A novel efficient solver for Ampere's equation in general toroidal topologies based on singular value decomposition techniques Articles uri icon

publication date

  • April 2020

start page

  • 109214

end page

  • 109229


  • 406

International Standard Serial Number (ISSN)

  • 0021-9991

Electronic International Standard Serial Number (EISSN)

  • 1090-2716


  • A new method is proposed to solve Ampere's equation in an arbitrary toroidal domain in which all currents are known, given proper boundary conditions for the magnetic vector potential. The novelty of the approach lies in the application of singular value decomposition (SVD) techniques to tackle the difficulties caused by the kernel associated by the curl operator. This kernel originates physically due to the magnetic field gauge. To increase the efficiency of the solver, the problem is represented by means of a dual finite difference-spectral scheme in arbitrary generalized toroidal coordinates, which permits to take advantage of the block structure exhibited by the matrices that describe the discretized problem. The result is a fast and efficient solver, up to three times faster than the double-curl method in some cases, that provides an accurate solution of the differential form of Ampere law while guaranteeing a zero divergence of the resulting magnetic field down to machine precision.


  • Physics


  • ampere's law; mhd; singular value decomposition; spectral method; svd; toroidal topology