Assessment of the accuracy of the integration variable selection method and its practical application terahertz range

• Main Authors: Klimov, Konstantin N, Konov, Kirill I, Belevtsev, Andrey M, Epaneshnikova, Irina K, Boldyreff, Anton S
• Format: Conference Proceeding
• Language: English
• Published: SPIE 20.09.2020
• ISBN: 1510638954; 9781510638952
• ISSN: 0277-786X
• DOI: 10.1117/12.2582075

The paper presents an assessment of the accuracy of the method of choosing an integration variable for the numerical solution of the Cauchy problem in terahertz range. An example of using the method to determine ray paths in inhomogeneous media in the approximation of geometric optics is given. Unlike numerical methods of integration, where one pre-selected variable is used as an integration variable, in the considered method the integration variable is selected at each step. This approach reduces the risk of shifting to adjacent phase trajectories, which is especially important in the terahertz range. In addition, we note that using this approach allows you to effectively use computer resources. The integration method with the choice of the integration variable at each step is described. A feature of the method is that the variable with the highest rate of change is selected as the integration variable. The accuracy of the method is investigated by the example of a problem with a well-known analytical solution. The dependence of the relative error of the solution on the grid pitch is investigated. Extreme values of the grid pitch at which the relative error drops sharply are calculated. The dependence of the relative error of the solution on the direction of propagation of the rays is investigated. Shows the application of the numerical modeling algorithm for the example of constructing ray paths in inhomogeneous media in the approximation of geometric optics for geometry with three spatial coordinates. The ray paths in 3D space are presented.