Exploring One-Cell Inversion Method for Transient Transport on GPU

• DOI: 10.48550/arxiv.2305.13555
• Publication Date: 2023-01-01
• Authors: Joanna Piper Morgan; Ilham Variansyah; Todd S. Palmer; Kyle E. Niemeyer
• Keywords: Speedup

To find deterministic solutions to the transient $S_N$ neutron transport equation, iterative schemes are typically used treat scattering (and fission) source terms. We explore one-cell inversion iteration scheme do this on GPU and make comparisons a scheme. examine convergence behavior, through analysis of spectral radii, both iterations. further boost parallel efficiency, we derive higher-order discretization method, simple corner balance (in space) multiple time), add more work threads gain accuracy. Fourier numerical method shows that it is unconditionally stable, but can produce negative flux alterations critically damped time. whole-problem all angle cell) sparse linear algebra framework, for schemes, quickly performant code GPUs. Despite requiring additional iterations convergence, those be done faster provide significant speedup over in quadrature sets at or below $S_{128}$. Going forward will two-dimensional implementation experiment with memory performance impacts framework including methods synthetic acceleration pre-conditioners scheme, then begin making direct traditionally implemented production code.