Methods of the kind obtain the viscosity solution of the

eikonal equation through numerical analysis.

It describes SIMD, shared memory, and distributed memory machine models; decomposition as a fundamental activity in parallel algorithmic design; key programming models; key concepts of performance analysis and optimization; and three case studies applying these concepts to the Single Shortest Path Problem, the

Eikonal equation, and computation of the two-dimensional convex hull.

An approximate solution which is valid for short wavelengths is the

eikonal equation (see, e.g., [22, 23]).

Equation (20) constitutes the

eikonal equation [16,17] as well as the dispersion equation for propagation of waves in an inhomogeneous anisotropic media with [??] = [??] and may be written as:

As regards the scientific review, the

eikonal equation is expressed, and some complex-valued solutions are defined corresponding to complex rays and caustics.

The phase of the wave packet can be obtained from the corresponding

eikonal equation, which can be solved numerically on the characteristics (rays).

Expressing the solution U(r) of wave equation in terms of well known Luneberg-Kline series yields

Eikonal equation for phase s(r) and transport equation for amplitude.

It consists of iteratively solving the

Eikonal equation (Eq.

(1982) (29) proved that the mild-slope equation includes the

eikonal equation with diffraction effect and the energy conservation equation between two wave rays.

In [7], helix submanifolds in Euclidean space were studied by solving the

Eikonal equation. The applications of constant angle surfaces in the theory of liquid crystals and of layered fluids were considered by P.

The

eikonal equation. Waves move through [k.sub.i][dx.sub.i] = -d[PHI], where [k.sub.i] = - [delta][PHI]/[delta][x.sup.i] = (w/c , k), w is the frequency, k is the wavevector and [PHI] is called the eikonal.