Spectral interpolation bugfix

[KunkelAlexander]

XY interpolation and fix bug in spectral interpolation

XY Interpolation

• After careful experimentation, I decided that interpolating x = dens * cos(S/N) and y = dens * sin(S/N) is not a good idea since these fields are less well-behaved than the real and imaginary part of the wave function around the vortex
• I propose to interpolate the density and phase by default and switch back to the real and imaginary part around the vortex
• The switching is controlled by the repurposed runtime parameter SPEC_INT_VORTEX_THRESHOLD: If the laplacian of the phase field exceed this threshold, we interpolate the real and imaginary part

Runtime parameter

• In addition, the ghost boundary size of the spectral refinement algorithm is now a runtime parameter SPEC_INT_GHOST_BOUNDARY. A large ghost boundary increases interpolation accuracy but can negatively affect performance.

Bug

• The pull request also fixes a bug of the spectral interpolation routine: A simple bug with wrong variable assignment .

[KunkelAlexander]

@hyschive One thing that I still need to check is how to handle monotonicity: I know that monotonic interpolation introduces spurious oscillations for FDM which is why I never thought about how to properly enforce it in the spectral interpolation code. When interpolation density & phase, I manually check for negative densities and set them to 0. When interpolating RE/IM and if CONSERVE_MASS is on, DENS is interpolated separately and RE/IM are rescaled. But in this case, the spectral interpolation can introduce negative densities which cause the simulation to fail. I guess it would be possible to just carry order the monotonicity check from the quartic interpolation code and enable it when interpolating RE/IM and other fields that cannot become negative (like the density for the Poisson solver). What do you think?

[hyschive]

@KunkelAlexander Sorry for missing your message above. I agree with your suggestion. Do you prefer to apply the monotonic constraint everywhere or only for cells with negative values?

[KunkelAlexander]

@hyschive I am sorry for missing your message. Personally, I would prefer only applying the constraint to cells with negative values. Do you think that is okay?

[hyschive]

@hyschive I am sorry for missing your message. Personally, I would prefer only applying the constraint to cells with negative values. Do you think that is okay?

@KunkelAlexander Agree