Parametric Model-Order Reduction for Radiation Transport Simulations Based on an Affine Decomposition of the Operators

摘要

This work presents a data-driven, projection-based parametric reduced-order model (ROM) for the neutral particle radiation fransport (linear Boltzmann fransport) equation. The ROM utilizes the method of snapshots with proper orthogonal decomposition. The novelty of the work is in the detailed proposal to exploit the parametrically affine transport operators to intrusively, yet efficiently, build the reduced fransport operators in real time in a matrix-free manner compatible with sweep-based fransport solvers. This affine-based ROM is applied to one-dimensional (1-D), two-dimensional (2-D), and 2-D multigroup fransport benchmarks and is found to significantly outperform less intrusive ROMs in terms of speed for a desired accuracy level. The ROM has an 18.2 to 89.4 speedup with an error range of 0.0002 to 0.01 for the 1-D benchmark, a 1120x to 4870x speedup with an error range of 0.0009 to 0.01 for the 2-D benchmark, and a 54 600x to 399 800x speedup with an error range of 0.00022 to 0.01 for the multigroup 2-D benchmark. Even higher speedups are expected for three-dimensional multigroup fransport problems.