We describe a static load balancing algorithm based on Kohonen Self-Organizing Maps (SOM) for a class of parallel computations where the communication pattern exhibits spatial locality and we present initial results. The topology preserving mapping achieved by SOM reduces the communication load across processors, however, it does not take load balancing into consideration. We introduce a load balancing mechanism into the SOM algorithm. We also present a preliminary multilevel implementation which resulted in significant execution time improvements. The results are promising to further improve SOM based load balancing for geometric graphs.