http://www.k-wave.org/forum/topic/how-to-determine-the-least-squares-error-of-the-numerical-result Support for the k-Wave MATLAB toolbox en-US Wed, 13 May 2026 03:13:40 +0000 http://bbpress.org/?v=1.0.2 q http://www.k-wave.org/forum/search.php http://www.k-wave.org/forum/topic/how-to-determine-the-least-squares-error-of-the-numerical-result#post-3947 Tue, 08 Oct 2013 16:01:02 +0000 Bradley Treeby 3947@http://www.k-wave.org/forum/ <p>Hi bmezhou,</p> <p>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 -&gt; Modelling Nonlinear Wave Propagation.</p> <p>Brad. </p> http://www.k-wave.org/forum/topic/how-to-determine-the-least-squares-error-of-the-numerical-result#post-3946 Tue, 08 Oct 2013 02:16:12 +0000 bmezhou 3946@http://www.k-wave.org/forum/ <p>Hi Bradley,</p> <p>Thank you for your reply.</p> <p>I want to know, how did you determine the time of each point in the analytical solution?</p> <p>Did you perform any interpolation or did you use the following sentence:</p> <p> <code>t = 0: dt: (number_points_period)*dt;</code> </p> http://www.k-wave.org/forum/topic/how-to-determine-the-least-squares-error-of-the-numerical-result#post-3944 Mon, 07 Oct 2013 09:09:31 +0000 Bradley Treeby 3944@http://www.k-wave.org/forum/ <p>Hi bmezhou,</p> <p>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.</p> <p>I hope that helps,</p> <p>Brad. </p> http://www.k-wave.org/forum/topic/how-to-determine-the-least-squares-error-of-the-numerical-result#post-3941 Sun, 06 Oct 2013 15:21:32 +0000 bmezhou 3941@http://www.k-wave.org/forum/ <p>In Treeby et al. (2012), the numerical results are compared with the analytical solution in Fig. 3(c).</p> <p>However, the time axis of these two data may not accord with each other due to dispersion. </p> <p>Thus, can anyone tell me how to calculate <code>the least squares error</code>? </p>