Locally stabilized explicit method for fast transient analysis of inhomogeneously-meshed plane structures

This paper describes an explicit and locally stabilized transient analysis method for fast simulation of inhomogeneously-meshed conductor planes. An existing explicit leapfrog scheme has a strict numerical stability condition by which a time step size is forced to be small if there exists small reactances in the circuit. Such small reactances are extracted from the small meshes, which are locally used to represent small apertures on the conductor planes. Therefore, the fully-explicit method is not suitable for the circuit including the small reactances. For an arbitrary time step size, the proposed locally stabilized explicit (LSE) method adopts the unconditionally stable explicit (USE) method to remove instability related to low reactance parts in the circuit. By doing so, the proposed method enables to use a relatively-large time step size compared with the explicit leapfrog scheme and reduce the time taken for a preprocessing, which includes solving a generalized eigenvalue problem and tends to be large in the existing USE method. The proposed method is applied to transient simulations of two types of power/ground planes to evaluate the adequacy. Numerical results show that our approach can improve the efficiency of the USE method and be much faster than a conventional SPICElike simulator and the explicit leapfrog scheme in transient simulations.