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- research-articleJanuary 2023
A sweep-based low-rank method for the discrete ordinate transport equation
Journal of Computational Physics (JOCP), Volume 473, Issue Chttps://doi.org/10.1016/j.jcp.2022.111748AbstractThe dynamical low-rank (DLR) approximation is an efficient technique to approximate the solution to matrix differential equations. Recently, the DLR method was applied to radiation transport calculations to reduce memory requirements ...
Highlights- A low-rank scheme for solving radiation transport equation implicitly.
- The ...
- research-articleDecember 2022
A low-rank power iteration scheme for neutron transport criticality problems
Journal of Computational Physics (JOCP), Volume 470, Issue Chttps://doi.org/10.1016/j.jcp.2022.111587AbstractComputing effective eigenvalues for neutron transport often requires a fine numerical resolution. The main challenge of such computations is the high memory effort of classical solvers, which limits the accuracy of chosen ...
Highlights- Solving eigenvalue problems for nuclear systems requires a significant amount of memory.
- research-articleDecember 2021
A high-order/low-order (HOLO) algorithm for preserving conservation in time-dependent low-rank transport calculations
Journal of Computational Physics (JOCP), Volume 447, Issue Chttps://doi.org/10.1016/j.jcp.2021.110672Graphical abstract Highlights- A low-rank method is used to compute a closure in radiative transfer simulations.
Dynamical low-rank (DLR) approximation methods have previously been developed for time-dependent radiation transport problems. One crucial drawback of DLR is that it does not conserve important quantities of the calculation, which ...
- research-articleJune 2016
Moment closures based on minimizing the residual of the PN angular expansion in radiation transport
Journal of Computational Physics (JOCP), Volume 314, Issue CPages 682–699https://doi.org/10.1016/j.jcp.2016.03.030In this work we present two new closures for the spherical harmonics ( P N ) method in slab geometry transport problems. Our approach begins with an analysis of the squared-residual of the transport equation where we show that the standard truncation ...
- articleAugust 2010
Robust and accurate filtered spherical harmonics expansions for radiative transfer
Journal of Computational Physics (JOCP), Volume 229, Issue 16Pages 5597–5614https://doi.org/10.1016/j.jcp.2010.03.043We present a novel application of filters to the spherical harmonics (P"N) expansion for radiative transfer problems in the high-energy-density regime. The filter we use is based on non-oscillatory spherical splines and a filter strength chosen to (i) ...
- articleAugust 2008
Semi-implicit time integration for PN thermal radiative transfer
Journal of Computational Physics (JOCP), Volume 227, Issue 16Pages 7561–7586https://doi.org/10.1016/j.jcp.2008.04.029Implicit time integration involving the solution of large systems of equations is the current paradigm for time-dependent radiative transfer. In this paper we present a semi-implicit, linear discontinuous Galerkin method for the spherical harmonics (P"N)...
- articleFebruary 2008
On solutions to the Pn equations for thermal radiative transfer
Journal of Computational Physics (JOCP), Volume 227, Issue 5Pages 2864–2885https://doi.org/10.1016/j.jcp.2007.11.027We present results for the spherical harmonics (P"n) method for solving problems of time-dependent thermal radiative transport. We prove a theorem that demonstrates that in the streaming limit, the spatially and temporally continuous P"n equations will ...