  In the wake of the intense effort made for the experimental CILEX project,
numerical simulation cam- paigns have been carried out in order to finalize the
design of the facility and to identify optimal laser and plasma parameters.
These simulations bring, of course, important insight into the fundamental
physics at play. As a by-product, they also characterize the quality of our
theoretical and numerical models. In this paper, we compare the results given
by different codes and point out algorithmic lim- itations both in terms of
physical accuracy and computational performances. These limitations are illu-
strated in the context of electron laser wakefield acceleration (LWFA). The
main limitation we identify in state-of-the-art Particle-In-Cell (PIC) codes is
computational load imbalance. We propose an innovative algorithm to deal with
this specific issue as well as milestones towards a modern, accurate high-per-
formance PIC code for high energy particle acceleration.
