Data-Driven Acceleration of Thermal Radiation Transfer Calculations with the Dynamic Mode Decomposition and a Sequential Singular Value Decomposition

TL;DR

This paper introduces a novel acceleration method for radiative transfer calculations using dynamic mode decomposition and sequential SVD, significantly reducing computational effort in complex thermal radiation problems.

Contribution

The paper develops a DMD-based acceleration technique with sequential SVD updates that automatically determines the number of solution vectors, improving efficiency in nonlinear radiative transfer calculations.

Findings

Reduces transport sweeps by a factor of 3 in standard problems

Achieves several thousand-fold speedup in near-scattering regimes

Improves convergence by a factor of 20 in radiating shock simulations

Abstract

We present a method for accelerating discrete ordinates radiative transfer calculations for radiative transfer. Our method works with nonlinear positivity fixes, in contrast to most acceleration schemes. The method is based on the dynamic mode decomposition (DMD) and using a sequence of rank-one updates to compute the singular value decomposition needed for DMD. Using a sequential method allows us to automatically determine the number of solution vectors to include in the DMD acceleration. We present results for slab geometry discrete ordinates calculations with the standard temperature linearization. Compared with positive source iteration, our results demonstrate that our acceleration method reduces the number of transport sweeps required to solve the problem by a factor of about 3 on a standard diffusive Marshak wave problem, a factor of several thousand on a cooling problem where the effective scattering ratio approaches unity, and a factor of 20 improvement in a realistic, multimaterial radiating shock problem.