Open AccessSolving the circuit equations using tensor decompositions
Author(s) -
Владимир Ланцов
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1889/2/022097
Subject(s) - tensor (intrinsic definition) , computer science , electronic circuit , representation (politics) , electronics , decomposition , computational science , matrix decomposition , computer engineering , mathematical optimization , mathematics , engineering , electrical engineering , ecology , politics , political science , law , pure mathematics , biology , eigenvalues and eigenvectors , physics , quantum mechanics
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.