Mathematics

On the resonances of an inhomogeneous dielectric ball, coated with graphene

O. S. Skvortsov

Penza State University, Penza

Abstract: Background. The purpose of the work is the development, software implementation and testing of algorithms designed to find resonant frequencies in an inhomogeneous dielectric ball coated with graphene. The relevance of the task is due to the widespread use of graphene in the technical field due to its unique properties. Materials and methods. The Galerkin method is applied to discretize a vector integro-differential equation, piecewise constant basic vector functions on a three-dimensional body and on its surface are determined, and a parallel algorithm for solving the problem using the MSMPI library is developed. Results. The effectiveness of the parallel algorithm, which makes it possible to detect the desired resonances under specified conditions, has been confirmed. Conclusions. An effective parallel algorithm has been created for discretization of the integro-differential equation, finding the determinant of the matrix and searching for resonant frequencies.

Keywords: resonance search, inhomogeneous bulk body, graphene coating, singular integro-differential equation, basic functions, Galerkin method, dielectric ball, parallel algorithm

UDC: 517.968.73

DOI: 10.21685/2072-3040-2024-4-6