## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 744-757 |

Number of pages | 14 |

Journal | Journal of Computational Physics |

Volume | 305 |

DOIs | |

State | Published - Jan 15 2016 |

## Keywords

- Equilibrium
- Finite elements
- Grad-Shafranov equation
- Integral equations
- Magnetic confinement fusion
- Plasma
- Quadrature by expansion

## ASJC Scopus subject areas

- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics