Variational principles for three-dimensional magnetostatics based on helicity
Peter Robert Kotiuga · Journal of Applied Physics · 1988
Following Anderson and Arthurs [Int. J. Electron. 56, 571 (1984)], a variational formulation for three-dimensional magnetostatics based on helicity is considered. The advantages of formulating problems in terms of the magnetic field as opposed to the vector potential are given. It is shown that when the extremal is constrained to be solenoidal and μ=1, the Euler–Lagrange equation of the proposed functional involves a first-order differential operator whose square is the Laplace–Beltrami operator. This implies that the condition number of any discretization is the square root of the corresponding number for the Laplace–Beltrami operator.