http://www.k-wave.org/forum/topic/how-to-choose-reference-sound-speed Support for the k-Wave MATLAB toolbox en-US Tue, 12 May 2026 23:08:50 +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-choose-reference-sound-speed#post-1104 Fri, 07 Dec 2012 12:52:27 +0000 bencox 1104@http://www.k-wave.org/forum/ <p>Hi Zak,</p> <p>Thanks for this; it's raised an interesting point. If you replace <code>kgrid.k_max</code> by <code>max(kgrid.k)</code> it should work. </p> <p>The reason that these are not the same is because we have defined <code>kgrid.k_max</code> as the maximum wavenumber supported by the grid in every direction, in other words it is defied as <code>kgrid.k_max = min([kgrid.kx_max, kgrid.ky_max])</code>. However, there will be components whose wavenumbers in both directions are maximum, and so the absolute value <code>sqrt(kgrid.kx_max.^2 + kgrid.ky_max.^2)</code> will be bigger than <code>kgrid.k_max</code>.</p> <p>Ben </p> http://www.k-wave.org/forum/topic/how-to-choose-reference-sound-speed#post-1099 Wed, 05 Dec 2012 21:23:56 +0000 zak 1099@http://www.k-wave.org/forum/ <p>Hi Dr. Cox,</p> <p>I tried your suggestion by setting c_ref = c_min and dt &lt; (2/(c_ref * max(k))) * asin(c_ref/max(c)), but the code prompted a warning saying "time step may be too large for a stable simulation" and the simulated results blowed up.</p> <p>Here are my codes:</p> <p>Nx=512;<br /> dx=0.5e-3;<br /> kgrid=makeGrid(Nx,dx,Nx,dx);</p> <p>medium.sound_speed=1500*ones(Nx,Nx);<br /> medium.sound_speed(:,200:300)=3000;<br /> medium.density=1000*ones(Nx,Nx);<br /> medium.density(:,200:300)=2000;<br /> medium.sound_speed_ref=1500;</p> <p>(2/(medium.sound_speed_ref*kgrid.k_max))*asin(medium.sound_speed_ref/max(medium.sound_speed(:)))<br /> ans =<br /> 1.111111111111111e-07</p> <p>kgrid.t_array=(0:2000)*1e-7;</p> <p>source.p0=makeDisc(Nx,Ny,Nx/2,100,10);</p> <p>sensor.mask=zeros(Nx,Nx);<br /> sensor.mask(Nx/2,400)=1;</p> <p>input_args = {'Smooth', true, 'PMLInside', true, 'PMLSize', 10, 'DataCast', 'gpuArray-single', 'DataRecast', true,'PlotPML', false, 'PlotSim', false};</p> <p>p=kspaceFirstOrder2D(kgrid, medium, source, sensor, input_args{:});</p> <p>However, if I used the default dt=5e-8 which is calculated by the criteria dt = CFL * dx_min / c_max, then there's no problem. </p> http://www.k-wave.org/forum/topic/how-to-choose-reference-sound-speed#post-850 Tue, 23 Oct 2012 21:06:18 +0000 bencox 850@http://www.k-wave.org/forum/ <p>Hi Zak,</p> <p>You could neglect the k-space adjustment, but there would be no advantage to doing so (other than no having to make a decision about c_ref!) There would be disadvantages though: there would be no phase error correction at all, and you would have to satisfy a stability requirement which is always going to be more stringent:</p> <p><code>dt &lt; 2/(k_max * c_max)</code></p> <p>Ben </p> http://www.k-wave.org/forum/topic/how-to-choose-reference-sound-speed#post-848 Tue, 23 Oct 2012 14:45:47 +0000 zak 848@http://www.k-wave.org/forum/ <p>Hi Dr. Cox</p> <p>Thanks for your help.</p> <p>From your suggestion, I can set c_ref = c_min, then estimate the upper bound of the time step. As such, the phase errors is not worse than the k-space adjustment being left out. But I wonder if we can just neglect the k-space adjustment when doing simulations in heterogeneous media so there is no c_ref to be determined in the first place.</p> <p>Zak </p> http://www.k-wave.org/forum/topic/how-to-choose-reference-sound-speed#post-843 Tue, 23 Oct 2012 10:34:08 +0000 bencox 843@http://www.k-wave.org/forum/ <p>Hi Zak,</p> <p>Good question. The k-space model is certainly unconditionally stable if you choose c_ref &gt; max(c), in other words the solution won't 'blow up'. Unfortunately the phase errors can become very large, so while the solution will be stable it might also be completely wrong.</p> <p>The alternative is to choose c_ref&lt;min(c) in which case the phase errors are bounded (they will never be worse than if the k-space correction term sinc(ckdt/2) were just left out) but now the model could become unstable and it is necessary for the timesteps to satisfy the stability criterion:</p> <p><code>dt &lt; (2/(c_ref * max(k))) * asin(c_ref/max(c))</code></p> <p>Hope that helps you choose,</p> <p>Ben </p> http://www.k-wave.org/forum/topic/how-to-choose-reference-sound-speed#post-838 Tue, 23 Oct 2012 04:11:22 +0000 zak 838@http://www.k-wave.org/forum/ <p>Hi, Dr. Cox and Dr. Treeby,</p> <p>I am trying to model the photoacoustic wave propagation in heterogeneous media, where the heterogeneity is only a small part but very strong (in terms of both sound speed and mass density) compared to rest of the media, e.g. bone or skull in soft tissue.</p> <p>In heterogeneous media, <a href="http://link.aip.org/link/jasman/v111/i1/p53/s1/html">this paper</a> says that the k-space method is expected to be unconditionally stable if the reference sound speed c_ref in the k-space operator is chosen to be the maximum sound speed in the media (c_max), and this is also the default choice of the k-Wave.</p> <p>However, in your recent paper of nonlinear wave propagation, it says the phase errors will be introduced in the simulation if the c_ref doesn't match the local sound speed. The k-space operator will over compensate for the actual phase error introduced by the finite difference time step if c_ref is much larger than the local sound speed.</p> <p>So I am not sure how to choose the proper c_ref in my case. On one hand, it seems I should choose c_max as c_ref given what the first paper says; on the other hand, this choice is problematic according to your paper since the sound speed in most part of the media (c_0) is much smaller than c_max; it indicates that I should set c_ref = c_0.</p> <p>Should I choose c_ref be to c_max or c_0? Or is there any other choice?</p> <p>Thank you very much! </p>