Parameter Identification for a Dispersive Dielectric in 2D Electromagnetics: Forward and Inverse Methodology With Statistical Considerations

摘要

We present methodology for obtaining forward solutions to Maxwell's equations in two dimensions, in the presence of a Debye medium. Perfectly Matched Layer (PML) absorbing boundary conditions are used to absorb incoming energy at the finite boundaries. A time-domain, PDE formulation is presented, and a finite difference time-domain (FDTD) algorithm is used to obtain numerical solutions. A least squares formulation of the inverse problem results from a careful consideration of the noise model for data generation. The inverse problem is solved with varying levels of noise in the data, and a frequency domain analysis is given that provides an explanation of the results. The results and analysis motivate strategies for solving the inverse problem that decrease computational cost. Finally, a result from the statistical theory of large samples is used to obtain estimates of the variability in parameter estimates that is due to the variability in the noisy data.