Adaptive angle and parallel multigrid for deterministic shielding problems

Abstract

Traditionally, solver technology and the space/angle discretisations are intimately linked; sweep-based (wavefront) methods are typically used with DG FEM in space and Sn in angle to solve the Boltzmann-transport equation. These parallelise well (scaling to >100,000 cores) on structured grids, however achieving good scaling on unstructured grids is still an open problem. This talk will focus on alternate space/angle discretisations and solver technology we have been developing within the Applied Modelling and Computation Group (AMCG) at Imperial College. These approaches enables the use of traditional angular discretisations like Pn, Sn, along with new approaches based on linear and haar wavelets. We can use these angular discretisations to perform regular and goal-based anisotropic adaptivity in angle, focusing resolution in important directions. We have also been developing multigrid solver technology which does not require sweep-based methods, allowing the possibility of excellent scaling on unstructured grids.