Taylor states in stellarators: A fast high-order boundary integral solver

Dhairya Malhotra, Antoine Cerfon, Lise Marie Imbert-Gérard, Michael O'Neil

Research output: Contribution to journalArticlepeer-review


We present a boundary integral equation solver for computing Taylor relaxed states in non-axisymmetric solid and shell-like toroidal geometries. The computation of Taylor states in these geometries is a key element for the calculation of stepped pressure stellarator equilibria. The integral representation of the magnetic field in this work is based on the generalized Debye source formulation, and results in a well-conditioned second-kind boundary integral equation. The integral equation solver is based on a spectral discretization of the geometry and unknowns, and the computation of the associated weakly-singular integrals is performed with high-order quadrature based on a partition of unity. The resulting scheme for applying the integral operator is then coupled with an iterative solver and suitable preconditioners. Several numerical examples are provided to demonstrate the accuracy and efficiency of our method, and a direct comparison with the leading code in the field is reported.

Original languageEnglish (US)
Article number108791
JournalJournal of Computational Physics
StatePublished - Nov 15 2019


  • Generalized Debye sources
  • Laplace-Beltrami
  • Plasma equilibria
  • Stellarator
  • Taylor state

ASJC Scopus subject areas

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


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