Deterministic radiative transfer equation solver on unstructured tetrahedral meshes: Efficient assembly and preconditioning - Archive ouverte HAL Access content directly
Journal Articles Journal of Computational Physics Year : 2021

Deterministic radiative transfer equation solver on unstructured tetrahedral meshes: Efficient assembly and preconditioning

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Abstract

Due to its integro-differential nature, deriving schemes for numerically solving the radiative transfer equation (RTE) is challenging. Most solvers are efficient in specific scenarios: structured grids, simulations with low-scattering materials... In this paper, a full solver, from the discretization of the steady-state monochromatic RTE to the solution of the resulting system, is derived. Using a mixed matrix-ready/matrix-free approach, our solver is able to discretize and solve a 45.7 billion unknown problem on 27 thousand processes in three minutes for a full physics involving scattering, absorption, and reflection. Because of the high dimensionality of the continuous equation, the linear system would have had more than 6 ×1015 nonzero entries if assembled explicitly. Our approach allows for large memory gains by only storing lower dimension reference matrices. The finite element-based solver is wrapped around open-source software, FreeFEM for discretization, PETSc for linear algebra, and hypre for the algebraic multigrid infrastructure. Overall, deterministic results are presented on arbitrarily-decomposed unstructured grids for radiative transfer problems with scattering, absorbing, and reflecting heterogeneities on up to 27 thousand processes.
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Dates and versions

hal-03196806 , version 1 (13-04-2021)

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Pierre Jolivet, Mohd Afeef Badri, Y. Favennec. Deterministic radiative transfer equation solver on unstructured tetrahedral meshes: Efficient assembly and preconditioning. Journal of Computational Physics, 2021, 437, pp.110313. ⟨10.1016/j.jcp.2021.110313⟩. ⟨hal-03196806⟩
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