Structure-Preserved Reduced-Order Modeling for Frequency-Domain Solution of the Darwin Model With a Gauged Potential Formulation

In this article, the proper orthogonal decomposition (POD) is applied for parametric analysis in the gauged potential formulation of the Darwin model, considering both capacitive and inductive effects. Due to the large contrast in material parameters, the resulting system matrix is ill-conditioned. In addition, the condition number of the corresponding snapshot complex matrices is very huge. To improve the stability of the POD method, a structured-preserving strategy is considered and implemented for different unknown potentials, namely, the magnetic vector potential (MVP) A, the electric scalar potential (ESP) φ, and the Lagrange multiplier p. In addition, a greedy algorithm is proposed to select the snapshots adaptively. Two numerical examples, including a parallel plate capacitor and a modified RLC device structure, are provided to illustrate the capability of the proposed POD in model-order reduction in the frequency-domain solvers.