Parallel implementation of evolutionary partial differential equations by collocation optical-electronic schemes

Evgeniy A. Bashkov; Olga A. Dmitrieva; Nadiia H. Huskova; Svyatoslav Y. Vishnevskyi; Andrzej Kotyra; Ainur Ormanbekova

doi:10.1117/12.2664488

12 December 2022 Parallel implementation of evolutionary partial differential equations by collocation optical-electronic schemes

Evgeniy A. Bashkov, Olga A. Dmitrieva, Nadiia H. Huskova, Svyatoslav Y. Vishnevskyi, Andrzej Kotyra, Ainur Ormanbekova

Author Affiliations +

Proceedings Volume 12476, Photonics Applications in Astronomy, Communications, Industry, and High Energy Physics Experiments 2022; 1247612 (2022) https://doi.org/10.1117/12.2664488
Event: Photonics Applications in Astronomy, Communications, Industry, and High Energy Physics Experiments 2022, 2022, Lublin, Poland

Abstract

The problem of parallel solution of partial differential equations with the help of the method of lines that ensures the reduction of the initial problem to the Cauchy problem described by a system of ordinary differential equations is considered. As a basic method, collocated multi-step block difference schemes are proposed. Obtaining a numerical solution in this case becomes possible only with the use of high-performance computing, usually with parallel architecture. This problem becomes especially important in the implementation of mathematical models based on systems of partial differential equations when it comes to the need for discretization of the solution search area, which can be significantly complicated by the geometric configuration of the boundaries. Solution of systems of this order cannot be obtained without involving multiprocessor computers. But by simply increasing the processing power, this problem cannot be solved. Only by combining the advantages of supercomputers and modern numerical simulation methods we can expect a significant improvement in the numerical solution of partial differential equations (PDEs).

Citation Download Citation

Evgeniy A. Bashkov, Olga A. Dmitrieva, Nadiia H. Huskova, Svyatoslav Y. Vishnevskyi, Andrzej Kotyra, and Ainur Ormanbekova "Parallel implementation of evolutionary partial differential equations by collocation optical-electronic schemes", Proc. SPIE 12476, Photonics Applications in Astronomy, Communications, Industry, and High Energy Physics Experiments 2022, 1247612 (12 December 2022); https://doi.org/10.1117/12.2664488

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
6 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Partial differential equations

Numerical analysis

Computing systems

Mathematical modeling

Ordinary differential equations

Error analysis

Error control coding

Show All Keywords

Keywords/Phrases

Search In:

Publication Years