A new approach for the computation of short range wake fields for ultra relativistic bunches in linear accelerators is presented. The method is based on the direct numerical solution of Maxwell equations for arbitrary 3D-geometry using a specialized split-operator scheme. This approach guarantees exact propagation of longitudinal waves. In addition, it enables the application of a moving computational window. These ideas have been realized in the development of PBCI; a highly efficient, pararallelized wake field code. Detailed simulation results for several accelerator components, including the TESLA 9-cell structure and a rectangular collimator are given. INTRODUCTION The X-FEL and the ILC projects require high quality beams with ultra short electron bunches. In order to predict the energy spread and emittance growth of such bunches, an accurate knowledge of the short range wake fields induced in the different accelerator components is necessary. Due to the geometrical complexity involved, however, the computation of wake fields and potentials for long accelerator structures is generally accessible only to numerical simulations. In the course of the past 20 years, several wake field simulation codes for rotationally symmetric structures have been developed and used with considerable success in the design of linear accelerators [1,2]. The use of a ‘moving window’ in the simulation of ultra relativistic bunches (Bane, Weiland [3]) and the indirect path wake potential integration (Napoly et al [4]) represent, thereby two important milestones in this development. It is however surprising to note that only very recently, the issue of generalizing these two approaches for simulations in 3D-geometry was addressed. In [5] a general procedure for the indirect integration of wake fields in 3D-structures with incoming and outgoing beam pipes is given. In [6] a semi-implicit 3D-discretization technique for Maxwell equations with no dispersion in the longitudinal direction is proposed. The latter is prerequisite for a moving window implementation since in this case, the numerical phase velocity of longitudinal waves must exactly match the speed of light in vacuum. In this work, we present simulation results obtained with the newly developed code Parallel Beam Cavity Interaction (PBCI) which is designed for massively parallel wake field simulations in arbitrary 3D-geometry. The algorithms used include a purely explicit and (quasi) dispersionless split-operator scheme as well as a domain decomposition approach for highly balanced parallel computations. A brief description of these algorithms is given in the following section. The rest of the paper is dedicated to the numerical results obtained for some relevant accelerator components in the context of the XFEL and ILC projects. NUMERICAL METHOD The general framework used in this paper for the simulation of bunch induced electromagnetic wakes is the Finite Integration Technique (FIT) [7]. The time-discrete update equation of FIT can be written compactly as