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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.
The envelope of these wave- fronts is then used to construct a new set of points, and the process is repeated in the limit the Eikonal solution is obtained.
Chapters four through six are heavy with mathematics, discussing wave reduction with data processing, integral solutions to the wave equation with boundary and initial value conditions--using a variety of mathematical tools including Green's functions, Kirchoff integral formula, and the eikonal equation--and decomposition and continuation of seismic wave field using Fourier integrals.
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.
There are several ways of doing this, basically grouped into two methods: straight or curved ray theory (Cerveny, 2001) or numerically resolving the wave equation with some constraints, such us the eikonal equation (Vidale, 1988).
high- and low-energy asymptotics of the Green function, the scattering matrix, and ray and eikonal expansions).
the phase integral or Eikonal L = [integral] n * ds becomes a minimum.