Spectral Derivative in 3d using NumPy and the RFFT

The Fast Fourier Transform works in arbitrary dimensions. Hence, we can also use it to derive n-dimensional fields spectrally. In this video, we clarify the details of this procedure, including how to adapt the np.meshgrid indexing style. Here is the code: github.com/Ceyron/machine-lea...
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Timestamps:
00:00 Intro
00:53 Defining domain and grid creation
03:40 Define function and analytical derivatives
06:29 Visualization and Discussion
11:10 Wavenumber grid creation
14:10 Taking the spectral derivative
16:57 Qualitative comparison of analytical and spectral derivative
17:28 Quantitative comparison
18:21 Outro

[@EveryThing-up4tm]

Yet another outstanding video. Would you be working on a solver for the compressible Navier-Stokes equations? Would really love to see the compressible and incompressible flow comparision.

[@MachineLearningSimulation]

Thanks a lot 😊
That would indeed be a nice comparison. Currently, I have a video on a pseudo-spectral incompressible NS solver in the pipeline. Unfortunately, I do not have much experience with compressible NS. Probably, a pseudo-spectral treatment might no longer be possible due to potential discontinuities. Do you have a good resource on simple compressible solvers?

[@EveryThing-up4tm]

@@MachineLearningSimulation I don't know any particular literature. But maybe you can consider Sod's shock tube problem which is in book by E. F. Toro and C. Laney.

[@alonsorodriguez5613]

That was a remarkable video. Please do more videos with 3D surfaces in Plotly.

[@MachineLearningSimulation]

Thanks a lot :). I love these vizs with plotly too. In 3d, matplotlib is very limited. The problem with 3d, as I also noticed in the video, is that it's additionally hard to read and interpret. It's still helpful, though, I will definitely also have it in future videos ;).

[@alonsorodriguez5613]

@@MachineLearningSimulation Thank you very much!!!!!!

[@dukeofdoom2]

Great videos.Please do some pygame VFX videos. Something like the bomb explosion or liquid lava they have in Spelunky 2.

[@MachineLearningSimulation]

Thanks :).
Unfortunately, I am not familiar with pygame. :/

[@lennarddegraaf9232]

Do you have to multiple by N ^ (number of dimensions) when your domain is not non-dimensional?

[@lennarddegraaf9232]

I mean when doing the spectral differentiation

[@MachineLearningSimulation]

Hi, thanks for the comment. :)
At which point in the process of taking the spectral derivatives do you think we have to multiply by N^d? Can you give a time stamp. What do you mean by non non-dimensional (having an extent per dimension different than one?)