| Issue |
EPJ Web Conf.
Volume 224, 2019
IV International Conference “Modeling of Nonlinear Processes and Systems” (MNPS-2019)
|
|
|---|---|---|
| Article Number | 01004 | |
| Number of page(s) | 6 | |
| Section | Mathematical Methods in Physics | |
| DOI | https://doi.org/10.1051/epjconf/201922401004 | |
| Published online | 09 December 2019 | |
https://doi.org/10.1051/epjconf/201922401004
Reflection Method for Mathematical Modeling of Potential Fields in Multi-Layer Media
Penza State University, Computer Engineering, RU-440026, Penza, Russia
* e-mail: yaremki@mail.ru
Published online: 9 December 2019
In this paper, potential fields in areas with plane and circular symmetry have been studied. In this case, the field potential is defined as the sum of solutions of Dirichlet model boundary value problems. The reflection method is used for the modeling of stationary thermal fields in multilayer media. By applying the reflection method, we found analytical solutions of boundary value problems with boundary conditions of the fourth kind for the Laplace equations and developed new computational algorithms. The developed algorithms can be easily implemented and transformed into a computer code. First of all, these algorithms implement consistent solutions of the Dirichlet problems for the model domains that allows using libraries of subroutines. Secondly, they have high algorithmic efficiency. It has been shown that reflection method is identical to the method of transformation operators and proved that transformation operator can be decomposed into a series of successive reflections from the external and internal boundaries. Finally, a physical interpretation of the reflection method has been discussed in detail.
© The Authors, published by EDP Sciences, 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.