In Treeby et al. (2012), the numerical results are compared with the analytical solution in Fig. 3(c).
However, the time axis of these two data may not accord with each other due to dispersion.
Thus, can anyone tell me how to calculate the least squares error?
Hi bmezhou,
This figure is comparing both the k-space PSTD and leapfrog PSTD schemes with the exact solution. The error is computed by comparing the time traces recorded at a particular grid point in space using Eq. (13). An example of the time traces is shown in Fig. 3(a). The numerical dispersion introduced by the leapfrog time scheme introduces a distortion of the wave compared to the analytical solution, which is reflected in the error plot.
I hope that helps,
Brad.
Hi Bradley,
Thank you for your reply.
I want to know, how did you determine the time of each point in the analytical solution?
Did you perform any interpolation or did you use the following sentence:
t = 0: dt: (number_points_period)*dt;
Hi bmezhou,
We simply extracted the data from both the analytical solution and the k-Wave simulation for the same time points. There's a very similar example of how we did this in the toolbox under Numerical Analysis -> Modelling Nonlinear Wave Propagation.
Brad.
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