Solving the circuit equations using tensor decompositions

作     者：V N Lantsov 

作者机构：Computer Engineering and System Control Department Vladimir State University named after Alexander and Nikolay Stoletovs Vladimir Gorky Str. 87 600000 Russian Federation 

出 版 物：《Journal of Physics: Conference Series》 

年 卷 期：2021年第1889卷第2期

学科分类：07[理学] 0702[理学-物理学] 

摘      要：Tensor decomposition methods are widely used for solving high-dimensional and multi-dimensional problems. These approaches have a huge potential for reducing computational costs in the simulation of electronic circuits and in the CAD systems for electronics. Simulation of modern radio-frequency (RF) circuits, especially for RF integrated circuits, is one of the areas of extensive scientific research and development. The main problem of analysis methods for circuit design of RF electronics is the significant computational costs associated with the high dimensions to be solved. This paper shows that the computational costs of circuit design are largely determined by the costs of solving a system of linear algebraic equations (SLAE). The problems of the solving of SLAE are indicated in the paper. Further development of methods for solving and reducing computational costs requires the use of new approaches, one of which is proposed in this paper. The article presents the developed algorithm for converting a second-order matrix into a higher-order tensor. In this paper algorithms and software tools for tensor decompositions, as well as methods for solving SLAE in the representation of equations in tensor format are investigated. The results of numerical experiments and the results of comparison with traditional methods are presented.