Towards Robust Numerical Solvers for Nuclear Fusion Simulations Using JOREK

Master thesis (2023)

Authors

A.S. Quinlan Electrical Engineering, Mathematics and Computer Science

Contributors

V.N.S.R. Dwarka Numerical Analysis - EEMCS (mentor)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2023 Alex Quinlan
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Published Date

29-09-2023

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

One of the most well-established codes for modeling non-linear Magnetohydrodynamics (MHD) for tokamak reactors is JOREK, which solves these equations with a Bézier surface based finite element method. This code produces a highly sparse but also very large linear system. The main solver behind the code uses the Generalized Minimum Residual Method (GMRES) with a physics-based preconditioner. Even with the preconditioner there are issues with memory and computation costs and the solver doesn’t always converge well. This work contains the first thorough study of the mathematical properties of the underlying linear system, enabling us to diagnose and pinpoint the cause of hampered convergence. In particular, analyzing the spectral properties of the matrix and the preconditioned system with numerical linear algebra techniques will open the door to research and investigate more performant solver strategies, such as projection methods.