The computer based simulation of electromagnetic waves is used in many industrial areas like the development of antennas, e.g. Often, such simulations are very time consuming. In this thesis, new possibilities will be presented how one of the most frequently used method - the Finite Difference Time Domain method (FDTD) - can be accelerated with the help of wavelets. Increasing the accuracy of an FDTD simulation usually requires a higher spatial resolution. This causes an increase of the amount of data and hence an increase of the simulation time. In this thesis, methods are presented, developed, and investigated, how a wavelet-transform based data compression can reduce the amount of data and therefore the simluation time. The basic part of the thesis is a computer aided concatenation of simulation and transformation operators. On the one hand, this allows for an adaptive compression of fields by means of neglecting coefficients. On the other hand, the creation of an analytic subgrid method for the FDTD is demonstrated.