Homogeneous points in FieldConvert
FieldConvert uses nplanes points with PolyEvenlySpaced distribution for homogeneous expansion.
However, fftw implicitly assumes that the points distribution is FourierEvenlySpaced. Therefore, when using fftw the output is the solution at the Fourier points stretched to the polynomial points, which is clearly incorrect.
MVM seems to be working properly, although I would expect performing some operations (specially the HomogeneousFwdTrans used in PhysDeriv) using the polynomial points to cause problems (at least a loss of accuracy).
A quick fix for this could be switching to Fourier points (but the domain would get shorter) or disabling fftw in FieldConvert (at least until we have a better solution).