A Reduced Basis Method for Radiative Transfer Equation

Linear kinetic transport equations play a critical role in optical tomography, radiative transfer and neutron transport. The fundamental difficulty hampering their efficient accurate numerical resolution lies the high dimensionality of physical velocity/angular variables fact that problem is multiscale nature. Leveraging existence hidden low-rank structure hinted by diffusive limit, this work, we design test angular-space reduced order model for linear equation, first such effort based on celebrated basis method (RBM). Our built upon high-fidelity solver employing discrete ordinates angular space, an asymptotic preserving upwind discontinuous Galerkin synthetic accelerated source iteration resulting system. Addressing challenge parameter values (or directions) being coupled through integration operator, novel ingredient our iterative procedure where macroscopic density constructed from RBM snapshots, treated explicitly allowing sweep, then updated afterwards. A greedy algorithm can proceed to adaptively select representative samples space form surrogate solution space. second novelty least squares reconstruction strategy, at each relevant locations, enabling robust over arbitrarily unstructured set toward density. Numerical experiments indicate effective computational cost reduction variety regimes.