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• W2954094954 abstract "The discrete ordinates discontinuous Galerkin ($S_N$-DG) method is a well-established and practical approach for solving the radiative transport equation. In this paper, we study a low-memory variation of the upwind $S_N$-DG method. The proposed method uses a smaller finite element space that is constructed by coupling spatial unknowns across collocation angles, thereby yielding an approximation with fewer degrees of freedom than the standard method. Like the original $S_N$-DG method, the low memory variation still preserves the asymptotic diffusion limit and maintains the characteristic structure needed for mesh sweeping algorithms. While we observe second-order convergence in scattering dominated, diffusive regime, the low-memory method is in general only first-order accurate. To address this issue, we use upwind reconstruction to recover second-order accuracy. For both methods, numerical procedures based on upwind sweeps are proposed to reduce the system dimension in the underlying Krylov solver strategy." @default.
• W2954094954 created "2019-07-12" @default.
• W2954094954 creator A5000504797 @default.
• W2954094954 creator A5005248564 @default.
• W2954094954 date "2019-07-01" @default.
• W2954094954 modified "2023-10-16" @default.
• W2954094954 title "Low-memory, discrete ordinates, discontinuous Galerkin methods for radiative transport" @default.
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• W2954094954 doi "https://doi.org/10.48550/arxiv.1907.01027" @default.
• W2954094954 hasPublicationYear "2019" @default.
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