Superior Discretizations and AMG Solvers for Anisotropic Diffusion via Hyperbolic Operators

Explore advanced techniques for discretizing and solving extremely anisotropic diffusion problems in this seminar presented by Ben Southworth from Los Alamos National Laboratory. Delve into the challenges posed by heat conduction in magnetic confinement fusion, where anisotropy ratios can reach 10^9-10^10. Discover a novel approach that reframes elliptic and parabolic problems from a hyperbolic operator perspective. Learn about the development of continuous and discontinuous discretizations for mixed systems using stabilization techniques from hyperbolic problems. Examine the application of algebraic multigrid (AMG) solvers based on approximate ideal restriction (AIR) to efficiently solve the resulting block matrix systems. Compare the effectiveness of these new methods to traditional discretizations and AMG solvers, revealing significant improvements in both error reduction and computational efficiency for extremely anisotropic regimes.