In the context of time-domain simulation of integrated circuits, one often encounters large systems of coupled differential-algebraic equations. Simulation costs of these systems can become prohibitively large as the number of components keeps increasing. In an effort to reduce these simulation costs a twofold approach is presented in this paper. We combine maximum entropy snapshot sampling method and a nonlinear model order reduction technique, with multirate time integration. The obtained model order reduction basis is applied using the Gauß-Newton method with approximated tensors reduction. This reduction framework is then integrated using a coupled-slowest-first multirate integration scheme. The convergence of this combined method verified numerically. Lastly it is shown that the new method results in a reduction of the computational effort without significant loss of accuracy.
Purpose
The maximum entropy snapshot sampling (MESS) method aims to reduce the computational cost required for obtaining the reduced basis for the purpose of model reduction. Hence, it can significantly reduce the original system dimension whilst maintaining an adequate level of accuracy. The purpose of this paper is to show how these beneficial results are obtained.
Design/methodology/approach
The so-called MESS method is used for reducing two nonlinear circuit models. The MESS directly reduces the number of snapshots by recursively identifying and selecting the snapshots that strictly increase an estimate of the correlation entropy of the considered systems. Reduced bases are then obtained with the orthogonal-triangular decomposition.
Findings
Two case studies have been used for validating the reduction performance of the MESS. These numerical experiments verify the performance of the advocated approach, in terms of computational costs and accuracy, relative to gappy proper orthogonal decomposition.
Originality/value
The novel MESS has been successfully used for reducing two nonlinear circuits: in particular, a diode chain model and a thermal-electric coupled system. In both cases, the MESS removed unnecessary data, and hence, it reduced the snapshot matrix, before calling the QR basis generation routine. As a result, the QR-decomposition has been called on a reduced snapshot matrix, and the offline stage has been significantly scaled down, in terms of central processing unit time.
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