Finite-difference solution of scattering by a rectangular cylinder (TM) using exact mesh termination (original) (raw)

Abstract

Finite Difference Techniques for solution of "steady state'' frequency domain Helmboltz equation is quite simple and straightforward. Howeuer, for open regions, the finite difference mesh needs to be terminated so that the proper boundary conditions are imposed for the sohtion. A hybrid method is described in this paper which guarantees that the boundaly conditions generated for the termination of the open region mesh is exact. The conditions are generated from the Green's functions. The technique is applied to the solution of electromagnetic scattering by conducting cylinders (TM case).

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What numerical methods are compared in this study of electromagnetic scattering?add

The research compares a finite-difference approach with a boundary-element method, demonstrating excellent agreement in computed total currents.

What experimental setup is used for analyzing scattering by the rectangular cylinder?add

The setup involves a square cross-section cylinder illuminated by a 1 GHz plane wave, with current measurements taken under various dimensions.

How does the proposed method handle boundary conditions for mesh termination?add

The method establishes exact boundary conditions for mesh termination based on evaluating electric fields at mesh nodes, enhancing computational accuracy with second-order differences.

What types of structures can the proposed method be applied to besides cylinders?add

The technique can also apply to asymmetric coplanar waveguides, multilayered dielectric substrates, and structures relevant to optical integrated circuits.

What issues arise with the finite-difference method under certain parameters?add

Parasitic resonances occur for certain dimensions (e.g., a=100 mm) when mesh parameters exceed specific limits, leading to divergent results.

Figures (4)

Figure 5 Calculated characteristic impedances as a function of electrode gap G, = b — a. The parameter is the electrode thickness ¢

Figure 5 Calculated characteristic impedances as a function of electrode gap G, = b — a. The parameter is the electrode thickness ¢

Figure 1 (a) Cross section of a rectangular cylindrical conductor, acting as a scatterer; (b) square mesh for the system of (a); (c) points used to evaluate magnetic field

Figure 1 (a) Cross section of a rectangular cylindrical conductor, acting as a scatterer; (b) square mesh for the system of (a); (c) points used to evaluate magnetic field

The transverse components of the electric and magnetic ields are

The transverse components of the electric and magnetic ields are

TABLE 1 Total current (/) on the cylinder of Figure 1, for a=b, 6 =0, E,;=1V/m, and f = 1 GHz, obtained by the finite-difference method (FD) and the boundary-element method (BE). Given also are the step size (s), the number of steps along a(n,), and the number of pulses per conductor side (n) for the boundary-element method. The phase of the electric field is zero at the conductor axis

TABLE 1 Total current (/) on the cylinder of Figure 1, for a=b, 6 =0, E,;=1V/m, and f = 1 GHz, obtained by the finite-difference method (FD) and the boundary-element method (BE). Given also are the step size (s), the number of steps along a(n,), and the number of pulses per conductor side (n) for the boundary-element method. The phase of the electric field is zero at the conductor axis

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