For the simulated fieldmap case, the block of code that supposedly runs the non-preconditioned case here:
https://github.com/ClaireYLin/regularized-field-map-estimation/blob/070c803e922a8b424c80d615828b827aebc38669/examples/example_simu_fieldmap.m#L109
is actually deferring to the default precon which is 'ichol' here:
https://github.com/ClaireYLin/regularized-field-map-estimation/blob/070c803e922a8b424c80d615828b827aebc38669/functions/fmap_est_pcg_ls.m#L54

I will fix this.