RUDN University and NSI RAS mathematicians proposed an express method for calculation of the propagation of light

RUDN University and NSI RAS mathematicians proposed an express method for calculation of the propagation of light

Mathematicians from RUDN University and the Nuclear Safety Institute of the RAS (NSI RAS) have proposed a numerical method for solving equations describing the propagation of light in a medium.

The mathematicians have demonstrated that such a method produces fairly good results on representative model problems.

“Computational complexity — the so-called ‘computational costs’ of the approach we are talking about — does not exceed that of other approaches. Although, we solve a linear boundary value problem, and that, of course, is less laborious than solving a non-linear problem,” explained Petr Vabishevich, the author of the study and a member of the Research Center for Computational Methods in Applied Mathematics of the RUDN University.

Vabishevich and his co-authors modelled the equation for anisotropic media. From the point of view of physics, this is an environment in which the physical properties of light propagation in different directions are not the same. Materials with these properties are now widely used in optical devices.

Besides optics, the eikonal equation is also used to numerically solve equations describing the motion of a fluid. Such modelling is necessary to create realistic pictures in computer graphics — for example, in the film “Pirates of the Caribbean” the water was not just drawn but calculated on a physical level. The speed of calculation, which could potentially be improved by the method developed by mathematicians at RUDN University and NSI RAS, plays a key role in such cases.

The article:
Numerical solution of boundary value problems for the eikonal equation in an anisotropic medium of Computational and Applied Mathematics
Volume 362, 15 December 2019, Pages 55-67
DOI: /10.1016/j.cam.2019.05.016ttps://www.sciencedirect.com/science/article/pii/S0377042719302511?via%3Dihub

Main Publications View all
15 Nov 2017
RUDN University scientists publish results of their scientific researches in highly-recognized in whole world and indexed in international databases journals (Web of Science, Scopus ect.). That, of course, corresponds to the high status of the University and its international recognition. Publications of June-September 2017 ( In Journals of categories Q1-Q3)
International Projects View all
Similar newsletter View all
19 Apr
A huge pizza and a jug of water, why should 5G networks be sliced? The winners of RUDN science competition explain

RUDN summarized the results of the scientific competition "Project Start: work of the science club ". Students of the Faculty of Physics, Mathematics and Natural Sciences have created a project for a managed queuing system using a neural network to redistribute resources between 5G segments. How to increase flexibility, make the network fast and inexpensive and reach more users — tell Gebrial Ibram Esam Zekri ("Fundamental Computer Science and Information Technology", Master's degree, II course) and Ksenia Leontieva ("Applied Mathematics and Computer Science", Master's degree, I course).

19 Apr
Lyricists and physicists are now on equal terms: the first humanitarian laboratory opened in RUDN

What is your first association with the word “laboratory”? Flasks and beakers? Microscopes and centrifuges? Yes, many of us would answer the same way.

19 Apr
The National Demographic Report 2023 was published with the participation of RUDN. Demographic well-being of Russian regions

The National Demographic Report, 2023 Demographic Well-Being of Russian Regions (hereinafter - the National Demographic Report) was prepared by the scientific team of the Institute of Demographic Studies of the Federal Research Center of the Russian Academy of Sciences, the Vologda Scientific Center of the Russian Academy of Sciences, Peoples' Friendship University of Russia, the Center for Family and Demography of the Academy of Sciences of the Republic of Tatarstan, as well as with the participation of leading scientists from the Republic of Bashkortostan, Stavropol Krai, Volgograd, Ivanovo, Kaliningrad, Nizhny Novgorod, Sverdlovsk Oblasts and Khanty-Mansi Autonomous Okrug–Yugra.

Similar newsletter View all