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

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