Model Reduction and Simulation of Nonlinear Circuits via Tensor Decomposition
Model Reduction and Simulation of Nonlinear Circuits via Tensor Decomposition
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DOI：
10.1109/tcad.2015.2409272
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发表时间：
2015-03
影响因子：
2.9
通讯作者：
Haotian Liu;L. Daniel;N. Wong
中科院分区：
文献类型：
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作者：
Haotian Liu;L. Daniel;N. Wong
非线性电路(尤其是高度非线性电路)的模型降阶一直是一个具有理论和数值挑战性的任务。在本文中，我们利用张量(即矩阵的高阶推广)，提出了一种基于张量的非线性模型降阶算法，我们称之为TNMOR算法，用于有效地模拟非线性电路。与现有的非线性模型降阶方法不同，在TNMOR中，高阶非线性被张量捕获，然后被分解和降阶为紧凑的基于张量的降阶模型。因此，TNMOR完全避免了密集的降阶系统矩阵，如果存在这些张量的相对低阶近似，这反过来又允许更快的模拟和更小的存储需求。对暂态和周期性稳态分析的数值实验证实了TNMOR的优越精度和效率，特别是在高度非线性的情况下。
Model order reduction of nonlinear circuits (especially highly nonlinear circuits) has always been a theoretically and numerically challenging task. In this paper, we utilize tensors (namely, a higher order generalization of matrices) to develop a tensor-based nonlinear model order reduction algorithm we named TNMOR for the efficient simulation of nonlinear circuits. Unlike existing nonlinear model order reduction methods, in TNMOR high-order nonlinearities are captured using tensors, followed by decomposition and reduction to a compact tensor-based reduced-order model. Therefore, TNMOR completely avoids the dense reduced-order system matrices, which in turn allows faster simulation and a smaller memory requirement if relatively low-rank approximations of these tensors exist. Numerical experiments on transient and periodic steady-state analyses confirm the superior accuracy and efficiency of TNMOR, particularly in highly nonlinear scenarios.