On-the-Fly ROM-Based Acceleration of SI-DSA for Implicit Time Marching of the Radiative Transfer Equation
This work addresses computational inefficiencies in radiative transfer simulations for researchers in computational physics or engineering, though it is incremental as it builds on existing SI-DSA methods.
The paper tackles the performance deterioration of the DSA preconditioner in implicit time marching of the radiative transfer equation and the lack of exploitation of low-rank structures in classical SI-DSA, resulting in a method that achieves 1.4× to 2.0× speedup over classical SI-DSA with marginal overhead.
In implicit time marching of the radiative transfer equation (RTE), the resulting linear systems are commonly solved using source iteration with diffusion synthetic acceleration (SI-DSA). Despite its widespread success, the performance of the DSA preconditioner may deteriorate when the RTE cannot be well approximated by its diffusion limit. Moreover, classical SI-DSA does not exploit low-rank structures of the solution manifold across time steps when the solution evolves smoothly. To address these limitations, we develop an on-the-fly reduced-order-model (ROM)-based acceleration for SI-DSA in implicit time marching of the RTE. Instead of relying on a diffusion approximation, the proposed approach constructs ROMs directly from the underlying kinetic formulation while exploiting low-rank structures in the temporal evolution of the solution. The method is fully offline-free and constructs ROMs to enhance both initial guesses and preconditioners on the fly during time marching. To handle streaming solution data, we design efficient and memory-lean ROM construction and adaptive update strategies based on dynamical mode decomposition, incremental low-rank singular value decomposition, and error indicators. Numerical experiments demonstrate that the proposed method consistently accelerates implicit time marching, delivering $1.4\times$ to $2.0\times$ speedup over classical SI-DSA while incurring only marginal overhead for ROM construction and updates.