Algorithm of Solving for RF Circuit Equations by Using the Tensor Decompositions

One of the new approaches, which has a huge potential for reducing computational costs in the simulation of electronic circuits and CAD systems, is the tensor decomposition approach. Advances in recent years in the field of methods of tensor decompositions have significantly reduced memory for storage and reduced the computational time in solving high dimensional problems. 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 microwave 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 number of equations (unknowns) can reach hundreds of thousands or more. Most of popular software tools for circuit simulation used both direct and iterative methods for solving the SLAE. The problems of these methods are indicated in the paper. Therefore, further development of methods for solving and reducing computational costs requires the use of new approaches, one of which is proposed in this paper and is associated with the use of tensor decompositions. The article presents the developed algorithm for converting a second-order matrix into a higher-order tensor. In the 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.