Vectorial solution to double curl equation with generalized coulomb gauge for magneto static problems

In this paper, a solution to the double curl equation with generalized Coulomb gauge is proposed based on the vectorial representation of the magnetic vector potential. Coulomb gauge is applied to remove the null space of the curl operator and hence the uniqueness of the solution is guaranteed. However, as the divergence operator cannot act on the curl-conforming edge basis functions directly, the magnetic vector potential is used to be represented by nodal finite elements. Inspired by the mapping of Whitney forms by mathematical operators and Hodge operators, the divergence of the magnetic vector potential, as a whole, can be approximated by scalar basis functions. Hence, the magnetic vector potential can be expanded by vector basis functions, and the original equation can be rewritten in a generalized form and solved in a more natural and accurate way.