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K. Nikolova, and X. Li, “Adjoint sensitivity analysis of dielectric discontinuities using FDTD,” Electromagnetics 27, 123–140 (Feb. 2007). N. K. Nikolova, Ying Li, Yan Li, and M. H. Bakr, “Sensitivity analysis of scattering parameters with electromagnetic time-domain simulators,” IEEE Trans. Microwave Theory Tech. 54, 1598–1610 (Apr. 2006). 42. M. H. Bakr, N. K. Nikolova, and P. A. W. Basl, “Self-adjoint S-parameter sensitivities for lossless homogeneous TLM problems,” Int. J. of Numerical Modelling: Electronic Networks, Devices and Fields 18, 441–455 (Nov.

Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenna Propagat. 14, 302– 307 (May 1966). A. Taflov, Computational Electrodynamics: The Finite Difference Time Domain Method. Norwood, MA: Artech House, 1995. 3. J. P. Berenger, “A perfectly matched layer for the absorption of electromagneticwaves,” J. of Comp. Phys. 114(2), 185–200 (Oct. 1994). 4. W. C. Chew and W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw.

1 The Variations in the System Matrices Due to Forward Perturbation (j,k) K(pn = L) K(pn = L+ΔL) ΔK E M (pn = L) M (pn = L + ΔL) ΔM DttE N (pn = L) N (pn = L + ΔL) ΔN DtE (j + 1,k) (j – 1,k) (j,k + 1) (j,k – 1) hy 2 hy 2 0 E≠0 0 0 0 ≠0 0 0 0 ≠0 hy 2 hy 2 0 E≠0 0 0 0 ≠0 0 0 0 ≠0 hz 2 hz 2 0 E≠0 0 0 0 ≠0 0 0 0 ≠0 hz 2 hz 2 0 E≠0 0 0 0 ≠0 0 0 0 ≠0 –2(hy 2 + hz 2) –2(hy 2 + hz 2) 0 E≠0 −μr εr1 (Δh/cΔt)2 −μr εr2 (Δh/cΔt)2 −μr Δεr (Δh/cΔt)2 ≠0 −μr μo σ1 Δh2/Δt −μr μo σ2 Δh2/Δt −μr μo Δσ (Δh2/Δt) ≠0 ∆ +pn R j , k = ∆ pn R j , k = −μr Δεr (Δh/cΔt)2Dtt E(j,k) – μr μo Δσ (Δh2/Δt) Dt E(j,k), Δεr = εr2 − εr1 and Δσ = σ2 – σ1 Source: M.

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