Cycle-Free Polytopal Mesh Sweeping for Boltzmann Transport
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In this talk, we discuss a form of permutative preconditioning that enables matrix-free methods for solving (linear) transport equations, with applications in nuclear reactor simulations, notably in discrete ordinate and discontinuous Galerkin (dG) angular discretisations of the (linear) Boltzmann Transport Equation (BTE), where efficient transport modelling is crucial for reactor modelling and safety analysis. Mesh design plays a critical role in numerical methods, including dG finite element methods. Without careful handling, transport solvers can develop cyclic dependencies, leading to costly computational corrections. We present a novel property of bounded Voronoi tessellations and an accompanying algorithm that enables cycle-free, matrix-free dG discretisations of the BTE. This approach broadens the applicability of dG methods for transport problems on polytopal meshes, offering a robust, scalable, and parallel-friendly framework. We will explore this method in detail and demonstrate its effectiveness through computational experiments, showcasing both efficiency and adaptability to complex geometries.
