Automated Parallel Solution of Unstructerd PDE problems. Guy Blelloch, Anja Feldmann, Omar Ghattas, John Gilbert, Gary Miller, David O'Hallaron, Eric Schwabe, Jonathan Shewchuk, Shang-Hua Teng; Communication of the ACM, to appear.
Abstract
This article describes Archimedes, an automated system for solving partial differential equations over complex domains using distributed memory supercomputers. Archimedes is intended to allow researchers in engineering and science to solve physical problems on irregularly shaped objects or regions.
The tasks of such a system are manifold. First, Archimedes discretizes the domain being modelled by generating an unstructured mesh which fills the region. Then, the domain is partitioned into separate subdomains, which are placed onto individual processors. Communication is routed between these processors. Code is generated to solve a PDE in parallel.
The geometric properties of the mesh can be exploited to find provably good partitions with good load balance and a relatively small amount of communication between subdomains. Machine-dependent heuristics for placement and routing are developed for iWarp and the Connection Machine CM-5. A parallel finite element algorithm can be written using simple primitives which hide each machine's underlying communication mechanisms. We consider how to optimize finite element algorithms using standard program transformations. We give sample performance figures on iWarp.

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