Iterative method for solving the eikonal equation

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389021%3A_____%2F16%3A00469375" target="_blank" >RIV/61389021:_____/16:00469375 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1117/12.2257326" target="_blank" >http://dx.doi.org/10.1117/12.2257326</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1117/12.2257326" target="_blank" >10.1117/12.2257326</a>

Result language

angličtina

Original language name

Iterative method for solving the eikonal equation

Original language description

The paper present principles and derivation of the iterative method for solving the eikonal equation. The eikonal equation, which defines the relationship between the phase of the optical wave Φ(r) and the refractive index n(r), i.e. |grad Φ(r)|2 = n2(r), represents the fundamental equation in geometrical optics. It describes the evolution of the wavefront, which is given by the equation Φ (r) = C, of the electromagnetic wave in the limit of infinite frequency or zero wavelength. The eikonal equation is the nonlinear partial differential equation (PDE) of the first order. This classification makes the eikonal equation of rather diffcult to solve, both analytically and numerically. Several algorithms have been developed to solve the eikonal equation: Dijkstra's algorithm, fast marching method, fast sweeping method, label-correcting methods, etc. Major disadvantage of these methods is that their convergence puts rather high requirements on the density of the computing grid. It is known that finite element method (FEM) offers much more memory and time efficient approach to solve PDEs. Unfortunately, FEM cannot be applied to solve eikonal equation directly due to its first order. In order to provide the fast and memory efficient solution of the eikonal equation, it is suggested to solve a generalized version of the eikonal equation, which is of the second order and which can be solved using FEM

Czech name

—

Czech description

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Type

D - Article in proceedings

CEP classification

BH - Optics, masers and lasers

OECD FORD branch

—

Project

<a href="/en/project/GA13-10365S" target="_blank" >GA13-10365S: Planar acoustic metamaterials with the active control of acoustic impedance</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2016

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Proceedings of SPIE 10151, Optics and Measurement International Conference 2016

ISBN

978-1-5106-0753-8

ISSN

0277-786X

e-ISSN

—

Number of pages

6

Pages from-to

—

Publisher name

SPIE, Society of Photo-Optical Instrumentation Engineers

Place of publication

Bellingham

Event location

Liberec

Event date

Oct 11, 2016

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

000393154700035