Low-Rank Tensor Product Approximations for the Radiative Transfer Equation in Plane-Parallel GeometryColloquium CRC 1720

by Matthias Schlottbom

Tuesday May 12, 2026, 2:15 PM → 3:15 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

The radiative transfer equation (RTE) is a fundamental model for describing the transport, absorption, and scattering of radiation in various applications, ranging from medical imaging to nuclear physics. However, its dependence on both spatial and angular variables leads to high-dimensional problems that pose significant computational challenges.
In this talk, I will present a low-rank tensor product framework for efficiently approximating stationary radiative transfer problems in plane-parallel geometry. The approach exploits the tensor product structure of the phase space to formulate the discrete RTE as a short sum of Kronecker products. This structure enables the use of a preconditioned and rank-controlled Richardson iteration in Hilbert spaces, allowing for rigorous control of both error and tensor rank.
A key component of the method is a preconditioner constructed via exponential sum approximations, which is compatible with the low-rank tensor structure and transforms the problem into an equivalent formulation in a Euclidean metric. The resulting algorithm is able to identify quasi-optimal ranks during iteration automatically. We present numerical examples that indicate the computational performance.