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I need to perform the Helmholtz decomposition of a 2D flow. An old and obvious problem is the numerical differentiation (largely amplifying the noise).

I do understand the procedure I am just looking for useful tips and tricks or a literature reference -- surely I am not the first one to perform the task.

I am aware that there was a matlab package where the decomposition was implemented. But it worked only for square input matrices.

Do you know any algorithm other than straightforward discretization of integrals and derivatives?

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