Knowledge of the local groundwave-propagation characteristics is essential in wireless systems. Although Maxwell's equations establish the theoretical background, only a limited number of highly idealized groundwave-propagation problems have mathematically exact and/or approximate solutions. Therefore, semi-analytical/numerical and pure numerical simulation methods are almost the only way to handle realistic groundwave-propagation problems. To a certain extent, numerical simulators should be capable of taking non-flat, penetrable terrain and inhomogeneous atmospheric effects into account. Unfortunately, a generally applicable simulator has not yet appeared; there are many methods that have been developed under different assumptions and approximations, valid in different parameter regimes. It is therefore a challenge to apply these methods to the same physical problems, to do comparisons, and to evaluate numerical results. With all these factors in mind, a new MATLAB-based package GrMoMPE is introduced. It is first validated and calibrated, and then applied to some characteristic groundwave-propagation problems. The introduction of GrMoMPE has made it possible to do direct and accurate comparisons and reliable physical interpretations.