Solving the eikonal equation by the FSM method in Julia language

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Abstract

There are two main approaches to the numerical solution of the eikonal equation: reducing it to asystemofODES(methodofcharacteristics)andconstructingspecializedmethodsforthenumericalsolutionof this equation in the form of a partial differential equation. The latter approach includes the FSM (Fast sweeping method) method. It is reasonable to assume that a specialized method should have greater versatility. The purpose of this work is to evaluate the applicability of the FSM method for constructing beams and fronts. The implementation of the FSM method in the Eikonal library of the Julia programming language was used. The method was used for numerical simulation of spherical lenses by Maxwell, Luneburg and Eaton. These lenses were chosen because their optical properties have been well studied. A special case of flat lenses was chosen as the easiest to visualize and interpret the results. The results of the calculations are presented in the form of images of fronts and rays for each of the lenses. From the analysis of the obtained images, it is concluded that the FSM method is well suited for constructing electromagnetic wave fronts. An attempt to visualize ray trajectories based on the results of his work encounters a number of difficulties and in some cases gives an incorrect visual picture.

About the authors

Christina A. Stepa

RUDN University

Email: 1042210111@pfur.ru
ORCID iD: 0000-0002-4092-4326
ResearcherId: GLS-1445-2022

PhD student of Probability Theory and Cyber Security

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Arseny V. Fedorov

RUDN University

Email: 1042210107@rudn.ru
ORCID iD: 0000-0002-3036-0117
Scopus Author ID: 57219092618
ResearcherId: AGY-9849-2022

PhD student of Probability Theory and Cyber Security

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Migran N. Gevorkyan

RUDN University

Email: gevorkyan-mn@rudn.ru
ORCID iD: 0000-0002-4834-4895
Scopus Author ID: 57190004380
ResearcherId: E-9214-2016

Candidate of Sciences in Physics and Mathematics, Associate Professor of Department of Probability Theory and Cyber Security

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Anna V. Korolkova

RUDN University

Email: korolkova-av@rudn.ru
ORCID iD: 0000-0001-7141-7610
Scopus Author ID: 36968057600
ResearcherId: I-3191-2013

Docent, Candidate of Sciences in Physics and Mathematics, Associate Professor of Department of Probability Theory and Cyber Security

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Dmitry S. Kulyabov

RUDN University; Joint Institute for Nuclear Research

Author for correspondence.
Email: kulyabov-ds@rudn.ru
ORCID iD: 0000-0002-0877-7063
Scopus Author ID: 35194130800
ResearcherId: I-3183-2013

Professor, Doctor of Sciences in Physics and Mathematics, Professor of the Department of Probability Theory and Cyber Security of Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University); Senior Researcher of Laboratory of Information Technologies, Joint Institute for Nuclear Research

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation; 6 Joliot-Curie St, Dubna, 141980, Russian Federation

References

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