High-power ultra-wideband electrical-pulse generation using a doped silicon photoconductive switch
✍ Scribed by B. Vergne; V. Couderc; A. Barthélémy; M. Lalande; V. Bertrand; D. Gontier
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 288 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0895-2477
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✦ Synopsis
over the cross section of the nanowire which is embedded in vacuum. We solve this equation numerically [13] for a nanowire 30 nm in size (side dimension) illuminated by an incident field of wavelength ϭ 400 nm, with the electric-field vector perpendicular to the axis of the nanowire. In Table 1, we compare the numerical values obtained for the electric-field distribution within the nanowire from the application of the Levin transform for three different values of the convergence factor and the matrix inversion for N ϭ 8. The unknowns 1-4 correspond to the values of E x and 5-8 correspond to values of E y . The Levin transform result converges rapidly to match with that from the matrix inversion as the smaller value of C f ϭ 10 Ϫ4 is approached. The convergence for higher values of N is slower and work is currently in progress to use initial vectors from a bi-CG algorithm.
4. CONCLUSION
In this paper, we have provided the numerical results of applying a vector-sequence acceleration method, namely, the Levin transform, to accelerate the convergence of the iterative solution of a system of linear equations. The system of equations is obtained when the MoM is applied to solve an integral equation. Indeed, the transform can be applied to any situation where the solution of Ax ϭ b is needed. Our results for the conducting strip show the most promise, as the convergence is quite rapid. The results of current distribution on a thin wire antenna are also satisfactory, although the convergence is slower than the strip problem. In the case of scattering from a nanowire, the transform provided accurate results for small values of N but it did not seem to converge for large N. In order to solve this problem, work is currently in progress to use various transforms to accelerate the convergence of vectors obtained in the iterations of the bi-CG algorithm. Finally, we have noted that the application of a specific vector-sequence accelerator is dependent on the type of matrix involved in the sense that one may observe dramatic convergence in some situations more than in others.