Model order reduction of an electro-quasistatic problem using CLN method

The Cauer ladder network (CLN) method, as proposed by Kameari et al. (2018), has been extensively studied to construct a reduced model of magneto-quasistatic (MQS) Finite Element (FE) models. In this case, this method enables the construction of an equivalent electrical circuit based on resistances and inductances as well as a reduced basis where the solution of a reduced problem is sought. In this article, we propose to extend the applicability of the CLN method to the development of reduced models for FE electro-quasistatic (EQS) models. It appears that the derivation of the reduction of an EQS model is not similar to the one of an MQS model. After development, the process of reduction using CLN leads to consider two electrical circuits based on the cascade association of resistances and capacitances. Each circuit is associated with a reduced basis constructed by applying the self-adjoint Lanczos method. The reduced solution to the EQS problem is got by first solving the circuit equations to determine the voltages and the currents at the terminals of the resistances and capacitances. Then, the approximated solution of the FE EQS model is got by a linear combination of the vectors of the two reduced bases weighted by the currents (or the voltages) previously calculated. An error estimator is also derived, enabling to calculate the distance between the reduced solution and the FE solution without solving the FE model. The proposed approach has been applied on an industrial application, a resin-impregnated paper bushing, in order to evaluate the accuracy in function of the size of the reduced bases as well as the efficiency in terms of computation time.