A fast, accurate and easy to implement Kapur–Rokhlin quadrature scheme for singular integrals in axisymmetric geometries

Toler, Evan; Cerfon, A. J.; Malhotra, D.

doi:10.1017/S002237782300020X

Title: A fast, accurate and easy to implement Kapur–Rokhlin quadrature scheme for singular integrals in axisymmetric geometries

Abstract

Many applications in magnetic confinement fusion require the efficient calculation of surface integrals with singular integrands. The singularity subtraction approaches typically used to handle such singularities are complicated to implement and low-order accurate. In contrast, we demonstrate that the Kapur–Rokhlin quadrature scheme is well-suited for the logarithmically singular integrals encountered for a toroidally axisymmetric confinement system, is easy to implement and is high-order accurate. As an illustration, we show how to apply this quadrature scheme for the efficient and accurate calculation of the normal component of the magnetic field due to the plasma current on the plasma boundary, via the virtual-casing principle.

Authors:

;

Publication Date:: Fri Apr 14 00:00:00 EDT 2023

Sponsoring Org.:: USDOE

OSTI Identifier:: 1970062

Grant/Contract Number:: FG02-86ER53223

Resource Type:: Published Article

Journal Name:: Journal of Plasma Physics

Additional Journal Information:: Journal Name: Journal of Plasma Physics Journal Volume: 89 Journal Issue: 2; Journal ID: ISSN 0022-3778

Publisher:: Cambridge University Press (CUP)

Country of Publication:: United Kingdom

Language:: English

Citation Formats


                    Toler, Evan, Cerfon, A. J., and Malhotra, D. A fast, accurate and easy to implement Kapur–Rokhlin quadrature scheme for singular integrals in axisymmetric geometries.  United Kingdom: N. p., 2023. 
Web.  doi:10.1017/S002237782300020X.

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                    Toler, Evan, Cerfon, A. J., & Malhotra, D. A fast, accurate and easy to implement Kapur–Rokhlin quadrature scheme for singular integrals in axisymmetric geometries.  United Kingdom.  https://doi.org/10.1017/S002237782300020X

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                    Toler, Evan, Cerfon, A. J., and Malhotra, D. Fri .  
"A fast, accurate and easy to implement Kapur–Rokhlin quadrature scheme for singular integrals in axisymmetric geometries".  United Kingdom.  https://doi.org/10.1017/S002237782300020X.

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@article{osti_1970062,

  title        = {A fast, accurate and easy to implement Kapur–Rokhlin quadrature scheme for singular integrals in axisymmetric geometries},

  author       = {Toler, Evan and Cerfon, A. J. and Malhotra, D.},

  abstractNote = {Many applications in magnetic confinement fusion require the efficient calculation of surface integrals with singular integrands. The singularity subtraction approaches typically used to handle such singularities are complicated to implement and low-order accurate. In contrast, we demonstrate that the Kapur–Rokhlin quadrature scheme is well-suited for the logarithmically singular integrals encountered for a toroidally axisymmetric confinement system, is easy to implement and is high-order accurate. As an illustration, we show how to apply this quadrature scheme for the efficient and accurate calculation of the normal component of the magnetic field due to the plasma current on the plasma boundary, via the virtual-casing principle.},

  doi          = {10.1017/S002237782300020X},

  journal      = {Journal of Plasma Physics},

  number       = 2,

  volume       = 89,

  place        = {United Kingdom},

  year         = {Fri Apr 14 00:00:00 EDT 2023},

  month        = {Fri Apr 14 00:00:00 EDT 2023}

}

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Similar Records

Title: A fast, accurate and easy to implement Kapur–Rokhlin quadrature scheme for singular integrals in axisymmetric geometries

Abstract

Citation Formats

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Corrected trapezoidal rules for boundary integral equations in three dimensions journal, November 2021

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Solution of stellarator boundary value problems with external currents journal, May 1987

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Numerical methods for solving some problems of the theory of plasma equilibrium in toroidal configurations journal, August 1973

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A magnetic diagnostic code for 3D fusion equilibria
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An integral equation technique for the exterior and interior neumann problem in toroidal regions
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Tokamak equilibria with strong toroidal current density reversal
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External inductance of an axisymmetric plasma
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High-order accurate methods for Nyström discretization of integral equations on smooth curves in the plane
journal, June 2013

Use of the virtual-casing principle in calculating the containing magnetic field in toroidal plasma systems
journal, September 1972

ECOM: A fast and accurate solver for toroidal axisymmetric MHD equilibria
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Tokamak elongation – how much is too much? Part 2. Numerical results
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Designing stellarator coils by a modified Newton method using FOCUS
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