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Introduction

Electromagnetic radiation and scattering problems are old problems in the sense that they have been research topics for over 100 years. They are also new and challenging problems since there are still a lot of unsolved problems. Since the development of digital computer technology, computing electromagnetic scattering and radiation involving a complicated geometry became possible. Computational electromagnetics (CEM) based on advanced numerical technology and state-of-the-art computer technology becomes a very active research area in electromagnetic fields. Today, the major numerical methods in computational electromagnetics are the differential equation solver and the integral equation solver in both frequency and time domains. The finite element method is the most widely used method for differential equations in the frequency domain. The finite difference time domain method is a popular one for differential equations in the time domain. A popular numerical method in the past 30 years is the Method of Moments (MoM), which was proposed for electromagnetics by Harrington [1]. The method of moments is an integral equation solver. There are thousands papers published on these methods.

The problem we are going to tackle is how to predict the full-scale aircraft radar cross section (RCS) combining the state-of-the-art of CEM techniques and the state-of-the-art of massively parallel processing technologies. Practical RCS prediction using numerical methods has long been thought of as unrealistic. This is because numerical solutions, while exact in concept, demanded amounts of computation too large to accomplish in the past. The RCS prediction of a fighter-sized aircraft using MoM, for example, requires the solution of a matrix equation whose dimension can easily exceed 100,000. The impossibility of such computations also discouraged efforts to improve other aspects of CEM techniques.

Successful developments of massively parallel processing (MPP) technologes have moved us into a position from which the opportunity now looks much better for solving the above-mentioned problem. Parallel computing not only drastically improves speed, and promises much more, it also prompts new developments in CEM techniques by bettering the prospects of real problem solutions.

In this thesis, we discuss the development and implementation of computational electromagnetics techniques on massively parallel architectures. We focus on advanced numerical formulations and parallel implementation for electromagnetic scattering problems. The goal of this work is to demonstrate the possibility of predicting RCS for full-scale aircraft by applying efficient computational eletromagnetic techniques and massively parallel processing. The exact surface patch model, a parametric patch model proposed by Wilkes and Cha [2], is used for scattering from conducting bodies with or without dielectric coatings. Electric field, magnetic field, and combined field integral equations are derived for unknown surface currents. A sophisticated and complicated computer program package, called ParaMoM, has been developed by Cha's group at the Syracuse Research Corporation (SRC). ParaMoM utilizes the curvilinear surface patches in conjunction with a new type of basis function developed at SRC. We extend ParaMoM to treat electromagnetic scattering from conducting bodies coated with dielectric material. The ParaMoM code is parallelized on three MIMD (multiple instruction, multiple data) distributed memory systems. Thinking Machine Corporation's CM-5, the Intel Paragon, and the IBM SP-1 are representative of the state-of-the-art massively parallel processing architectures. The parallel ParaMoM code is called ParaMoM-MPP. The CM-5 implementation is discussed in detail and the difference of other two implementations is given when it is necessary. The Intel and IBM SP-1 implementations are done by Mr. Gang Cheng at the Northeast Parallel Architecture Center. This dissertation includes this for the purpose of comparison and completeness. The work porting the ParaMoM-MPP code to the network cluster is also done by Mr. Gang Cheng.

The performance, scalability, and portability of the ParaMoM-MPP code are discussed. Some of the Electromagnetic Code Consortium (EMCC) benchmark cases are computed and the results are in good agreement with the EMCC benchmark measurement data.

The thesis is organized into six chapters. The parametric patch model of the moment method formulation for scattering from arbitrarily shaped three dimensional conducting bodies is derived in Chapter 2. The parametric patch model and a set of basis functions proposed by Wilkes and Cha [2] are described in Section 2.1, the electric field integral equation (EFIE) formulation is derived in Section 2.2, the magnetic field integral equation (MFIE) formulation is developed in Section 2.3, and the combined field integral equation formulation is discussed in Section 2.4. The electric field integral equation for electromagnetic scattering from coated conducting bodies is given in Chapter 3. The impedance boundary condition is used to formulate the electric field integral equation. The parallel implementation is given in Chapter 4. The parallel algorithms for matrix fill and factor/solve are given in detail. An out-of-core matrix fill algorithm is discussed. In Chapter 5, we present not only performance measurements and numerical results but also a brief comparison between ParaMoM-MPP and PATCH, which is a parallel MoM code [43]. The conclusion is presented in Chapter 6.

In the rest of this chapter, we review numerical methods using integral equations and their parallel implementations. Particularly, in Section , we review surface patch development in the integral equation approach using different numerical techniques. In Section , parallel implementation of some integral equation methods is reviewed.




Next: Integral Equation Methods Up: Application of Massively Parallel Previous: List of Figures


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Sat Dec 3 17:51:03 EST 1994