title: ÐÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ ÐºÐ²Ð°Ð·Ð¸Ð½ÑÑÑÐ¾Ð½Ð¾Ð²ÑÐºÐ¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¿ÑÐ¸ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ Ð¶Ð¸Ð´ÐºÐ¾ÑÑÐ¸ Ñ ÑÐ²ÐµÑÐ´ÑÐ¼ ÑÐµÐ»Ð¾Ð¼
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: The application of quasi-Newton methods in fluid-structure interaction
Creators: name: Ð¡Ð°Ð¼ÑÑÐ¸ÑÐµÐ², ÐÐ²Ð³ÐµÐ½Ð¸Ð¹
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: 2021
Subjects: Ð²ÑÑÐ¸ÑÐ»Ð¸ÑÐµÐ»ÑÐ½Ð°Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÐºÐ°
ÐºÐ²Ð°Ð·Ð¸Ð½ÑÑÑÐ¾Ð½Ð¾Ð²ÑÐºÐ¸Ðµ Ð¼ÐµÑÐ¾Ð´Ñ
Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ Ð¶Ð¸Ð´ÐºÐ¾ÑÑÐ¸ Ð¸ ÑÐ²ÐµÑÐ´Ð¾Ð³Ð¾ ÑÐµÐ»Ð°
computational mathematics
quasi-newton methods
fluid-structure interaction

description: Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð¸ÑÑÐ»ÐµÐ´ÑÐµÑÑÑ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸Ð¼Ð¾ÑÑÑ ÐºÐ²Ð°Ð·Ð¸Ð½ÑÑÑÐ¾Ð½Ð¾Ð²ÑÐºÐ¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ðº ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°Ñ, Ð²Ð¾Ð·Ð½Ð¸ÐºÐ°ÑÑÐ¸Ñ Ð¿ÑÐ¸ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ Ð¶Ð¸Ð´ÐºÐ¾ÑÑÐ¸ Ð¸ ÑÐ²ÐµÑÐ´Ð¾Ð³Ð¾ ÑÐµÐ»Ð°. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ, Ð±ÑÐ»Ð¾ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½Ð¾ ÑÑÐ¾ Ð¾ÑÐ¸Ð³Ð¸Ð½Ð°Ð»ÑÐ½Ð°Ñ ÑÑÐµÐ¼Ð° Ð¼ÐµÑÐ¾Ð´Ð° IQN-BG Ð½Ðµ Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÐµÑ Ð¿Ð¾Ð»ÑÑÐ¸ÑÑ ÑÐµÑÐµÐ½Ð¸Ðµ Ð¼Ð¾Ð´ÐµÐ»ÑÐ½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð±ÑÐ»Ð¸ Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ñ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² IQN-BG Ð¸ IQN-CBQ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¿ÑÐ¾ÑÐµÐ´ÑÑÑ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð´Ð»Ð¸Ð½Ñ ÑÐ°Ð³Ð° Ð¼ÐµÑÐ¾Ð´Ð°, Ð° ÑÐ°ÐºÐ¶Ðµ Ð³Ð¸Ð±ÑÐ¸Ð´Ð½Ð¾Ð³Ð¾ Ð¿Ð¾Ð´ÑÐ¾Ð´Ð°, Ð² ÐºÐ¾ÑÐ¾ÑÐ¾Ð¼ ÑÐ°ÑÑÑ Ð¸ÑÐµÑÐ°ÑÐ¸Ð¹ Ð²ÑÐ¿Ð¾Ð»Ð½ÑÐµÑÑÑ Ð¿ÑÐ¸ Ð¿Ð¾Ð¼Ð¾ÑÐ¸ ÑÐµÐ»Ð°ÐºÑÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð³Ð¾ Ð¼ÐµÑÐ¾Ð´Ð°. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð¾ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ Ð½Ð°ÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð¿ÑÐ¸Ð±Ð»Ð¸Ð¶ÐµÐ½Ð¸Ñ Ð½Ð° ÑÑÐ¾Ð´Ð¸Ð¼Ð¾ÑÑÑ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð². ÐÐ°ÐºÐ¾Ð½ÐµÑ, Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½Ð¾ ÑÑÐ¾ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ IQN-BG Ð¸ IQN-CBG Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑ Ð½Ð°Ð¹ÑÐ¸ ÑÐµÑÐµÐ½Ð¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð·Ð° ÑÐ°Ð·ÑÐ¼Ð½Ð¾Ðµ Ð²ÑÐµÐ¼Ñ Ð¸ Ð´Ð°Ð¶Ðµ ÑÑÐ¿ÐµÑÐ½Ð¾ ÐºÐ¾Ð½ÐºÑÑÐ¸ÑÑÑÑ Ñ Ð¾Ð´Ð½Ð¸Ð¼ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¾Ð¹ ÑÐµÐ»Ð°ÐºÑÐ°ÑÐ¸Ð¸. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ Ð¼Ð¾Ð³ÑÑ Ð±ÑÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ñ Ð² Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ Ð¶Ð¸Ð´ÐºÐ¾ÑÑÐ¸ Ð¸ ÑÐ²ÐµÑÐ´Ð¾Ð³Ð¾ ÑÐµÐ»Ð°, Ð° ÑÐ°ÐºÐ¶Ðµ Ð² Ð´ÑÑÐ³Ð¸Ñ Ð¾Ð±Ð»Ð°ÑÑÑÑ Ð°ÐºÑÐ¸Ð²Ð½Ð¾Ð³Ð¾ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ ÐºÐ²Ð°Ð·Ð¸Ð½ÑÑÑÐ¾Ð½Ð¾Ð²ÑÐºÐ¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð².
description: In the given work we investigated the applicability of quasi-Newton methods to solve problems arising from fluid-structure interaction modeling. As a result, we have shown that original numerical scheme of IQN-BG does not allow us to solve particular model problem. We have developed modifications based on step length optimization and mixed approach, some iterations of which are made by using relaxation procedure. We have shown that initial approximation highly affects convergence of modified methods. At last, we have shown that modified IQN-BG and IQN-CBG methods not only allow us to find the solution in a reasonable time, but also they can succesfully compete with one dynamic relaxation method. Results of the given work can be used in fluid-structure interaction modeling and in other areas in which quasi-Newton methods can be applied.