Reflection Method for Mathematical Modeling of Potential Fields in Multi-Layer Media

Abstract

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.