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### Abstract

The aim of this thesis is the study of the simulation of electrically large structures and the application of the results to automotive Electromagnetic Compatibility (EMC). The theoretical and experimental work carried out has led to the development of computational tools and to the further understanding of the mechanisms involved in the representation of solid surfaces by means of wire-grid simplifications. The work was done in the context of a European project GUIDELINES FOR ELECTROMAGNETIC COMPATIBILITY MODELLING FOR AUTOMOTIVE REQUIREMENTS (GEMCAR). The first two chapters of the thesis contain a description of the GEMCAR project, a brief overview of some of the existing numerical methods for electromagnetic simulations (particularly, the ones used in GEMCAR), and the explanation of efficient, general simulation strategies that can be applied to different methods. The concept of adaptive sampling and its application are also introduced there. The main original contributions of this thesis are presented in Chapters 3 through 6. They consist of theoretical and experimental work as follows. We present, in Chapter 3, a modified version of the Numerical Electromagnetics Code (NEC). This version, which we have called Parallel NEC, has been adapted to run on parallel supercomputers, taking advantage of the combined processing power and memory of several processors working as a team. Parallel NEC has been implemented in two different supercomputing architectures to test the portability of the code. The original NEC routines in charge of the calculation and filling of the interaction matrix have been modified to work in a parallel environment. The matrix is now distributed among the available processors and the elements of the matrix are locally and individually calculated by their "owners". Thus the number of integrals carried out to build the complete matrix equation gets shared, diminishing the necessary runtime for this time-consuming operation. The system of equations is also solved using a parallel version of the Gauss-Doolitle algorithm. However, the most important feature of Parallel NEC is the possibility to use the distributed memory of the processors. This allows the calculation of problems of a size never achieved before using this numerical method without the need of using disk-space as swap memory. The code has been tested with models containing over 20.000 segments, exhibiting execution times comparable to those obtained with a single-processor PC calculating models of one tenth of that size in terms of the number of segments. Parallel NEC is also able to adapt itself automatically to its environment. It will detect the number of available processors and will take advantage of all available memory and calculating resources. The validation of Parallel NEC has been carried out in two steps. First, it was validated using simulation results obtained with other numerical methods. Then, it was validated by using experimental data from the GEMCAR project. The experimental setup as well as the validation are presented in Chapter 4. With the purpose of validating the numerical models developed in GEMCAR, we participated in a number of experimental campaigns carried out at Spiez, Switzerland in 2000 and 2001 using the VERIFY (Vertical EMP Radiating Indoor Facility), an EMP simulator belonging to the Swiss Defense Procurement Agency. Measurements of electric and magnetic fields inside a real vehicle (a Volvo S80) featuring different levels of complexity were carried out. These measurements were performed at 8 different points inside the car and at two points on the surface of the body-shell. The above-mentioned levels of complexity consisted of (1) a "simple test case", comprising the vehicle body-shell (without all doors or glazing), (2) a "medium complexity case" which, this time, included the doors, and (3) a "complex case", consisting of the complete car with all mechanical, electrical and electronic equipment installed. The data used in Chaper 4 refer to the "simple test case", although the "medium test case" measurements are also available . Other partners of the GEMCAR project carried out experimental testing on the three models using other sources of illumination (see Chapters 1 and 4). It is interesting to mention for completeness that, as part of the GEMCAR project, a cable harness was installed following the approximate path of the original cabling of the car, but composed of single wires with 50 R terminations. Current measurements were made at 4 observation points located at the ends of the branches of the harness. These current measurements are not given here as the subject of this thesis was limited to field measurements and simulations only1. The developed code was applied to analyze the penetration of electromagnetic fields inside the vehicle's body shell (i.e., the simple case). The computed results agree well with those obtained with the other methods and with the experimental data obtained from measurements. The application of the code to such a large problem permitted the observation of some issues raised by the application of the so-called Equal Area Rule (EAR) for the calculation of the segments' lengths and radii. In Chapter 5, we discuss the wire-grid representation of metallic surfaces in numerical electromagnetic modeling. We present the origins and the evolution of surface wire-grid modeling and, considering two types of geometries, namely (I) a simple cube, and (2) a complex structure represented by the metallic car shell used in Chapter 4, we show that the Equal Area Rule is accurate as long as the wire-grid consists of a simple square mesh. For more complex body-fitted meshes, such as rectangular and triangular grids, the Equal Area Rule appears to be less accurate in reproducing the electromagnetic field scattered by metallic bodies. In Chapter 6 we present a theoretical development that leads, for the case of a square grid representation of a surface, to the same formula proposed by the Equal Area Rule. This development is, to the best of our knowledge, the first physical and mathematical interpretation of the EAR as of today. Our development shows, however, a different value for the radius of the segments if the representation of the surface uses other polygons, such as in the case of a rectangular or a triangular mesh. To compare the two methods (the traditional versus the new EAR), we carried out a simple numerical test and found that the Equal Area Rule does not always predict the optimum wire radius for the mesh-representation of a surface. ------------------------------ 1The interested reader is referred to: A. Rubinstein, F. Rachidi, D. Pavanello, and B. Reusser. Electromagnetic field interaction with vehicle cable harness: An experimental analysis. In International Conference on Electromagnetic Compatibility, EMC Europe. Sorrento, volume 1, Sep 2002. Proceedings.