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Watch a technical conference presentation from the 2024 MFEM Workshop exploring an innovative approach to solving the Grad-Shafranov equation in magnetic confinement devices. Discover how researchers developed a Newton-based free-boundary solver using adaptive finite elements and preconditioning strategies to address the challenges of plasma equilibrium calculations in tokamak configurations. Learn about the implementation of shape calculus for Jacobian matrix evaluation, block factorization techniques for linear system solutions, and the successful application of this method to find Taylor state equilibrium where traditional Picard-based solvers fail. Gain insights into the unique contributions including global constraint handling, preconditioning strategies, nonlocal reformulation, and adaptive finite element implementation that enable robust convergence of the nonlinear residual to 1e-6 in just a few iterations.
