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High-Level Modeling and Design Techniques
Published in Soumya Pandit, Chittaranjan Mandal, Amit Patra, Nano-Scale CMOS Analog Circuits, 2018
Soumya Pandit, Chittaranjan Mandal, Amit Patra
The model order reduction approach is an algorithmic approach for transformation of a large set of mathematical equations to a much smaller one. The technique is general in the sense that as long as the equations of the original circuit are known (may be through SPICE simulations), the internal structural details and operating principles are not required. These reduced order models simulate much more efficiently, while accurately approximating the response of a real circuit. This approach is discussed here for linear time invariant (LTI) and linear time varying (LTV) systems. A fairly complete survey of model order reduction techniques is provided by Roychowdhury in [157, 156], which forms the basis of the following material.
Discrete orthogonal polynomials reduced models based on shift-transformation and discrete Walsh functions
Published in International Journal of Systems Science, 2022
Zhao-Hong Wang, Yao-Lin Jiang, Kang-Li Xu
Numerical simulation of large-scale dynamical systems plays an important role in studying complex physical phenomena. Nevertheless, the inherent large-scale nature of the systems often leads to unmanageable demands on limited computation resources. In particular, by means of the finite element method or a finite difference method, one numerically solves the partial differential equations, which can lead to a large-scale system. Since the number of state variables of such a system might exceed , a fast and reliable simulation may be impossible. Model order reduction (MOR) can dramatically reduce the computational cost during simulation. Up to now, MOR has been successfully applied in integrated circuits design (Rewieński & White, 2003; Tan, 2005), finite element analysis (Qu, 2004), and machine learning (Mohamed, 2018; Mohseni & Khorsand, 2019; Zhang et al., 2019).
Krylov subspace approximation for quadratic-bilinear differential system
Published in International Journal of Systems Science, 2018
The technique of model order reduction (MOR) has become common means in many different settings such as simulation, optimisation and control of large-scale systems arising in many disciplines such as the discretisation of computational fluid dynamic system (Benner, 2004), control, the modelling process of the integrated circuit design (Antoulas, 2005), structural dynamics, mixers, switch-capacitor filters, microelectro mechanical systems (MEMS), high-speed clock networks and RF circuits. Even in modelling of chemical reaction kinetics, Lötstedt and Ferm (2006), Higham (2008) and Jahnke (2011) declare, though the system is very small, there still exist hundreds of reactants reacting each other, so in order to model the process, the number of the equations is very large. The high order is undesirable in optimisation, simulation and control, because of factors such as the increasing need for complex hardware and degraded computational speed. So many model reduction techniques boom, which is to capture the dynamics of the complex system with little number of states. For the framework of model reduction, see details in Baur, Benner, and Feng (2014) and Jiang (2010).
A proper orthogonal decomposition analysis method for transient nonlinear heat conduction problems. Part 1: Basic algorithm
Published in Numerical Heat Transfer, Part B: Fundamentals, 2020
Qiang-Hua Zhu, Yu Liang, Xiao-Wei Gao
The fundamental purpose of developing model order reduction method is its ability to solve large-scale problems quickly. However, the time savings of the POD-based ROM for transient nonlinear heat conduction problem using these basic algorithms are not pronounced as the linear one. Especially when quadrilateral isoparametric element is adopted, the reduction in computing time is very small. This is disadvantage to the application of POD-based model reduction technology in the field of nonlinear heat conduction. Therefore, it is necessary to study advanced algorithms further, which can really achieve highly efficient solution of the related transient nonlinear heat conduction problems by the POD-based ROM. This work will be presented in Part 2.