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

Naixing Feng, Yuxian Zhang, Guo Ping Wang, Qingsheng Zeng, William T. Joines
2020 Remote Sensing  
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
more » ... s, 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.
doi:10.3390/rs13010094 fatcat:s4wgblze4vhrhj5t4ssna26dty