Search

Your search keyword '"AUTOMATIC differentiation"' showing total 2 results
Start Over Descriptor "AUTOMATIC differentiation" Language russian
2 results on '"AUTOMATIC differentiation"'

1. A comparison of two approaches to the global stability analysis using the example of the cylinder flow problem

Author

Golubkov Valentin and Garbaruk Andrey

Subjects
global stability analysis, navier–stokes equations, jacobian, automatic differentiation, Mathematics, QA1-939, Physics, QC1-999
Abstract

In the paper, the two main approaches to calculating the Jacobian of the Navier–Stokes equations, namely, the continuum (CA) and discrete (DA) approaches, have been directly compared for the first time. The DA to calculating this Jacobian was implemented based on in-house finite-volume code for hydrodynamics simulation (in addition to the already existing CA). The DA was successfully verified by comparison between the obtained numerical result and that of solving the transient Navier–Stokes equations. The comparison of these approaches was carried out using the example of a laminar flow past a cylinder by a perfect gas at the near-critical Reynolds numbers (Re = 50 and 60). It was established that the CA predicted the growth rate of perturbations more accurately, while the DA did their frequency and amplitude in toto. The results obtained allow to assert that both CA and DA are equivalent in terms of accuracy, and the choice of a particular approach for analyzing the stability may be determined by other criteria, e. g., ease of implementation, computational work and so on.

Published
2023
Full Text
View/download PDF

2. Software tools for metrological auto-tracking of calculations with inaccurate data in Java

Subjects
обратный метод, автоматическое дифференцирование, error estimation, прямой метод, java, chain rule, оценка погрешности, backward mode, forward mode, operator overloading, цепное правило, перегрузка операторов, automatic differentiation
Abstract

Данная работа посвящена созданию Ð¿Ñ€Ð¾Ð³Ñ€Ð°Ð¼Ð¼Ð½Ñ‹Ñ ÑÑ€ÐµÐ´ÑÑ‚Ð² оценки погрешности результатов ÐºÐ¾ÑÐ²ÐµÐ½Ð½Ñ‹Ñ Ð¸Ð·Ð¼ÐµÑ€ÐµÐ½Ð¸Ð¹ с использованием метода автоматического дифференцирования. Данный метод позволяет оценивать значение Ð¿Ñ€Ð¾Ð¸Ð·Ð²Ð¾Ð´Ð½Ñ‹Ñ Ð²Ñ‹Ñ‡Ð¸ÑÐ»ÑÐµÐ¼Ñ‹Ñ Ñ„ÑƒÐ½ÐºÑ†Ð¸Ð¹, основан на цепном правиле и представлен двумя режимами работы – прямым и обратным. Оба режима были разработаны в библиотеке на языке программирования Java. Задачи, которые решались в Ñ Ð¾Ð´Ðµ исследования: 1. изучение принципов работы автоматического дифференцирования, его прямого и обратного режимов, 2. разработка библиотеки на языке Java, 3. выполнение тестирования, 4. сравнение с существующими библиотеками. При создании структуры разрабатываемой программной библиотеки использовалась перегрузка операторов для методов, Ñ€ÐµÐ°Ð»Ð¸Ð·ÑƒÑŽÑ‰Ð¸Ñ ÑÐ»ÐµÐ¼ÐµÐ½Ñ‚Ð°Ñ€Ð½Ñ‹Ðµ арифметические операции, для ÐºÐ¾Ñ‚Ð¾Ñ€Ñ‹Ñ Ð±Ñ‹Ð» создан специальный класс-тестировщик. Проведены анализ и сравнение с другими существующими библиотеками. Отмечены преимущества реализованной библиотеки по занимаемой памяти, затрачиваемому времени на компиляцию, объему кода и простоты понимания пользователем., This work is devoted to the development of a tool for software evaluation of the measurement results’ error using the method called automatic differentiation. This method is based on the chain rule of derivatives calculations and is represented by two modes – forward and backward. Both modes were developed in a library using programming language Java. The research contained the following goals: 1. the study of the automatic differentiation, its forward and backward modes, 2. Java library development, 3. testing, 4. comparison with existing libraries. When creating classes, operator overloading was used for implementing the elementary arithmetic operations, for which a special tester class was created. Analysis and comparison with other existing libraries was carried out. As a result, the advantages of the implemented library were marked: the volume of occupied memory, the time spent on compilation, the amount of code and simplicity for user.

Published
2021
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results