CGFFTConjugate Gradient Fast Fourier Transform
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This is also illustrated in Figure 5, which shows the number of CGFFT iterations, with and without "marching on in angle" as a function of K for Muscle1.
Let us conclude by stressing the importance of choosing the largest possible value for the CGFFT stop criterion (NRMSE CGFFT), in order to get the most benefit from "marching on in angle." When, for example, for Leg2 (N = 32, K = 64), the CGFFT stop criterion is reduced by a factor of 10, the number of CGFFT iterations is almost doubled, from 1216 to 2148, while the resulting reduction in the NRMSE on the total field, from 3.2 to 2.8%, is not significant.
The effort needed for the summations in (42) to compute the field on the mesh [G.sub.cas]([rho], [[rho].sub.S]) is much more important but remains lower than that needed for the CGFFT solution, as can be seen from the circles in Figure 4.
(7) Choose the CGFFT stop criterion, with the aid of Figure 3(a), and solve the forward problem in a homogeneous environment with "marching on in angle."
By considering scattering in a homogeneous environment, the efficiency of the CGFFT procedure is exploited.
Caption: Figure 4: CPU times for the different steps in the forward problem for Leg2 with K = 64 sources: (1) solution of equation (5) for [G.sub.hom] ([rho], [[rho].sub.S]) with CGFFT and "marching on in angle"; (2) computation of the incident field [G.sub.1]([rho], [[rho].sub.S]); (3) computation of the scattered field [G.sup.scat.sub.hom]([[rho].sub.R], [[rho].sub.S]); (4) one CGFFT iteration; (5) the summation (42) to obtain the total field [G.sub.cas]([rho], [[rho].sub.S]).
Caption: Figure 5: The total number of CGFFT iterations as a function of the number of sources K for the "marching on in angle" and conventional approaches, for Muscle1 with N =16.