Efficient high-order singular quadrature schemes in magnetic fusion

Dhairya Malhotra, Antoine J. Cerfon, Michael O'Neil, Evan Toler

Research output: Contribution to journalArticlepeer-review


Several problems in magnetically confined fusion, such as the computation of exterior vacuum fields or the decomposition of the total magnetic field into separate contributions from the plasma and the external sources, are best formulated in terms of integral equation expressions. Based on Biot-Savart-like formulae, these integrals contain singular integrands. The regularization method commonly used to address the computation of various singular surface integrals along general toroidal surfaces is low-order accurate, and therefore requires a dense computational mesh in order to obtain sufficient accuracy. In this work, we present a fast, high-order quadrature scheme for the efficient computation of these integrals. Several numerical examples are provided demonstrating the computational efficiency and the high-order accurate convergence. A corresponding code for use in the community has been publicly released2.

Original languageEnglish (US)
Article number024004
JournalPlasma Physics and Controlled Fusion
Issue number2
StatePublished - 2020


  • boundary integral equations
  • magnetically confined plasma
  • potential theory
  • singular quadratures

ASJC Scopus subject areas

  • Nuclear Energy and Engineering
  • Condensed Matter Physics


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