Mapping large-scale FEM-graphs to highly parallel computers with grid-like topology by self-organization

We consider the problem of mapping large scale FEM graphs for the solution of partial differential equations to highly parallel distributed memory computers. Typically, these programs show a low-dimensional grid-like communication structure. We argue that conventional domain decomposition methods that are usually employed today are not well suited for future highly parallel computers as they do not take into account the interconnection structure of the parallel computer resulting in a large communication overhead. Therefore we propose a new mapping heuristic which performs both, partitioning of the solution domain and processor allocation in one integrated step. Our procedure is based on the ability of Kohonen neural networks to exploit topological similarities of an input space and a grid-like structured network to compute a neighborhood preserving mapping between the set of discretization points and the parallel computer. We report about results of mapping up to 44,000-node FEM graphs to a 4096-processor parallel computer and demonstrate the capability of the proposed scheme for dynamic remapping considering adaptive refinement of the discretization graph