As an example of the application of the algorithm, consider again the relaxation of the GW shown in Figure 4. The GW has 200 segments (which is indeed a very large number) and the information of one cycle is summarized in Table 1. From the measurements, it follows that as the number of blocks increases, the time to solve the equations becomes dominant over the time to compute the interactions with the surface. Hence, a very large $M$ should not be used.
Table 1.
Time (in Seconds) to Compute One Cycle of the GW-Surface Interaction (Equation 12) and to Obtain and Solve Equation 26
$M$123
surface 0.200 0.221 0.229
solution 0.201 0.394 0.777
$M$123
surface 0.200 0.221 0.229
solution 0.201 0.394 0.777

Note. When the number of blocks $M$ is bigger than 1, it is necessary to consider additionally Equations 30 and 32. The calculations correspond to the GW in Figure 4, which has 200 segments. During one cycle the GW-surface interaction is computed $1.37×106$ times and the solution is performed $20.1×103$ times. The numerical experiments have been carried out with an Intel Core i7-4500U (1.8 GHz).

Figure 6.

Lateral deviation of joint index $i=50$ in Figure 4 as function of the number of cycles (up to 100). Each relaxation curve has a total of $132×103$ points. The results are shown for different number of VS.

Figure 6.

Lateral deviation of joint index $i=50$ in Figure 4 as function of the number of cycles (up to 100). Each relaxation curve has a total of $132×103$ points. The results are shown for different number of VS.

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