By P.R. Turner
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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.
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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.