Mathematics, Parallel Computing and Reservoir Simulation

This paper will highlight, by way of examples, a few seemingly very diierent mathematical problems and show how they have direct relevance to the construction of eecient computational procedures for the simulation of oil reservoirs on parallel computers. 1 Partitioning of graphs Consider a graph G(V; E), having a set of vertices connected by edges. We associate work with each vertex and communication (or dependencies) with each edge. Our problem is to partition the graph into two parts such that the two sets are similar in size. We further want the dependencies (i.e., the number of edges) between the two sets to be as small as possible.