I saw many examples of application of FFT for computation of convolutions and solving PDEs ( like Poisson equation ). It is very strightforward and efficient if I work with rectangular (orthogonal) lattice.However, I don't see how exatly modify the transformation if the lattice is sampled along non-orthogonal lattice vectors eg. like this lattice:I guess, I can still use common algorithms or libraries ( like FFTW) because they care just about the n-dimensional array of numbers (they are agnostic to position of sampling points in real space ) ... but after that I have to transfrom the results by the lattice vectors somehow (or it's reciprocal vectors)( ? am I right? ).Especially I'm interested in three application:solving posisson equation covolution of two functions gradient ofthe function.
FFT on non-orthogonal lattice ( for computing convolutions and solving PDEs )
fourier transform