A hybrid TT/QTT discontinuous Galerkin method with fixed-matrix upwinding for three-dimensional transient multigroup neutron transport
We develop a hybrid tensor-train/quantized tensor-train (TT/QTT) upwind discontinuous Galerkin method for three-dimensional transient multigroup neutron transport. The central contribution is a fixed-matrix upwind construction: two spatial DG matrices serve all directions and energy groups, with signed and absolute direction-cosine factors preserving Kronecker structure. For homogeneous materials on uniform Cartesian grids, operator rank bounds are independent of mesh size, group count and direction count at fixed scattering order. We derive a conditional global step-defect bound and enforce group-integrated balance of the compressed system. Crank-Nicolson tests show second-order convergence on a separable manufactured solution whose finest final state occupies 13 kB instead of 35 TB, a compression factor of $2.7\times10^9$. A modified rank-adaptive basis-update and Galerkin integrator (TT-BUG) advances passive and active bursts with approximately half a billion unknowns. Selected runs are 15-20 times faster than AMEn at comparable verified scalar-flux errors. In the reported anisotropic active-burst configurations, TT-BUG takes 14.3 s on one processor versus 716 s for OpenSn on 24 processors: approximately 50 times less wall time and 1200 times less allocated processor-time cost. This compares reported configurations rather than matched physical errors. OpenSn provides an independent discretization check. The modified TT-BUG source-onset and saturation treatment is tested numerically; its order, convergence and general tolerance-to-error relation remain unproved.