Stefan Brunner | Searcharxiv

arXiv2026

Domain decomposition dynamical low-rank for multi-dimensional radiative transfer equations

In this paper, we propose a domain decomposition dynamical low-rank method to solve high-dimensional radiative transfer problems and similar kinetic equations. The algorithm uses a separate low-rank approximation on each spatial subdomain, which means that, for a given accuracy, we can often use a smaller overall rank compared to classic dynamical low-rank methods. In particular, we can solve problems with point sources efficiently, that for classic algorithms require almost full rank. Our algorithm only transfers boundary data between subdomains and is thus very attractive for distributed memory parallelization, where classic dynamical low-rank algorithms suffer from global data dependency. We demonstrate the efficiency of our algorithm by a number of challenging test examples that have both very optical thin and thick regions.

math.NA↗

arXiv2026

Efficient SN-like and PN-like Dynamic Low Rank methods for Thermal Radiative Transfer

Dynamic Low Rank (DLR) methods are a promising way to reduce the computational cost and memory footprint of the high-dimensional thermal radiative transfer (TRT) equations. The TRT equations are a system of nonlinear PDEs that model the energy exhchange between the material temperature and the radiation energy density; due to their high dimensionality, solving the TRT equations is often bottleneck in multi-physics simulations. DLR methods represent the solution in terms of time-evolving SVD-like factors of angle and space. Although previous work has explored DLR methods for TRT, most of the methods have limitations that make them impractical for realistic scenarios and uncompetitive with current non-DLR production codes. Here we develop new PN-like and SN-like Dynamic Low Rank (DLR) methods for TRT. In the SN-like DLR method, we use the time-evolving angular basis functions to select time-evolving angles; this DLR formulation enables us to use the highly optimized SN transport sweep as our main computational kernel, and results in a practical way of leveraging low-rank methods in production TRT codes. In contrast, our PN-like DLR method uses an even-parity formulation and results in positive-definite linear systems to solve for each time step. We demonstrate the methods on several challenging, highly heterogenous problems in two spatial dimensions $(4$D) that these DLR schemes can give significant reduction in angular artifacts (``ray effects'') with the same cost as gold-standard SN methods.

math.NA↗