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Location: RE 104

 

Title: Mixed Finite Elements Methods for Fusion Energy

Plasma confinement stands at the heart of fusion energy research. In magnetic confinement fusion, hot plasma fuel is held together with strong magnetic fields: the pressure of the plasma pushes out, but the magnetic field lines wrap around the plasma and counteract this force, acting like a corset.

We will discuss computational methods to optimize this magnetic confinement:

Mathematically, this is a non-linear, PDE-constrained optimization problem. Numerically, we solve it with matrix-free finite elements built in the JAX framework to run efficiently on GPU and TPU accelerators.

There are a number of features that are crucial to respect in the discretization: The magnetic field is divergence-free and we need control over its topological structure during the optimization.

Much of this can be understood in the framework of differential forms and complexes. Without diving too deep into the theory, we will see how these results can help us in constructing stable and well-posed discrete problems on non-contractible toroidal domains. We will encounter some interesting connections between exterior calculus, numerical analysis, and algebraic topology.