### Abstract

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 language | English (US) |
---|---|

Article number | 108791 |

Journal | Journal of Computational Physics |

Volume | 397 |

DOIs | |

State | Published - Nov 15 2019 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Journal of Computational Physics*,

*397*, [108791]. https://doi.org/10.1016/j.jcp.2019.06.067

**Taylor states in stellarators : A fast high-order boundary integral solver.** / Malhotra, Dhairya; Cerfon, Antoine; Imbert-Gérard, Lise Marie; O'Neil, Michael.

Research output: Contribution to journal › Article

*Journal of Computational Physics*, vol. 397, 108791. https://doi.org/10.1016/j.jcp.2019.06.067

}

TY - JOUR

T1 - Taylor states in stellarators

T2 - A fast high-order boundary integral solver

AU - Malhotra, Dhairya

AU - Cerfon, Antoine

AU - Imbert-Gérard, Lise Marie

AU - O'Neil, Michael

PY - 2019/11/15

Y1 - 2019/11/15

N2 - 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.

AB - 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.

KW - Generalized Debye sources

KW - Laplace-Beltrami

KW - Plasma equilibria

KW - Stellarator

KW - Taylor state

UR - http://www.scopus.com/inward/record.url?scp=85070217157&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85070217157&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2019.06.067

DO - 10.1016/j.jcp.2019.06.067

M3 - Article

AN - SCOPUS:85070217157

VL - 397

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

M1 - 108791

ER -