AI & ML
Boundary Projection Acceleration for 2D One-cell Inversions in the Scattering Limit
arXiv cs.NA0 views
arXiv:2611.06951v1 Announce Type: new 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 ($P_1$) 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 $P_{1}Q$ 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 $P_{1}Q$ 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.
Source:https://arxiv.org/abs/2611.06951PreviousThermoLLM: LLM-Based Multi-Zone HVAC Control with a Spatiotemporal ContextNextA physics-based adaptive low-rank method for 6D Vlasov simulations
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