Jean E. Patterson

Application of massively parallel computation to integral equation models of electromagnetic scattering

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.

Parallel Computation Applied to Electromagnetic Scattering and Radiation Analysis

Abstract We have been applying the computational power of parallel processing to the solution of large-scale electromagnetic scattering and radiation problems. Several analysis codes have been implemented on the Jet Propulsion Laboratory/California Institute of Technology Mark IIIfp Hypercubes. The first code to be implemented was the Numerical Electromagnetics Code (NEC-2) from Lawrence Livermore National Laboratory. At first we simply ported it to run in the parallel processing environment. Since that time, taking advantage of the large hypercube memory and fast computation. we have enhanced parallel NEC to permit iterative design and analysis. Three other codes, frequency domain finite elements, time domain finite difference, and frequency selective surfaces, have been largely or completely developed within this parallel processing environment. Because of the massive problem size of the typical electromagnetics problem, our work is an important influence in determining the development of hardware, syst...

Scalable solutions to integral-equation and finite-element simulations

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 problems 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.

Constructing matrix Green's functions for radiation and scattering problems

A method for constructing a Greens 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 Greens function approach is also extended to represent incrementally larger objects. Savings in computation time over using the free-space Greens 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.<<ETX>>

Hypercube parallel architecture applied to electromagnetic scattering analysis

The authors code the algorithms for two electromagnetic codes, the Numerical Electromagnetic Code (NEC) and the Finite Difference Time Domain Code (FDTD), for the Mark III Hypercube. The execution times for these codes are evaluated. For both codes large speedup factors are found when runs on 32 nodes are compared to runs on one node and to runs on a VAX 11/750. The accuracy of these codes is verified by comparisons with versions running on sequential machines and with published results. >

Helmholtz Finite Elements Performance On Mark III and Intel iPSC/860 Hypercubes

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.

Concurrent electromagnetic scattering analysis

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.

Application of the hypercube parallel processor to a large-scale moment method code

The applicability of a parallel computing architecture to the solution of a large-scale moment-method code is investigated. Specifically, the NEC (Numerical Electromagnetics Code) method-of-moments scattering program is implemented on a hypercube parallel processor. The accuracy and the increase in the speed of execution on this parallel architecture are demonstrated. The results show a very large reduction in execution time for large problems. The great potential of this parallel processor is shown for interactive solution of large NEC problems as well as other moment-method techniques such as the finite-element method.<<ETX>>

Numerical algorithms for the hypercube concurrent processor

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 Maxwells 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.

Electromagnetic Scattering Analysis On A Hypercube Parallel Architecture

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 Maxwells 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.