Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical analysis of eikonal equation   The Maxwell equations have a fairly simple form. However, finding solutions
of Maxwell's equations is an extremely difficult task. Therefore, various
simplifying approaches are often used in optics. One such simplifying approach
is to use the approximation of geometric optics. The approximation of geometric
optics is constructed with the assumption that the wavelengths are small
(short-wavelength approximation). The basis of geometric optics is the eikonal
equation. The eikonal equation can be obtained from the wave equation
(Helmholtz equation). Thus, the eikonal equation relates the wave and geometric
optics. In fact, the eikonal equation is a quasi-classical approximation (the
Wentzel-Kramers-Brillouin method) of wave optics. This paper shows the
application of geometric methods of electrodynamics to the calculation of
optical devices, such as Maxwell and Luneburg lenses. The eikonal equation,
which was transformed to the ODE system by the method of characteristics, is
considered. The resulting system is written for the case of Maxwell and
Luneburg lenses.

18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat