http://www.k-wave.org/forum/topic/smooth-is-required-for-strong-heterogeneity Support for the k-Wave MATLAB toolbox en-US Tue, 12 May 2026 23:33:31 +0000 http://bbpress.org/?v=1.0.2 q http://www.k-wave.org/forum/search.php http://www.k-wave.org/forum/topic/smooth-is-required-for-strong-heterogeneity#post-685 Tue, 14 Aug 2012 22:34:56 +0000 bencox 685@http://www.k-wave.org/forum/ <p>Hi Huangchao, </p> <p>k-Wave uses a spectral method for calculating the gradients of the field, so is based on a representation of the field as a finite sum of Fourier components, which works well when everything is nice and smooth (and the Fourier coefficients decay rapidly) but is less good when there are sharp gradients as Gibbs-type errors are introduced. Essentially, the finite number of Fourier components is unable to describe the sharp step accurately. See Section VB in our latest paper "Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method" for more explanation. (See the <a href="http://www.k-wave.org/publications.php">publications</a> page).</p> <p>Kind regards,</p> <p>Ben </p> http://www.k-wave.org/forum/topic/smooth-is-required-for-strong-heterogeneity#post-681 Sun, 12 Aug 2012 05:03:08 +0000 huangchao 681@http://www.k-wave.org/forum/ <p>I did the following simulation:</p> <p>Nx=64;<br /> Ny=64;<br /> Nz=64;<br /> dx=1e-3;<br /> dy=1e-3;<br /> dz=1e-3;<br /> kgrid=makeGrid(Nx,dx,Ny,dy,Nx,dz);</p> <p>medium.sound_speed=1500*ones(Nx,Ny,Nz); % sound speed in water<br /> medium.density=1000*ones(Nx,Ny,Nz); % water density<br /> medium.sound_speed(:,:,50:64)=343; % sound speed in air<br /> medium.density(:,:,50:64)=1.2; % air density</p> <p>source.p0=makeBall(Nx,Ny,Nz,32,32,32,10);</p> <p>sensor.mask=[makeCartCircle(15e-3, 100);zeros(1,100)];</p> <p>input_args = {'Smooth', false,'CartInterp', 'nearest', 'DisplayMask','off', 'PMLInside', true, 'PMLSize', 10, 'PlotPML', false, 'PlotSim', false, 'DataCast', 'gsingle'};</p> <p>p=kspaceFirstOrder3D(kgrid,medium,source,sensor,input_args{:});</p> <p>Without smoothing the medium, the simulated pressure 'p' is blowing up, and if I smoothed the medium by setting the 'input_args' as</p> <p>input_args = {'Smooth', [false,true,true],'CartInterp', 'nearest', 'DisplayMask','off', 'PMLInside', true, 'PMLSize', 10, 'PlotPML', false, 'PlotSim', false, 'DataCast', 'gsingle'};</p> <p>Then 'p' looks reasonable. So I am wondering if this means that the medium needs to be smoothed if the variation of sound speed/density is very large. </p>