Core Concepts
Efficiently solving anisotropic heat flux equations using algebraic multigrid methods.
Abstract
The content introduces a novel solver technique for anisotropic heat flux equations, addressing challenges in discretization accuracy and efficient linear solvers. The approach combines finite element discretization with algebraic multigrid methods tailored to advective operators. Superior accuracy is demonstrated over other discretizations, especially in highly anisotropic regimes. The paper focuses on open field lines and the use of auxiliary variables to resolve heat flux accurately. Various numerical approaches and solver strategies are discussed, emphasizing the importance of alignment with magnetic field lines for effective solutions.
Stats
Achieving error 1000× smaller for anisotropy ratio of 10^9.
Fast convergence of iterative solver in highly anisotropic regimes.
Largest eigenvalues evolve according to leading factors in parameter regimes.