Mitigating Rays-Effect in Phase-Space Advection with Matrix-Free High-Dimensional DG Methods

Watch a technical conference presentation from the 2024 MFEM Workshop exploring innovative solutions for mitigating rays-effect in phase-space advection problems through matrix-free high-dimensional discontinuous Galerkin methods. Discover how advanced coordinate transformations and matrix-free formulations can effectively address numerical artifacts in deterministic transport simulations while maintaining computational efficiency. Learn about this novel approach that fully discretizes phase space up to six dimensions, offering a deterministic alternative to Monte Carlo simulations without compromising accuracy or scalability. Understand how the optimization of coordinate systems through alignment with net flux minimizes the rays-effect, and see numerical experiments demonstrating the effectiveness of this methodology in high-dimensional transport problems. Gain insights into how this approach reduces memory usage and improves computational efficiency by avoiding large sparse matrix assembly, making it particularly valuable for high-performance computing applications in scientific simulations.