Influence of the RHS on the convergence behaviour of the curl-curl equation

The vector potential formulation is widely used in electromagnetic field computation due to its robustness. Numerical experiences on the convergence behaviour of the non-gauged vector potential formulation (curl curl equation) are reported. The convergence of the system depends on the discretisation of the source variable (the right hand side of the equation). The system converges if the matrix equation is compatible, i.e. if the RHS is in the range of the curl-curl matrix. The compatibility is ensured when the current density is expressed by the curl of a source field (vector potential) and when this source field is projected on the space curl W¹, where W¹ is the space of the Whitney edge element. An explanation of the convergence behaviour is given through the analysis of the matrix structure: under the condition of the compatibility, the curl-curl equation is implicitly ganged by an iterative solver