Efficacious GPR Implementations of Z-Transform-Based Hybrid LOD-FDTD with Subgridding Scheme: Theoretical Formalism and Numerical Study
"> Figure 1
<p>3D interface between coarse and fine grids.</p> "> Figure 2
<p>Interpolation diagram of electric field <span class="html-italic">e<sub>x</sub></span> on the interface.</p> "> Figure 3
<p>Flowchart of hybrid subgridding LOD-FDTD method.</p> "> Figure 4
<p>Simulation configurations of the 3D rectangular waveguide.</p> "> Figure 5
<p>Transmission coefficient calculated by the analytical method and the ZT−LOD−FDTD method (CFLN = 1, 5, 10, and CFLN = 1 means that the time step is chosen as the CFL limit of the conventional FDTD method).</p> "> Figure 6
<p>The 3D model setup is a GPR system placed over a dielectric sphere buried in soil. Tx is the transmitting end, and Rx is the receiving end.</p> "> Figure 7
<p>Time−domain waveforms of <b><span class="html-italic">E</span></b>z at the receiving antenna calculated by three methods.</p> "> Figure 8
<p>Relative error of hybrid subgridding LOD−FDTD method.</p> "> Figure 9
<p>Comparisons of time-domain waveforms for different distances of transmitting and receiving antennas.</p> "> Figure 10
<p>3D classical GPR system for detecting multiple targets, Tx and Rx are respectively the transmitting and receiving ends.</p> "> Figure 11
<p>Time−domain waveforms of the <b><span class="html-italic">E</span></b>z (cylinder and sphere) at the receiving antenna are calculated by three methods respectively.</p> "> Figure 12
<p>Relative errors of hybrid subgridding LOD-FDTD method with different proportions (cylinder and sphere).</p> "> Figure 13
<p>Time snapshots of Ez amplitude calculated by hybrid subgridding LOD-FDTD method in multi-target scenario (<b>a</b>) snapshot 1. (<b>b</b>) snapshot 2. (<b>c</b>) snapshot 3. (<b>d</b>) snapshot 4.</p> "> Figure 14
<p>Time−domain waveforms of the <b><span class="html-italic">E</span></b>z (dispersive sphere) at the receiving antenna are calculated by three methods respectively.</p> "> Figure 15
<p>Relative errors of hybrid subgridding LOD-FDTD method with different proportions (dispersive sphere).</p> ">
Abstract
:1. Introduction
2. Materials and Methods
2.1. LOD-FDTD Method Based on the Z-Transform Technique
2.2. Hybrid LOD-FDTD with the Subgridding Scheme
3. Results and Discussion
3.1. Rectangular Waveguide
3.2. Dielectric Sphere
3.3. Multi-Target Detection with Dielectric Cylinder and Dielectric Sphere
3.4. Dispersive Sphere
4. Conclusions and Future Prospects
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Method | Memory Cost (MB) | Execution Time (s) |
---|---|---|
Fine-grid FDTD | 798.2 | 829.5 |
subgrid method (R = 3) | 142.4 | 62.0 |
subgrid method (R = 4) | 240.4 | 88.6 |
Method | Memory Cost (MB) | Execution Time (s) |
---|---|---|
Fine-grid FDTD | 1866.6 | 1182.4 |
subgrid method (R = 3) | 188.8 | 75.4 |
subgrid method (R = 4) | 390.0 | 129.9 |
Method | Memory Cost (MB) | Execution Time (s) |
---|---|---|
Fine-grid FDTD | 610.5 | 798.2 |
subgrid method (R = 3) | 59.2 | 142.2 |
subgrid method (R = 4) | 86.7 | 240.2 |
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Xie, G.; Song, Z.; Hou, G.; Fang, M.; Feng, N.; Huang, Z. Efficacious GPR Implementations of Z-Transform-Based Hybrid LOD-FDTD with Subgridding Scheme: Theoretical Formalism and Numerical Study. Remote Sens. 2022, 14, 5393. https://doi.org/10.3390/rs14215393
Xie G, Song Z, Hou G, Fang M, Feng N, Huang Z. Efficacious GPR Implementations of Z-Transform-Based Hybrid LOD-FDTD with Subgridding Scheme: Theoretical Formalism and Numerical Study. Remote Sensing. 2022; 14(21):5393. https://doi.org/10.3390/rs14215393
Chicago/Turabian StyleXie, Guoda, Ziheng Song, Guilin Hou, Ming Fang, Naixing Feng, and Zhixiang Huang. 2022. "Efficacious GPR Implementations of Z-Transform-Based Hybrid LOD-FDTD with Subgridding Scheme: Theoretical Formalism and Numerical Study" Remote Sensing 14, no. 21: 5393. https://doi.org/10.3390/rs14215393