Work

Low-Rank Tensor Product Richardson Iteration for Radiative Transfer in Plane-Parallel Geometry

Year: 2026

Type: article

Abstract: . The radiative transfer equation (RTE) has been established as a fundamental tool for the description of energy transport, absorption, and scattering in many relevant societal applications and requires numerical approximations. However, classical numerical algorithms scale unfavorably with respect to the dimensionality of such radiative transfer problems, where solutions depend on physical as well as angular variables. In this paper, we address this dimensionality issue by developing a low-rank tensor product framework for the RTE in plane-parallel geometry. We exploit the tensor product nature of the phase space to recover an operator equation where the operator is given by a short sum of Kronecker products. This equation is solved by a preconditioned and rank-controlled Richardson iteration in Hilbert spaces. Using exponential sums approximations, we construct a preconditioner that is compatible with the low-rank tensor product framework. The use of suitable preconditioning techniques yields a transformation of the operator equation in Hilbert space into a sequence space with a Euclidean inner product, enabling rigorous error and rank control in the Euclidean metric.

Source: SIAM Journal on Numerical Analysis

DOI: 10.1137/24m1648065

Authors: Markus Bachmayr, Riccardo Bardin, Matthias Schlottbom

Institutions: RWTH Aachen University, University of Twente

Language: English

Topic: Radiative Heat Transfer Studies

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Awards: Low-rank tensor product approximations for the radiative transfer equation, SFB 1481: Sparsity und singuläre Strukturen