Daniel S. Katz

Jet Propulsion Laboratory

California Institute of Technology

4800 Oak Grove Drive, MS 168-522

Pasadena, CA 91109

d.katz@ieee.org

This paper discusses the use of low-cost parallel computers, specifically the Beowulf system which was built at Caltech, to solve problems in computational electromagnetics. The focus of this paper is on application of the Finite-Difference Time-Domain (FDTD) method. Some discussion of applying the Finite-Element (FE) method to this type of machine is also provided.

The Beowulf systems is composed of 16 200 MHz Pentium Pro-based personal computers connected with a fast 16-way crossbar switch. The hardware parts used to build the system are all commodity components, costing less that $60,000 for the entire system, and all the software used (compilers, operating system, etc...) is freeware. The highest sustained application speed measured on this system is 1.2 GFlops.

As the FDTD method can be parallelized through a simple domain decomposition, the initial set-up is quite simple. However, data communication is required from one processor, with a given computational domain A, to all the processors whose computational domains share a boundary with A at each time step. The data that must be communicated is equivalent to the field components at the shared boundary with A.

The FE method is more complicated, as the distribution of the initial mesh cannot simply be based on a partitioning of physical space. Once this problem has been solved, and the mesh or matrix is distributed, the solution of the matrix can be performed using standard parallel numerical libraries.

- Performance, including comparison with other parallel and sequential computers;
- An estimate of scaling to larger systems, since the Beowulf system is only 16 processors at this time; and
- User experiences with this class machine (non-commercial, not vendor-supported);