  We present a novel solver for an analogue to Poisson's equation in the
framework of modified Newtonian dynamics (MOND). This equation is highly
non-linear and hence standard codes based upon tree structures and/or FFT's in
general are not applicable; one needs to defer to multi-grid relaxation
techniques. After a detailed description of the necessary modifications to the
cosmological N-body code AMIGA (formerly known as MLAPM) we utilize the new
code to revisit the issue of cosmic structure formation under MOND. We find
that the proper (numerical) integration of a MONDian Poisson's equation has
some noticable effects on the final results when compared against simulations
of the same kind but based upon rather ad-hoc assumptions about the properties
of the MONDian force field. Namely, we find that the large-scale structure
evolution is faster in our revised MOND model leading to an even stronger
clustering of galaxies, especially when compared to the standard LCDM paradigm.
