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An Integral Equation Approach to a Free Boundary Problem in Magnetic Confinement Fusion

Modeling, Computation, Nonlinearity, Randomness and Waves Seminar

An Integral Equation Approach to a Free Boundary Problem in Magnetic Confinement Fusion
Series: Modeling, Computation, Nonlinearity, Randomness and Waves Seminar
Location: Hybrid: Math 402/Online
Presenter: Even Toler, Courant Institute of Mathematical Sciences

To design and control magnetic confinement fusion reactors, one must compute the geometry of the confined plasma at equilibrium. In this talk, I present a new method for solving this free-boundary problem through integral equations and PDE-constrained optimization. I detail a formulation of the equilibrium equations that couples the Grad-Shafranov equation for the interior magnetic field with an integral equation for the exterior vacuum field. I introduce high order numerical methods for solving the associated integral equation, including a novel application of the Kapur-Rokhlin quadrature rule for singular integrals in axisymmetric magnetic confinement systems. Finally, I frame the coupled equations in the larger PDE-constrained optimization framework and discuss gradient descent methods for the optimization iteration.

 

Math, 402 and Zoom   https://arizona.zoom.us/j/85889389967  Password:  applied