title: Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ Ð´Ð»Ñ Ð½Ð°Ñ Ð¾Ð¶Ð´ÐµÐ½Ð¸Ñ Ð¼Ð¾Ð´ ÑÐ»ÐµÐºÑÑÐ¾Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð² ÑÐ»Ð»Ð¸Ð¿ÑÐ¸ÑÐµÑÐºÐ¾Ð¼ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐµ-ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐµ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Development of a program for finding electromagnetic field modes in an elliptical resonator cylinder
Creators: name: ÐÐ¾ÑÐºÐ¾Ð²Ð°, ÐÐ²Ð³ÐµÐ½Ð¸Ñ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2023
Subjects: ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ
Ð°Ð¿Ð¿ÑÐ¾ÐºÑÐ¸Ð¼Ð°ÑÐ¸Ñ
Ð¼ÐµÑÐ¾Ð´ ÐºÐ¾Ð½ÐµÑÐ½ÑÑ ÑÐ°Ð·Ð½Ð¾ÑÑÐµÐ¹
Ð¿ÑÐ¾Ð±Ð»ÐµÐ¼Ð° ÑÐ¾Ð±ÑÑÐ²ÐµÐ½Ð½ÑÑ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ð¹
QR-Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼
numerical methods
approximation
finite difference method
eigenvalue problem
QR algorithm

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð³Ð¾ Ð¿ÑÐ¾Ð´ÑÐºÑÐ°, Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑÐµÐ³Ð¾ ÑÐµÑÐ¸ÑÑ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÑÑ Ð·Ð°Ð´Ð°ÑÑ, Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½Ð½ÑÑ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»ÑÑ ÑÐ»ÐµÐºÑÑÐ¾Ð¼Ð°Ð³Ð½Ð¸ÑÐ½ÑÑ Ð¼Ð¾Ð´ Ð² ÑÐ»Ð»Ð¸Ð¿ÑÐ¸ÑÐµÑÐºÐ¾Ð¼ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐµ-ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐµ. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¸Ð²Ð¾Ð´Ð¸ÑÑÑ Ð¾Ð±Ð·Ð¾Ñ Ð¾ÑÐ½Ð¾Ð²Ð½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð´Ð»Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ Ð½Ð°ÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ñ Ð¼Ð¾Ð´, Ð² ÑÐ°ÑÑÐ½Ð¾ÑÑÐ¸, Ð¿ÑÐ¸Ð²Ð¾Ð´Ð¸ÑÑÑ Ð¾Ð±Ð·Ð¾Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð´Ð»Ñ Ð°Ð¿Ð¿ÑÐ¾ÐºÑÐ¸Ð¼Ð°ÑÐ¸Ð¸ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð² ÑÐ°ÑÑÐ½ÑÑ Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð´Ð½ÑÑ, Ð° ÑÐ°ÐºÐ¶Ðµ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐµÑÐµÐ½Ð¸Ñ Ð¿ÑÐ¾Ð±Ð»ÐµÐ¼Ñ ÑÐ¾Ð±ÑÑÐ²ÐµÐ½Ð½ÑÑ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ð¹. Ð ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ð° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð° Ð´Ð»Ñ Ð½Ð°ÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ñ ÑÐ»ÐµÐºÑÑÐ¾Ð¼Ð°Ð³Ð½Ð¸ÑÐ½ÑÑ Ð¼Ð¾Ð´ Ð² ÑÐ»Ð»Ð¸Ð¿ÑÐ¸ÑÐµÑÐºÐ¾Ð¼ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐµ-ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐµ. Ð Ð°Ð±Ð¾ÑÐ° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ Ð¿ÑÐ¾ÑÐµÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð° Ð¿ÑÐ¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸, Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ ÑÐ°ÑÑÑÑÑ Ð¿ÑÐ¸ Ð·Ð°Ð´Ð°Ð½Ð½ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸. ÐÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð° Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÐµÑ Ð½Ð°Ð¹ÑÐ¸ Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²ÐµÐ½Ð½ÑÑ ÑÐ¾ÑÐ¼Ñ Ð¼Ð¾Ð´ ÑÐ»Ð»Ð¸Ð¿ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ°-ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐ°, ÑÑÐ¾ Ð¼Ð¾Ð¶ÐµÑ Ð¿Ð¾Ð¼Ð¾ÑÑ Ð² ÑÐµÑÐµÐ½Ð¸Ð¸ Ð²Ð¾Ð¿ÑÐ¾ÑÐ° Ð¾ ÑÐ¾Ð¼, ÐºÐ°ÐºÐ¸Ð¼ Ð¾Ð±ÑÐ°Ð·Ð¾Ð¼ ÑÐ°Ð·Ð¼ÐµÑÑÐ¸ÑÑ Ð¸Ð·Ð»ÑÑÐ°ÑÐµÐ»Ð¸ Ð² ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐµ Ð´Ð»Ñ Ð±Ð¾Ð»ÐµÐµ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾Ð³Ð¾ Ð¾Ð±Ð¼ÐµÐ½Ð° ÑÐ¾ÑÐ¾Ð½Ð°Ð¼Ð¸ ÑÐµÑÐµÐ· ÑÐµÐ·Ð¾Ð½Ð°Ð½ÑÐ½ÑÑ Ð¼Ð¾Ð´Ñ.
description: This work is devoted to the development of a software product that allows solving a mathematical problem presented by a mathematical model of electromagnetic modes in an elliptical resonator cylinder. The paper provides an overview of the main methods for solving the problem of finding modes, in particular, an overview of methods for approximation of partial differential equations, as well as methods for solving the eigenvalue problem. In the course of the work, a program was implemented designed to find electromagnetic modes in an elliptical resonator cylinder. The operation of the program was tested with various parameters of the model, calculations were carried out with the specified parameters of the model. The program allows to find the spatial shape of the modes of an elliptical resonator cylinder, which can help in solving the problem of how to place the emitters in the resonator for more efficient photon exchange through the resonant mode.