditioning for solving neutron diffusion eigenvalue problem by finite element method

This study focuses on solving the multigroup diffusion eigenvalue problem using the finite element method. In particular, the study assesses the potential reduction of numerical costs associated with the preconditioning procedure implemented through the low-precision arithmetic. The eigenvalue problem is solved using the power iteration and Gauss–Seidel methods, both accelerated by Anderson’s method. The within-group linear system of equations is solved using the Conjugate Gradient (CG) method preconditioned by the ILU(0) factorization technique. Employing reduced-precision arithmetic aims at reducing the memory and computational costs of the preconditioning procedure. The study demonstrates that the eigenvalue algorithm admits the usage of half-precision arithmetic for the preconditioning, without a significant increase in the number of CG iterations as compared to the double precision arithmetic. This finding is supported through the evaluation of the algorithm’s performance for two-dimensional multi-group benchmarks featuring fine-mesh and coarse-mesh core patterns.