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1.1 Introduction We have illustrated the surface integral equation method. The integral equation is converted to a matrix equation by the method of moments, and the resulting equation is solved with a full matrix inversion. Surface lengths of the order of 40 to 100 wavelengths have been used in 4. Many practical problems such as near-grazing incidence or rough surfaces with large correlation lengths are considered large-scale rough surface problems. For such large-scale rough surface problems, a much larger surface length is required and a more efficient method is needed. A banded matrix iterative approach (BMIA) has been applied to rough surface scattering. In the BMIA, the original full matrix equation is decomposed into (a) a banded matrix which represents strong interaction and (b) the remainder of the full matrix which represents the weak interaction part. An iterative approach is then adopted. The size of the neighborhood varies depending on the rough surface statistics and the incident angle. It is always much less than the required surface length and is also much less than the tapering parameter g.

NOTE: Use the Document Outline window (View | Other Windows | Document Outline) to work with the controls on your form in outline view With outline view, you can more readily see which controls are on other controls and move the controls between containers such as Panel or TabControl controls

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Improvements to the BMIA method are further made by using the flat surface as a canonical grid (CAG or CG). We call the method BMIA/CAG. For two points outside the neighborhood, the Green's function connecting the two points on the rough surface is close to that of a flat surface. Thus in this case, the flat surface provides the CAG for distances larger than neighborhood distance. A Taylor expansion is carried out for the Green's function outside the neighborhood distance. The impedance matrix from the Green's function is decomposed into a sum of the banded matrix and the Taylor expanded flat surface impedance matrix that replaces the weak matrix from the BMIA method. The advantage of the canonical grid (flat surface in this case) is that the product of the Taylor expanded flat surface matrix and the surface current column vector can be computed by the fast Fourier transform (FFT). The BMIA/CAG is much faster than the customary full matrix inversion. When the method was first used in 1994 [Tsang et al. 1994, 1995], we studied rough surfaces with lengths up to 2500 wavelengths with 25,000 surface unknowns. The method was also applied to the case of near grazing incidence. We also make comparisons between using a large surface length and the method of using a periodic boundary condition which emulates a large surface length. Other methods known as the adaptive integral method [Belszynski et al. 1994; Anastassiu et al. 1998] and the pre-corrected FFT method [Phillips and White, 1997] are similar in concept to the BMIA/CAG.

Consider a tapered plane wave 1/Jinc(X, z) impinging upon a one-dimensional (I-D) rough surface with a random height profile z = f(x).

(5.1.1)

where wand 9 are as given in 4. Applying the boundary condition that 1/J(r) = 0 on the rough surface, the Fredholm integral equation of the first kind can be formed. For a point r = xx + f(x)z on the rough surface, the integral equation for the Dirichlet boundary condition is

dx'G(r, r')u(x')

For the Purchase Tracker sample application: Visual Studio created a default form for you when you created the Windows Application project (PTWin) In Solution Explorer, change the name of this default form from Form1 to ProductWin When you change the name of a form in Solution Explorer, Visual Studio changes the form name in the Code Editor accordingly NOTE: In prior versions of Visual Studio, the recommendation was to always remove the default form from the project, because changing the name of the default form did not change the name of the form class Visual Studio 2005 fixed that problem This form is a data entry form for products that can be purchased Add two Panel controls to the form, and set their Dock property Add a Label control to each of the panels to describe their contents to the user Add a Label and ComboBox control to the selection area panel Be sure to name the controls following your naming convention Add Label, TextBox, and other controls to the informational area panel, as shown in Figure 41 Be sure to name the controls following your naming convention

(5.1.2)

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u(x') =

Jl + (df(X')/dX')2()~~')

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