A Graph Model for Minimizing the Storage Overhead of Distributing Data for the Parallel Solution of Two-Phase Flows

We consider a finite element method for the parallel solution of two-phase flow problems using a level set approach. Here, two systems of equations result from the discretization of the governing partial differential equations. Rather than investigating the solution of these systems, we focus on finding a data distribution for their assembly. We formulate a new combinatorial problem that minimizes the overhead in storage requirement to represent the systems while, at the same time, balancing the computational effort to assemble these systems in parallel. We model this problem by introducing a weighted undirected graph. We then transform the problem to a (standard) graph partitioning problem in which a weighted sum of certain edges is minimized subject to balancing a weighted sum of all vertices. Numerical experiments are carried out illustrating the feasibility of the new approach for an application using up to 512 processes of a cluster of quad-core processors.