Solving large scale electromagnetic problems using a Linux cluster and parallel MLFMA

The second half of the 1990s has witnessed the development of two important concepts in computational sciences. First, the fast multipole method (FMM) and its multilevel variants (MLFMA) have evolved into a powerful technique allowing researchers to solve large scale problems in electromagnetics. The other is in the area of commodity parallel computing. The development of fast but inexpensive microprocessors, the evolution of Linux as a reliable and efficient operating system, and message passing standards (MPI) have prompted various researchers to construct inexpensive high performance parallel computers from commodity components. By combining the two technologies, that of the MLFMA and the commodity parallel computers, one can solve large scale electromagnetic simulations fairly inexpensively. However, in order to exploit the computing power offered by a cluster of personal computers, efficient parallel implementations of MLFMA using the message passing paradigm have to be developed. We have previously developed a portable, parallel library, called ScaleME, for MLFMA for electrodynamic and acoustic integral equation solvers (Velamparambil et al., 1998). This library uses MPI for communication and has been tested successfully on a variety of parallel computers. As an attempt to solve large scale electromagnetic scattering problems on parallel computers made from commodity components using ScaleME, we previously constructed a Linux network, called the Orion cluster, from commodity components. In this paper, we demonstrate the combined power of ScaleME and Orion through a set of test problems.