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I have a finite element solver where I am using tetrahedral elements. I am solving for electric potentials and then calculate the current densities in each element, which are constant in each element. Now, assume that I want to calculate Fourier transforms for current density in the $x$ direction ($J_x$). $$F(J_x(x,y,z))(k_x,k_y,k_z)=\sum_e\int_e{J_{x}}_eexp(-i2\pi(k_xx(\xi,\eta,\tau)+k_yy(\xi,\eta,\tau)+k_zz(\xi,\eta,\tau)))d\xi d\eta d\tau$$ Where I utilized the Gaussian quadrature rule to calculate the integral. I am taking Fourier space points to be on a rectangular grid. Therefore, I was expecting the inverse of the transform (I am using inverse FFT) to be a set of slice interpolations of the current density. However, the inverse transform is meaningless. I wanted to ask is there anyone who tried such a method (FT from a FE model) and can you tell me what is wrong overall because clearly, something is. Thanks in advance and have a nice day.

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