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Iterative method for solving the eikonal equation
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SYSNO ASEP 0469375 Druh ASEP C - Konferenční příspěvek (mezinárodní konf.) Zařazení RIV D - Článek ve sborníku Název Iterative method for solving the eikonal equation Tvůrce(i) Mokrý, Pavel (UFP-V) RID Číslo článku 101510Z Zdroj.dok. Proceedings of SPIE 10151, Optics and Measurement International Conference 2016, OAM 2016 Proceedings, 10151. - Bellingham : SPIE, Society of Photo-Optical Instrumentation Engineers, 2016 / Kovačičinová J. - ISSN 0277-786X - ISBN 978-1-5106-0753-8 Poč.str. 6 s. Forma vydání Tištěná - P Akce OAM 2016, Optics and Measurement International Conference 2016 Datum konání 11.10.2016 - 14.10.2016 Místo konání Liberec Země CZ - Česká republika Typ akce WRD Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova Iterative methods ; Finite element methods ; Data storage ; Electromagnetic radiation ; Geometrical optics ; Numerical analysis ; Partial differential equations ; Refractive index ; Wavefronts ; Algorithms ; eikonal equation Vědní obor RIV BH - Optika, masery a lasery CEP GA13-10365S GA ČR - Grantová agentura ČR Institucionální podpora UFP-V - RVO:61389021 UT WOS 000393154700035 EID SCOPUS 85012895392 DOI 10.1117/12.2257326 Anotace 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 Pracoviště Ústav fyziky plazmatu Kontakt Vladimíra Kebza, kebza@ipp.cas.cz, Tel.: 266 052 975 Rok sběru 2017
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