A generalized tree-cotree gauge for magnetic field computation

The discretization of the magnetostatic curl-curl equation using edge-based elements result in a singular matrix equation. As has been shown previously, this matrix may be made nonsingular by eliminating the matrix nullspace. A generalization of this process is presented in this paper that does not require setting field quantities to zero, thus allowing the gauge in vector potential solutions to be set in a more natural way, This process also makes it possible to solve for the electric or magnetic field directly in high frequency applications