期刊论文详细信息
JOURNAL OF COMPUTATIONAL PHYSICS 卷:305
Accurate derivative evaluation for any Grad-Shafranov solver
Article
Ricketson, L. F.1  Cerfon, A. J.1  Rachh, M.1  Freidberg, J. P.2 
[1] NYU, Courant Inst Math Sci, New York, NY 10012 USA
[2] MIT, Plasma Sci & Fus Ctr, Cambridge, MA 02139 USA
关键词: Plasma;    Equilibrium;    Magnetic confinement fusion;    Grad-Shafranov equation;    Finite elements;    Integral equations;    Quadrature by expansion;   
DOI  :  10.1016/j.jcp.2015.11.015
来源: Elsevier
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【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

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