Boundary Projection Acceleration for 2D One-cell Inversions in the Scattering Limit
Abstract
Efficient radiation transport on modern high-performance computers requires algorithms that expose spatial parallelism while maintaining robust convergence. One-cell inversion (OCI) replaces the spatially sequential transport sweep of source iteration with a cell-local solve, making discrete ordinates transport space-parallel, but its spectral radius approaches unity in diffusive problems, and existing accelerators such as transport synthetic acceleration reintroduce sweeps. Here we show that projecting the OCI residual onto a low-order angular space on cell boundaries accelerates convergence in scattering-dominated problems without a transport sweep. We implement the projection in a two-dimensional simple-corner-balance discretization with two angular bases: a linear (P1) basis and one augmented with a quadrant moment (P1Q). Fourier analysis of an infinite homogeneous medium shows that both corrections reduce the spectral radius in optically thick, highly scattering regimes, with P1Q being most effective. Across several test problems, including a modified version of the void-duct streaming benchmark, the method accelerates diffusive and scattering cases but does not uniformly improve convergence in streaming dominated problems. We also find that P1Q is a more robust accelerator than P1 in situations where the flux has strong angular variation. Boundary projection substantially improves OCI convergence in diffusive regimes, and these results delimit the regimes that require additional stabilization or richer projection spaces.
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BibTeX
@misc{morgan2026boundary,
title = {{Boundary Projection Acceleration for 2D One-cell Inversions in the Scattering Limit}},
author = {Joanna Piper Morgan and Todd S. Palmer and Ilham Variansyah and Kyle E. Niemeyer},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06951},
eprint = {2611.06951},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06951},
}
RIS
TY - UNPB
TI - Boundary Projection Acceleration for 2D One-cell Inversions in the Scattering Limit
AU - Joanna Piper Morgan
AU - Todd S. Palmer
AU - Ilham Variansyah
AU - Kyle E. Niemeyer
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.06951
UR - https://arxiv.org/abs/2611.06951
AB - Efficient radiation transport on modern high-performance computers requires algorithms that expose spatial parallelism while maintaining robust convergence. One-cell inversion (OCI) replaces the spatially sequential transport sweep of source iteration with a cell-local solve, making discrete ordinates transport space-parallel, but its spectral radius approaches unity in diffusive problems, and existing accelerators such as transport synthetic acceleration reintroduce sweeps. Here we show that projecting the OCI residual onto a low-order angular space on cell boundaries accelerates convergence in scattering-dominated problems without a transport sweep. We implement the projection in a two-dimensional simple-corner-balance discretization with two angular bases: a linear (P_1) basis and one augmented with a quadrant moment (P_1Q). Fourier analysis of an infinite homogeneous medium shows that both corrections reduce the spectral radius in optically thick, highly scattering regimes, with P_1Q being most effective. Across several test problems, including a modified version of the void-duct streaming benchmark, the method accelerates diffusive and scattering cases but does not uniformly improve convergence in streaming dominated problems. We also find that P_1Q is a more robust accelerator than P_1 in situations where the flux has strong angular variation. Boundary projection substantially improves OCI convergence in diffusive regimes, and these results delimit the regimes that require additional stabilization or richer projection spaces.
ER -