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Accurate derivative evaluation for any Grad-Shafranov solver. (English) Zbl 1349.76258
Summary: We present a numerical scheme that can be combined with any fixed boundary finite element based Poisson or Grad-Shafranov solver to compute the first and second partial derivatives of the solution to these equations with the same order of convergence as the solution itself. At the heart of our scheme is an efficient and accurate computation of the Dirichlet to Neumann map through the evaluation of a singular volume integral and the solution to a Fredholm integral equation of the second kind. Our numerical method is particularly useful for magnetic confinement fusion simulations, since it allows the evaluation of quantities such as the magnetic field, the parallel current density and the magnetic curvature with much higher accuracy than has been previously feasible on the affordable coarse grids that are usually implemented.

76M10 Finite element methods applied to problems in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
82D10 Statistical mechanical studies of plasmas
82D40 Statistical mechanical studies of magnetic materials
Full Text: DOI arXiv
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