Static magnetic field computation-an approach based on the domain-integrated field equations

An unconventional algorithm is presented to compute quasi-static magnetic fields. It aims to be as close to the physics as possible for the class of strongly heterogeneous media. Using edge-element expansion functions for the magnetic field strength and face-element expansion functions for the magnetic flux density, a system of linear algebraic equations in the expansion coefficients is constructed from the exact satisfaction, for each element, of the domain-integrated field equations and of the compatibility relations, combined with the least-square satisfaction, for each element, of the constitutive relation. The resulting system of equations is over-determined and is solved by minimizing the L²-norm of the residual. Accuracy and convergence are tested by applying the method to some two-dimensional problems whose solution is known analytically. A novel method to encompass an unbounded exterior domain is included in the method; it performs remarkably well