In this paper, we develop a parallel Fast Multipole Method (FMM) based solution for computing the scattered electromagnetic fields from a Perfect Electrically Conducting (PEC) surface. The main contributions of this work are the development of parallel algorithms with the following characteristics: 1) provably efficient worst-case run-time irrespective of the shape of the scatterer, 2) communication-efficiency, and 3) guaranteed load balancing within a small constant factor. We have developed a scalable, parallel code and validated it against surfaces for which solution can be computed analytically, and against serial software. The efficiency and scalability of the code is demonstrated with experimental results on an IBM xSeries cluster. Though developed in the context of this particular application, our algorithms can be used in other applications involving parallel FMM.

We present faster sequential and parallel algorithms for computing the solvent accessible surface area (ASA) of protein molecules. The ASA is computed by finding the exposed surface areas of the spheres obtained by increasing the van der Waals radii of the atoms with the van der Waals radius of the solvent. Using domain specific knowledge, we show that the number of sphere intersections is only O(n), where n is the number of atoms in the protein molecule. For computing sphere intersections, we present hash-based algorithms that run in O(n) expected sequential time and O(n/p) expected parallel time and sort-based algorithms that run in worst-case O(n log n) sequential time and O(n log n/p) parallel time. These are significant improvements over previously known algorithms which take O(n/sup 2/) time sequentially and O(n/sup 2//p) time in parallel. We present a Monte Carlo algorithm for computing the solvent accessible surface area. The basic idea is to generate points uniformly at random on the surface of spheres obtained by increasing the van der Waals radii of the atoms with the van der Waals radius of the solvent molecule and to test the points for accessibility. We also provide error bounds as a function of the sample size. Experimental verification of the algorithms is carried out using an IBM SP-2.