Hi Brad,
Would it be possible to set a heterogeneous alpha_power coefficient?
I guess it is impossible (otherwise, you would have allowed it) but, out of curiosity, could you explain the fundamental reason?
By the way, do you have a workaround for this when you deal with several different materials? Currently, I just split my simulation domain and run several simulations, one for each material...
Best regards,
Anthony
Hi Anthony,
The power law absorption in k-Wave is implemented using a fractional Laplacian operator. This can be evaluated efficiently in the spatial frequency domain using the FFT (e.g., see this paper). However, because the operator is applied in the frequency domain, the power law exponent cannot depend on spatial position.
If you are using CW sources and linear wave propagation, one way would be to choose a fixed value of alpha_power, and then tweak alpha_coeff to give the correct attenuation in dB/cm at the frequency of interest. Unfortunately, there is no work around in the more general case, which is one of the limitations of the approach.
Brad.
Hi Brad,
Thanks a lot for your answer. It arouse my curiosity so I quickly checked the state of the art on the subject and it seems there is currently no numerical method to solve this in the Fourier domain (I only fond some preliminary work about a finite difference method http://www.sciencedirect.com/science/article/pii/S0096300309001751).
Well, it seems I will continue to split my simulation domains for a while ;-)
Best regards :-)
Anthony
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