For illustration, Jain's scheme yields a solution with an error of 5.6×10−4 in 14 milliseconds (ms) whereas for approximately the same computational time, the CN computed solution has an accuracy level of 3.5×10−3.
By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation.
(b) Computed solution from HOC scheme with uniform grids.
(b) Computed solution by HOC scheme on uniform grids.
As with the static and multiple static correction approaches, the method requires a directly computed solution at zero frequency.
(a) shows the exact solution, (b) the solution obtained from HOC scheme on uniform grids, (c) the computed solution obtained from a HOC scheme on nonuniform grids, and (d) the computed solution of CD scheme on nonuniform grids.
Algorithm 2 starts by checking whether a previously computed solution for e already exists in the cache (cf. line 6).
The reported errors are the (l_{2} -norms of the errors between the computed sol_{2} -normshe exact sofuthen on finerrorsid.
It is important to note that, Equation (3.7) requires, at each time step, to solve a tri-diagonal system of linear equations where the right-hand side utilizes all the history of the computed solution up to that time.
(a) represents the exact solution, (b) the solution obtained by the HOC scheme on uniform grids, (c) the computed solution by the CD scheme on uniform grids, and (d) the solution obtained by the HOC scheme on nonuniform grids with (lambda=0.8). Figure 3 Nonuniform grids distribution in the xy -plane, (pmb{32^{2}}), (pmb{lambda=0.8}).
Figure 4 Computed solution obtained from HOC and CDS schemes for problem 2. (a) Exact solution.
