http://www.k-wave.org/forum/topic/result-verification-against-green-function Support for the k-Wave MATLAB toolbox en-US Wed, 13 May 2026 00:56:07 +0000 http://bbpress.org/?v=1.0.2 q http://www.k-wave.org/forum/search.php http://www.k-wave.org/forum/topic/result-verification-against-green-function#post-7952 Thu, 26 Nov 2020 13:57:53 +0000 Bradley Treeby 7952@http://www.k-wave.org/forum/ <p>Are you referring to Eqs. (17) and (18) in <a href="http://bug.medphys.ucl.ac.uk/papers/2010-Treeby-JASA.pdf">this paper</a>? This can be derived by splitting the wavenumber into real and imaginary parts similar to the derivation that follows in the same section of the paper. See also <a href="https://doi.org/10.1121/1.2977669">this paper</a>.</p> <p>Brad </p> http://www.k-wave.org/forum/topic/result-verification-against-green-function#post-7932 Tue, 24 Nov 2020 07:10:36 +0000 Anujkaushik 7932@http://www.k-wave.org/forum/ <p>Dear Professor,<br /> My question is how you converted the Eq.</p> <p>K(w) = w/c_0 - (alpha_0)x(-i)^(y+1)x(w)^y / cos(yxpi/2)</p> <p>to </p> <p>K(w) = w/c_0 + (alpha_0)xtan(yxpi/2)x(w)^y.</p> <p>Please clarify the mathematics between these two. </p> http://www.k-wave.org/forum/topic/result-verification-against-green-function#post-7929 Sat, 21 Nov 2020 23:16:12 +0000 aelbekkali 7929@http://www.k-wave.org/forum/ <p>Hi all</p> <p>I am looking for a formula for green function adapted to 3D model.<br /> I am with this k-wave 3D example<br /> <a href="http://www.k-wave.org/documentation/example_us_bmode_linear_transducer.php" rel="nofollow">http://www.k-wave.org/documentation/example_us_bmode_linear_transducer.php</a><br /> I need to compute the background green function of the medium<br /> any help? thanks you </p> http://www.k-wave.org/forum/topic/result-verification-against-green-function#post-4563 Sun, 08 Jun 2014 05:48:53 +0000 cleskiw 4563@http://www.k-wave.org/forum/ <p>by gain I mean the amplitude and phase difference in a sinusoid, when comparing the source sinusoid, and the sinusoid measured at some distance x away from the source. </p> http://www.k-wave.org/forum/topic/result-verification-against-green-function#post-4562 Sun, 08 Jun 2014 05:46:51 +0000 cleskiw 4562@http://www.k-wave.org/forum/ <p>Sorry I just saw this. For some reason I have to divide the K-Wave result by 2.6 to match the Greens function result.</p> <p>I plot the complex gain as a function of distance away from the source for both the K-Wave results and the Green Function result. The profiles look the same (ie a graph of gain vs distance x away from source), but are not identical unless I divide the K-Wave result by 2.6. </p> http://www.k-wave.org/forum/topic/result-verification-against-green-function#post-4557 Fri, 30 May 2014 11:22:27 +0000 bencox 4557@http://www.k-wave.org/forum/ <p>Hi Chris,</p> <p>When you say the gain is somewhat different, what do you mean?</p> <p>Ben </p> http://www.k-wave.org/forum/topic/result-verification-against-green-function#post-4556 Thu, 29 May 2014 20:50:14 +0000 cleskiw 4556@http://www.k-wave.org/forum/ <p>Yes that helped. Now the desired source waveform is what I measure with a sensor at the source location. The results also seem consistent with the Green Function result. The gain is somewhat different but is consistent across different values of x away from the source so that the envelope matches the Green Function envelope - just at a seemingly constant offset. </p> http://www.k-wave.org/forum/topic/result-verification-against-green-function#post-4555 Thu, 29 May 2014 00:49:04 +0000 bencox 4555@http://www.k-wave.org/forum/ <p>Hi Chris, </p> <p>Have you tried setting <code>source.p_mode = &#39;dirichlet&#39;;</code>? The default setting (<code>&#39;additive&#39;</code>) adds each successive sample from <code>source.p</code> to whatever amplitude is already at the source position, so the resulting wave amplitude differs from the amplitude defined in <code>source.p</code> and depends on the CFL number. However, using the setting <code>&#39;dirichlet&#39;</code> replaces the amplitude at the source position with the value in <code>source.p</code>, ie. forces it to be the value in <code>source.p</code>.</p> <p>Does that help?</p> <p>Ben </p> http://www.k-wave.org/forum/topic/result-verification-against-green-function#post-4552 Tue, 27 May 2014 23:09:51 +0000 cleskiw 4552@http://www.k-wave.org/forum/ <p>In a single source, single sensor, 2D homogeneous scenario should I not expect to be able to verify the k-Wave simulation result against the homogeneous acoustic 2D solution? I am specifically referring to the solution typically given by the 2D Green Function: G(x,x')=i/4*H_{0}^{1}(2*pi*f/c*|x-x'|), where H_{0}^{1} is the Hankel function.</p> <p>I've been trying to use a simple sinusoidal point source, with two sensor locations, one at the source and one at some x distance away. The sine wave I measure should be able to be predicted by applying the gain and phase shift given by the above equation, but I notice that even if I adjust the grid spacing, I do not get consistent results.</p> <p>I notice:<br /> 1) the source and sensor at the source give different values, and altering the grid resolution (making it finer) reduces the amplitude recorded by the sensor at the source by orders of magnitude while trying to converge on a consistent record (i.e. when verifying grid is fine enough)<br /> 2) If I tweak what I can to get the same result as the Green Function, they do not match if I change the distance of the target sensor.</p> <p>Nx = 128*8; % number of grid points in the x (row) direction<br /> Ny = 64; % number of grid points in the y (column) direction<br /> dx = 50e-3/Nx; % grid point spacing in the x direction [m]<br /> dy = dx; % grid point spacing in the y direction [m]<br /> kgrid = makeGrid(Nx, dx, Ny, dy);<br /> medium.sound_speed = 1500; % [m/s]<br /> [kgrid.t_array, dt] = makeTime(kgrid, medium.sound_speed);<br /> source.p_mask = zeros(Nx, Ny);<br /> source.p_mask(end - Nx/4, Ny/2) = 1;<br /> source_freq = 0.25e6; % [Hz]<br /> source_mag = 1; % [Pa]<br /> source.p = source_mag*cos(2*pi*source_freq*kgrid.t_array);<br /> source.p = filterTimeSeries(kgrid, medium, source.p);<br /> sensor.mask = zeros(Nx, Ny);<br /> sensor.mask(Nx/2, Ny/2) = 1;<br /> sensor.mask(end-Nx/4, Ny/2) = 1;<br /> sensor.record = {'p', 'p_final'};<br /> sensor_data = kspaceFirstOrder2D(kgrid, medium, source, sensor, 'PlotLayout', true);</p> <p>Do you have any issues with my approach, or notice any obvious errors?</p> <p>thanks,<br /> -Chris </p>