# Scalable angular adaptivity for Boltzmann transport

## TL;DR

This paper introduces a scalable angular adaptivity algorithm for Boltzmann transport that demonstrates linear scaling in runtime and memory, utilizing Haar wavelets for efficient anisotropic angular resolution.

## Contribution

It presents the first evidence of aling in both runtime and memory for angular adaptivity in Boltzmann transport using Haar wavelets and hierarchical FEM discretisation.

## Key findings

- Achieves aling in runtime and memory usage with adaptive angular resolution.
- Uses Haar wavelets for structured h-adaptivity in 2D angular domains.
- Employs a memory-efficient spatial discretisation and matrix-free multigrid methods.

## 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.