Метод вторинних джерел в електротехніці й погано обумовлені матриці

Abstract

A new approach to solving the problem of instability of a system of linear algebraic equations (SLAE) with an ill-conditioned matrix describing a discrete model of the Fredholm integral equation of the sec-ond kind, which reduces the calculation by the method of secondary sources of three-dimensional static and quasi-stationary electromagnetic fields of any geometry in inhomogeneous and nonlinear media, is considered. The essence of the new approach is all about. There is a method for correctly compiling a description of an electrical circuit. In this method, for the first time, when describing an electrical cir-cuit, the parameters of a specific task are taken into account, but they are not taking into account in other methods. As a result, the solution to the problem is stable even in the case of a SLAE with an ill-conditioned matrix. The disadvantage of this method is the description of the electrical circuit in the form of a graph. The description of the discrete model of the integral equation is proposed to be trans-formed to a form of representation that satisfies the method of describing the electric circuit. To achieve this goal, the following tasks have been completed. The requirements of the method of correct compila-tion of the description, which the form of the description of the discrete model of the integral equation must satisfy, are formulated. The analysis of the linear discrete model of the integral equation is carried out, the graph of the discrete model is constructed, and the requirements for the method of transform-ing this graph to the graph that meets the requirements of the method are formulated. A technique for transforming a graph of a discrete model into a graph that meets the requirements of the method has been developed. Final result: a description of a discrete model of the Fredholm integral equation of the second kind, compiled by the method of secondary sources in the form of a graph, satisfying the re-quirements of the method is presented.