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A low-rank method for two-dimensional time-dependent radiation transport calculations

Peng, Z.; McClarren, R. G.; Frank, M.

Abstract:
The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional problems to reduce the memory required and computational cost. In this work, a dynamical low-rank approximation method is developed for the time-dependent radiation transport equation in 1-D and 2-D Cartesian geometries. Using a finite volume discretization in space and a spherical harmonics basis in angle, we construct a system that evolves on a low-rank manifold via an operator splitting approach. Numerical results on five test problems demonstrate that the low-rank solution requires less memory than solving the full rank equations with the same accuracy. It is furthermore shown that the low-rank algorithm can obtain high-fidelity results at a moderate extra cost by increasing the number of basis functions while keeping the rank fixed.



Zugehörige Institution(en) am KIT Steinbuch Centre for Computing (SCC)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2020
Sprache Englisch
Identifikator KITopen-ID: 1000123347
Nachgewiesen in arXiv
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