An integral equation technique for the exterior and interior Neumann problem in toroidal regions

An integral equation technique for the Neumann problem of finding a function Φ satisfying ΔΦ = 0 with prescribed values of ∂Φ∂n on the boundary is described. Fourier representation of the potential Φ on the boundary with respect to two angle-like variables transforms the integral equation to an infinite set of linear equations for the Fourier coefficients of Φ. The singularity of the Green's function is treated by a regularization method: a function with the same singularity is subtracted and its analytically calculated Fourier-transform is added to the Fourier transformed integral equation. A computer code named NESTOR is developed. Applications include studies of toroidal magnetic vacuum fields and calculation of the vacuum field contribution for the 3D free-boundary equilibrium problem.

[1]  E. O. Brigham,et al.  The Fast Fourier Transform , 1967, IEEE Transactions on Systems, Man, and Cybernetics.

[2]  P. Merkel,et al.  Hera and other extensions of Erato , 1981 .

[3]  P. Garabedian,et al.  Magnetohydrodynamic Equilibrium and Stability of Stellarators , 1984 .

[4]  M. A. Jaswon,et al.  Integral equation methods in potential theory and elastostatics , 1977 .

[5]  A. Mirin,et al.  Design of heliac vacuum magnetic fields , 1985 .

[6]  S. Hirshman,et al.  MOMCON: A spectral code for obtaining three-dimensional magnetohydrodynamic equilibria , 1986 .

[7]  L. Delves,et al.  Numerical solution of integral equations , 1975 .

[8]  U. Schwenn.  Fourier versus difference methods in computing three-dimensional MHD equilibria , 1984 .

[9]  Elimination of stochasticity in stellarators , 1984 .

[10]  A Green’s Function Method for the Vacuum Contribution to the MHD Stability of Helically Symmetric Equilibria , 1982 .

[11]  A. Shestakov,et al.  Application of the implicit Fourier-expansion method to the calculation of three-dimensional equilibria by the iterative method☆ , 1984 .

[12]  W. Schneider,et al.  Erato Stability Code , 1984 .

[13]  Erich Martensen,et al.  Über eine Methode zum räumlichen Neumannschen Problem mit einer Anwendung für torusartige Berandungen , 1963 .

[14]  J. Hess.  Review of integral-equation techniques for solving potential-flow problems with emphasis on the surface-source method , 1975 .

[15]  H. Nussbaumer.  Fast Fourier transform and convolution algorithms , 1981 .