Download Finite Element and Finite Difference Methods in by M.A. Morgan (Eds.) PDF
By M.A. Morgan (Eds.)
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Extra resources for Finite Element and Finite Difference Methods in Electromagnetic Scattering
Rather than using a circular outer 40 1. Principles of Finite Methods in EM Scattering Figure 18 Boundary integral equation contour enclosing inhomogeneous dielectric cylinder. mesh boundary, let us use a conformai boundary, So, as per Fig. 18. This boundary must enclose the scatterei* and may, in fact, be con gruent with the boundary surface of the object, to be denoted as SBWithin the enclosed region, which contains inhomogeneous e(r) and μ(Γ), we can use the finite element method to approximate the solu tion of the Helmholtz equation in (51) (but using a:, y coordinates) for any specified Dirichlet BC on So· Let us define this BC using a ba sis function expansion (with unknown Ck coefficients) to represent the total field along the SO contour, having position variable s, m N = 2 So C kSk(s) (62) fc=l where g^ are the basis functions.
Efforts are underway to apply the F3 to scattering by 3-D ob jects of general shape and composition using the generalized CAP for mulation, as presented in Chapter 6, for computation of the forward A-operator. -operator. The exact field at a point out side of the surface, 5 # , depends upon the field (and normal derivative) over the entire Sß, as evidenced by the Green's function integral for- 1. Principles of Finite M e t h o d s in E M Scattering Figure 24 Conformai finite element m e s h for a semicircular dielectric cylindrical shell.
The unimoment solution proceeds by enclosing the scatterer within a separable mathematical boundary, which we will choose to be circular in the 2-D (r,0) cross section, as is illustrated in Fig. 11. Notice that there are two concentric circles, of radius r\ and Γ2, both of which enclose the scattering object. With specified Dirichlet BC's on the outer boundary, / ( r i , 0 ) = g(0), a finite method can be used to solve for nodal values of / ( r , Θ) for r < r\. A necessary attribute of the interior mesh construction is that a set of the solution nodes lies on the inner circle, r = Γ2.