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E - Bibliothèque et Archives Canada

E - Bibliothèque et Archives Canada

ldeally the basis

ldeally the basis functions set should r8~8mble and accurately represent the unknown current fundion. A limited number of basis sets are used typically in pracüœ. the most popular being: a) Functions which are nonzero only over a part of the domain (surface of the scatterer) of the fundion g(p'). The surface of the scattemr is divided into N segments and the basis funcüon is defineci relaüvely to the limit of one or more segments. Typical shapes of these functions indude: the pulse type. the pieceWise Ynear or sinusoidal types. b) FunctÏons which are nonzero over the entire perimeter of aie scatteter. They are usually sinusoids and their use is sirnilar to a Fourier series expansion of a function. Determining the best basis functions set from aie ones listeâ in a) is not obvious. lt is believeâ [14] that increasing the sophistication of basis functions beyond the pulse shape wïll rep-nt more smoothly the current and hem- is mon, accurate. The priœ to pay hmver is computational complexity. In some cases also the use of sinusoid function could lead in an evaluation of the integral operator maiout nwnerical integration. The fundons listed in b) are usually used when the current distribution is known to have rnainly a sinusoidal distribution. In this wrk the pulse basis function was used because it is simple and. as explained in the next several trials with pulse basis and pieceWise sinusoid basis funcüons based codes were done in the early stage of this investigation: 80th codes have similar accuracy for radiation patterns and curent distributions. Equation 2.1 1 is useâ as thr, numencal tachnique to =Ive br the wmnt by satisfying the boundary condition (vanishing e1-c fields on the scatteror surface) only et discrete poinîs. There is no guarante8 that behnieen these

points, the boundary conditions will be satisfkd. A mahod to force the boundary conditions (1 31 (in an average senci. at Ieast on the entire scatterer surface) is to use weighting funcüons in the domain of the integral. This means that equation 2.21 becomes (w~, R) ici an inner product which is a scalar operation. When both wigMing functions and basis functions are the sarne this is known as Galerkin methoci. In the literature [IS] this mcthod is considered adequate but not superior to a method using weigMing and basis function not equal but of the same order. Again trials wiai two ditferent codes ( one using the Galerkin rnethod and the other not) did not prove the superiority of one mahod over the other. It was beyond the scope of this work to investigate residuals of tangent electric field over the surface of the scatteren useâ. but from a aiment density and radiation pattern point of view. accurades of both codes (at least for the simple shape used) wiere sirnilar. The moment rnethod codes created in this work use the point matching method and pulse basis functions. It should be notexi that point matching is equivalent to using the impulse funmon as the wighting function. 2.4.3 Exp.rience with TDRS uid TEcn Two inâependent codes basad on the moment rnethod mtre ubilizeà during this investigation in addition to the codes cmated especially for each scattering am. The first code. TDRS (Tm, Dimmsional Radiation and Scattering) was obtaind from [2]. It uses the integral qualion and moment maniod with equal

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