Compact Matrix-Exponential-Based FDTD with Second-Order PML and Direct Z-Transform for Modeling Complex Subsurface Sensing and Imaging Problems

To simulate complex subsurface sensing and imaging problems with both propagating and evanescent waves by the finite-difference time-domain (FDTD) method, the highly-accurate second-order perfectly matched layer (SO-PML) formulations based on the direct Z-transform (DZT) and the matrix exponential (ME) techniques are compactly and efficiently proposed for modeling open-domain problems. During mathematical deductions, several manipulations, for example, convolution computations, formulation reorganizations, or variable substitutions, can be circumvented due to the fact that the ME-based method shows a compact first-order differential matrix form. Besides, any material attributes can be completely circumvented because of using electric and magnetic flux densities, consequently, the proposed DZT-SO-PML could be applied without needing any alteration. Moreover, the DZT-SO-PML method can not only preserve better absorption accuracies, but also attain palpable improvements in computational efficiencies, even if the distance between the DSP-SO-PML truncation and the target becomes closer for modeling 3D open-domain subsurface sensing and imaging problems. Finally, numerical examples have been carried out to illustrate and validate these proposed formulations.