Compatible Finite Element Discretization of Generalized Lorenz Gauged Charge-Free A Formulation with Diagonal Lumping in Frequency and Time Domains

The finite element implement of the generalized Lorenz gauged A formulation has been proposed for low-frequency modeling. However, the inverse of mass matrix of intermediate scalar in the finite element implement leads to additional computation cost and dense coefficient matrix. In this paper we propose to adopt a diagonal lumping mass matrix in the finite element discretization of the generalized Lorenz gauged double-curl operator in charge-free electromagnetic problems. Consequently, a sparser discrete system with improved condition number is thus obtained which is more favourable for low-frequency modeling in frequency-domain analysis. Furthermore, we apply the diagonal lumping formulation in time-domain analysis, showing that it can remedy spurious linear growth problem. Numerical examples are used to demonstrate the validity.