Automatic domain decomposition for a black-box PDE solver

We want to develop a tool to distribute in a black-box environment automatically a given arbitrary 2-D or 3-D mesh equally among a given number of processors. First we sort the nodes by their x-coordinate locally on each processor, afterwards globally by a sophisticated algorithm where we make use of the message passing paradigm. This results in a one-dimensional domain decomposition that may also run over dividing lines. The elements are sent around in a ring shift afterwards, where each processor takes the necessary element information out of the current basket in each tact. To be able to set up the linear system of equations resulting from the discretization purely local without communication, we also create an overlap, i.e. we also store on each processor the necessary node and element information of neighbouring processors. The re-sorting of refined meshes serves the purpose of load balancing, and for the resulting matrix it also serves as bandwidth optimizer.