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arXiv · 1901.04929

Scalable angular adaptivity for Boltzmann transport

S. Dargaville·A. G. Buchan·R. P. Smedley-Stevenson·P. N Smith·C. C. Pain
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Abstract

This paper describes an angular adaptivity algorithm for Boltzmann transport applications which for the first time shows evidence of $\mathcal{O}(n)$ scaling in both runtime and memory usage, where $n$ is the number of adapted angles. This adaptivity uses Haar wavelets, which perform structured $h$-adaptivity built on top of a hierarchical P$_0$ FEM discretisation of a 2D angular domain, allowing different anisotropic angular resolution to be applied across space/energy. Fixed angular refinement, along with regular and goal-based error metrics are shown in three example problems taken from neutronics/radiative transfer applications. We use a spatial discretisation designed to use less memory than competing alternatives in general applications and gives us the flexibility to use a matrix-free multgrid method as our iterative method. This relies on scalable matrix-vector products using Fast Wavelet Transforms and allows the use of traditional sweep algorithms if desired.

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S. Dargaville, A. G. Buchan, R. P. Smedley-Stevenson, P. N Smith, C. C. Pain. 2019-01-15. Scalable angular adaptivity for Boltzmann transport. https://doi.org/10.1016/j.jcp.2019.109124

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