I found out that Steven's notes on handling Nyquist frequency for derivatives very useful: http://math.mit.edu/~stevenj/fft-deriv.pdf
Here I have some questions that I would like some insights: How to handle partial_x*partial_y elegantly? Two typical cases: 1) Sometimes by transforming coordinates, a irregular grid works better -- then this partial_x*partial_y term appears. 2) The media is anisotropic. It looks like that there always exists a local transform that will convert the equation to be with pure 2nd order derivative, but not globally in a FD scheme. Thanks!
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