We present a model that comprehensively addresses the goals of partitioning an application software mesh into clusters of modules and assigning (or mapping) the clusters onto the most appropriate processors in the computational grid. Our approach to solving this challenging combinatorial problem is based on a computational model known as a cascaded Boltzmann machine, which advantageously blends the principles of neural computing and simulated annealing to achieve high quality partitions in a practical amount of execution time. We develop implementations of the algorithms, and focus on the study and refinement of the operational parameters that determine the performance of the Boltzmann algorithms. Through computational experimentation and empirical observations, we are able to characterize the speed and effectiveness of this partitioning and mapping process. We also note that the partitioning and mapping algorithm itself can be implemented as a parallel computation.