A Fast Multilevel Implementation of Recursive Spectral Bisection for Partitioning Unstructured Problems

Unstructured meshes are used in many large-scale scientiic and engineering problems, including nite-volume methods for computational uid dynamics and nite-element methods for structural analysis. If unstructured problems such as these are to be solved on distributed-memory parallel computers, their data structures must be partitioned and distributed across processors; if they are to be solved eeciently, the partitioning must maximize load balance and minimize interprocessor communication. Recently the recursive spectral bisec-tion method (RSB) has been shown to be very eeective for such partitioning problems compared to alternative methods. Unfortunately, RSB in its simplest form is rather expensive. In this report we shall describe a multilevel implementation of RSB that can attain about an order-of-magnitude improvement in run time on typical examples.