Two-step reduction procedure for parametric transient electromagnetic computations

The principal computational issue in Transient Electromagnetic Problems is the solution of large system of Differential Algebraic Equations (DAE´s) obtained after Finite Element (FE) discretization. Model Order Reduction (MOR) techniques provide a mechanism to generate reduced order models from the detailed description of the original FE network. These techniques can tremendously shorten computational times for transient and harmonic analysis. However, standard MOR techniques cannot be applied if the equation system incorporates time-varying matrices or parameters that are to be preserved in the reduced model. This necessitates the use of parametric MOR strategies so as to expedite optimization and design space exploration cycles. In this paper, we present a two step reduction procedure for parameterized transient electromagnetic computations. The first step involves the conversion of large system of parameterized DAE´s, obtained after FE discretization, into a pure Ordinary Differential Equation (ODE) model while symbolically preserving the parameters. The parametric ODE model is then reduced using multi-dimensional moment matching approach, which is used as the second stage of reduction. The parametric dependency is preserved in the reduced model and multiple simulations corresponding to different values of parameters can be carried out without repeating the reduction step. The proposed methodology is illustrated for a generic system with promising results and a significant saving in computational effort.