When developing numerical methods, or applying them to the simulation and design of engineering components, it inevitably becomes necessary to examine the scaling of the method with a problem's electrical size. The scaling results from the original mathematical development; for example, a dense system of equations in the solution of integral equations, as well as the specific numerical implementation. Scaling of the numerical implementation depends upon many factors; for example, direct or iterative methods for solution of the linear system, as well as the computer architecture used in the simulation. Scalability is divided into two components-scalability of the numerical algorithm specifically on parallel computer systems and algorithm or sequential scalability. The sequential implementation and scaling is initially presented, with the parallel implementation following. This progression is meant to illustrate the differences in using current parallel platforms and sequential machines and the resulting savings. Time to solution (wall-clock time) for differing problem sizes are the key parameters plotted or tabulated. Sequential and parallel scalability of time harmonic surface integral equation forms and the finite-element solution to the partial differential equations are considered in detail.

Integral equation methods are widely used in the analysis and the design of electromagnetic systems. Traditionally, the limiting parts of the simulation have been the memory required for storing the dense matrix and the computational time required for solving the matrix equation. We report on the extension of integral equation solutions to new wavelength regimes and on completion of the solution in an amount of time that is practical for engineering applications. The numerical solution of the integral equation is computed on scalable, distributed-memory parallel computers. Essential to the numerical solution was the development of a complex-valued, highly optimized, dense-matrix equation solution algorithm for scalable machines. A portion of the research outlined is the development of this production-level library routine for the solution of linear equations on parallel computers. A convenient interface, useful for integral equation solutions, among others, was specifically developed in this study. This algorithm has the conveniences offered by the sequential libraries, can be easily ported between parallel platforms, and has been placed in the public domain.

The large distributed memory capacities of hypercube computers are exploited by a finite element application which computes the scattered electromagetic field from heterogeneous objects with size large compared to a wavelength. Such problems scale well with hypercube dimension fo r large objects: by using the Recursive Inertial Partitioning algorithm and an iterative solver, the work done by each processor is nearly equal and communication overhead for the system set-up and solution is low. The application has been integrated into a user-friendly eirvironment on a graphics workstation in a local area network including hypercube host machines. Users need never know their solutions are obtained via a parallel computer. Scaling is shown by computing solutions for a series of models which double the number of variables for each increment of hypercube dimension. Timings are compared for the JPLICaltech Mark IIIfp Hypercube and the Intel iPSCI860 hypercube. Acceptable quality of solutions is obtained for object domains of hundreds of square wavelengths and resulting sparse matrix systems with order of 100,000 complex unknowns.

Capabilities of hypercube and parallel processing demonstrated. Report describes use of Mark III Hypercube computer to analyze scattering of electromagnetic waves. Purpose of study to assess utility of parallel computing in such computation-intensive problems as large-scale electromagnetic scattering. Two electromagnetic codes based on different algorithms converted to run on Mark III Hypercube. First code implements finite-difference, time-domain solution of Maxwell's curl equations. Second code is Numerical Electromagnetics Code (NEC-2) which embodies frequency-domain method and developed to analyze electromagnetic responses of antennas and other metallic structures. On Mark III Hypercube with 32 active nodes, largest lattice contains about 2,048,000 unit cells.

This paper examines the JPL/Caltech parallel processing system designed for rapid processing and transfer of large quantities of data from remote sensing instruments flown on NASA missions. Two remote sensing analysis applications that use this processing system are described: (1) an analysis system for retrieval of atmospheric parameters (such as species abundance, atmospheric temperature, and water vapor profiles) from data obtained by a Fourier transform IR spectrometer and (2) a prototype airborne SAR processing system. It is shown that a parallel processing system such as the JPL/Caltech system can offer supercomputer computational capability and high-volume data throughput and still be cost-effective.

A method for constructing a Green's function for an arbitrary scatterer or antenna consisting of multiple parts is presented. By exploiting the partitioning of the impedance matrix that naturally develops in a method-of-moments (MM) formulation when a number of objects are present, a matrix of numerical values representing the fields of one object in the presence of all others is computed. This matrix may be stored and used repeatedly when one of the scatterers or antennas is varied in location or shape. The matrix Green's function approach is also extended to represent incrementally larger objects. Savings in computation time over using the free-space Green's function and re-solving the large MM matrix repeatedly are considerable. The proposed technique has been implemented on the JPL/CIT Mark III Hypercube Computer and applied to radiation and scattering from a large array.<>

The computational power of the hypercube parallel computing architecture is applied to the solution of large-scale electromagnetic scattering and radiation problems. Three analysis codes have been implemented. A Hypercube Electromagnetic Interactive Analysis Workstation was developed to aid in the design and analysis of metallic structures such as antennas and to facilitate the use of these analysis codes. The workstation provides a general user environment for specification of the structure to be analyzed and graphical representations of the results.

A major objective of the Hypercube Matrix Computation effort at the Jet Propulsion Laboratory (JPL) is to investigate the applicability of a parallel computing architecture to the solution of large-scale electromagnetic scattering problems. Three scattering analysis codes are being implemented and assessed on a JPL/California Institute of Technology (Caltech) Mark 3 Hypercube. The codes, which utilize different underlying algorithms, give a means of evaluating the general applicability of this parallel architecture. The three analysis codes being implemented are a frequency domain method of moments code, a time domain finite difference code, and a frequency domain finite elements code. These analysis capabilities are being integrated into an electromagnetics interactive analysis workstation which can serve as a design tool for the construction of antennas and other radiating or scattering structures. The first two years of work on the Hypercube Matrix Computation effort is summarized. It includes both new developments and results as well as work previously reported in the Hypercube Matrix Computation Task: Final Report for 1986 to 1987 (JPL Publication 87-18).

Recent advances in high-speed microprocessor technology and in methods to couple large numbers of such processors into concurrent structures offer cost-effective means of obtaining super-computing performance. There is much interest in applying and in evaluating the actual performance on large, computationally-intensive problems. Of particular interest is the concurrent performance of large scale electromagnetic scattering problems. Two electromagnetic codes with differing underlying algorithms have been converted to run on the Mark III Hypercube. One is a time domain finite difference solution of Maxwell's equations to solve for scattered fields and the other is a frequency domain moment method solution. Important measures for demonstrating the utility of the parallel architecture are the size of the problem that could be solved and the efficiency by which the paralleling can increase the speed of execution.

With the development of concurrent computing architectures which promise cost-effective means of obtaining supercomputing performance, there is much interest in applying and in evaluating the actual performance on large, computationally-intensive problems. Of particular interest is the concurrent performance of large scale electromagnetic scattering problems. Two electromagnetic codes with differing underlying algorithms have been converted to run on the Mark III Hypercube. One is a time domain finite difference solution of Maxwell's equations to solve for scattered fields and the other is a frequency domain moment method solution. Important measures for demonstrating the utility of the parallel architecture are the size of the problem that can be solved and the efficiency by which the paralleling can increase the speed of execution.

The Hypercube Matrix Computation (Year 1986-1987) task investigated the applicability of a parallel computing architecture to the solution of large scale electromagnetic scattering problems. Two existing electromagnetic scattering codes were selected for conversion to the Mark III Hypercube concurrent computing environment. They were selected so that the underlying numerical algorithms utilized would be different thereby providing a more thorough evaluation of the appropriateness of the parallel environment for these types of problems. The first code was a frequency domain method of moments solution, NEC-2, developed at Lawrence Livermore National Laboratory. The second code was a time domain finite difference solution of Maxwell's equations to solve for the scattered fields. Once the codes were implemented on the hypercube and verified to obtain correct solutions by comparing the results with those from sequential runs, several measures were used to evaluate the performance of the two codes. First, a comparison was provided of the problem size possible on the hypercube with 128 megabytes of memory for a 32-node configuration with that available in a typical sequential user environment of 4 to 8 megabytes. Then, the performance of the codes was anlyzed for the computational speedup attained by the parallel architecture.