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a random displacement between 0 and 50% of the radius of the cylinder. The average distance from the grid point for all the cylinders is 0.27% of the radius. The cylinder has a complex dielectric constant of 20+i3 with a radius of 1/20 of a free-space wavelength (>'0)' The total area occupied by the square box is scaled to 78.54A~. The transverse electric (TE) case is considered with the angle of incidence = 30 . Three cylindrical modes are needed to represent the scattered field of each cylinder; that is, n = -1,0, and 1 in (9.4.5). Therefore, we have a total of 12,000 unknowns. We vary the summation indices (m) in (9.4.5) and (9.4.7)-(9.4.9) until the solution converges. We also vary the neighborhood distance r d to observe the changes in the solution. In (9.4.4), WOO is calculated for a = 1,2, and 3 whose centers are located at (x, y) = (-0.0004, -0.0011), (0.2496,0.2498), and (0.5161,0.5164) in Fig. 9.4.3, respectively. For the indirect summation of (9.4.7) using the SMCG method, we need to identify the neighboring cylinders associated with each cylinder, to compute the Bessel functions and Hankel functions, and to perform the convolutions using FFTs. We compare both the accuracy and the CPU time of the SMCG and those of direct summation for one iteration. For the direct summation, we extrapolate the CPU for the 4000 cylinders from that of the first 40 multiplied by 100. Table 9.4.1 shows the accuracy of the SMCG method versus direct summation, and Table 9.4.2 shows the

2.0 Expenditure ($B)

+ l2)1/2

2.3.53c

Object-oriented design begins with the domain model de ned during the object-oriented analysis phase and breaks it into speci c classes with clearly de ned properties and methods It then adds implementation details, such as security, serialization, and logging In cases where the OOA phase includes a large system, the OOD phase picks portions of the system and provides the details Now that most

(2.3.53d)

Equation (2.3.48) is the DDA matrix equation and is to be solved numerically. After the solution is obtained, we have the solution of the induced dipole moment Pi for every cell. The electric field at cell i is given by

Eo t -

(2 3 54 )

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development organizations are selecting fewer features to analyze at a time, there is more of an overlap between OOA and OOD and the transition from OOA to OOD is blurred The important thing that OOD does include that OOA does not is implementation details OOD de nes the classes, including the implementation details for properties and methods It incorporates implementation constraints, such as security, logging, load, and performance It includes architectural assumptions such as the location of the application s tiers (will there be an application server database server server farm and so on) Because of its technical nature, much of this step normally is done by the technical team, without much participation from the domain experts Most domain experts don t care how you implement security or obtain the desired performance levels, only that you do implement security and have a highly performant application This phase often makes use of design patterns A design pattern is a general, repeatable solution to a commonly occurring problem in software design For example, the need to have a class that can provide one and only one object has a design pattern called a Singleton The Singleton design pattern de nes the set of classes needed to implement that pattern and solve that problem (See the Additional Reading section for more information on design patterns) The result of this phase is a model that can readily be converted into code

(2.3.54b)

For the case of rectangular parallelepipeds the matrix equation of (2.3.48) is of dimension 3N x 3N where N is the number of rectangular parallelepipes and the factor 3 arises from the x, y and z components of the polarization vector. In the standard form, the matrix equation is (2.3.55) where Z is the impedance matrix and x is the unknown column vector and b is the right-hand side. Let the rectangular parallelepipeds be equally spaced in X, y and directions. Then (2.3.48) can be solved by using conjugate

0 1993 1994 1995 1996 1997 1998 1999 2000

gradient method (CGM) combined with fast Fourier transform (FFT) that will be discussed in Section 4. In applying CGM, we need to take the product ==t Z d and the product Z r where t denotes adjoint, d is the direction vector and r is the residual vector. For example, if there are two rectangular parallelepipeds, N = 2, then the impedance matrix Z is of dimension 6 x 6 and is

(2.3.56)

(2.3.57)

For the Purchase Tracker sample application: Add a form project item to the Windows Application project (PTWin) using the Inherited Form template, and inherit from your base form class (PTBaseWin) Name the form CustomerWin In the Data Sources window, select the Customer node and use the drop-down control list to select Details as the type of control to render NOTE: If your Data Sources window appears empty, ensure that the Windows Application project (PTWin) is the active project in Solution Explorer In the Data Sources window, select the CustomerPurchases property and use the drop-down control list to select None as the type of control to render The CustomerPurchases property is not rendered on the CustomerWin form

(2.3.58)

zt = [

ikr _ -

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