A Discrete Resistance Network Based on a Multiresolution Grid for 3D Ground-Return Current Forward Modeling
Abstract
:1. Introduction
2. Related Works
2.1. Background
2.2. GRC Calculation
2.3. Discrete Grid
2.4. Contributions
- (1)
- The proposed resistance network system does not require the continuity of regular elements to establish an equipotential surface for circulating currents on a face, and it maintains good symmetry, resulting in higher solving efficiency.
- (2)
- The grid is refined at the source point and near the surface to enhance accuracy. This helps avoid redundant elements caused by lateral extension in regular grid refinement, reduces the degrees of freedom, and improves the solving efficiency of the resistance network system.
- (3)
- For hanging nodes in a multiresolution grid’s discretized resistance network, we compared three different interpolation methods and determined that the ghost fine interpolation resistance value method is suitable for MR resistance network discretization.
3. 3D RN Method
3.1. Stereo NV-RN on an SG
3.2. MR Grid
3.3. MR Stereo NV-RN
3.3.1. Hanging Nodes
3.3.2. Hanging Node Interpolation
3.3.3. Boundary Conditions
4. Numerical Examples
4.1. Homogenous Model
4.1.1. Comparison of Solving Efficiency
4.1.2. Mesh Discretization Efficiency
4.2. Abnormal Body Model
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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NV-RN | KRN | MFEM-1 | MFEM-2 | MFEM-3 | MFEM-4 | MFEM-Bench | |
---|---|---|---|---|---|---|---|
Mesh Type | Hexahedron | Tetrahedron | |||||
Ground NoE (1.0 × 106) | 0.98 | 4.3 | 0.97 | 0.97 | 0.05 | 0.06 | 2.4 |
Line NoE | 10,598 | 62,222 | 6996 | 61,191 | 117,481 | ||
Total NoE (1.0 × 106) | 0.98 | 4.3 | 0.98 | 1.04 | 0.06 | 0.12 | 2.52 |
Run time (s) | 23 | 127 | 666 | 1253 | 640 | 846 | 33,744 |
Grid Type | Range (X, km) | Depth (Z, m) | CL | Grid Spacing (km) | Grid Number | DoFs | Solving | |
---|---|---|---|---|---|---|---|---|
Iter | Time | |||||||
MR1 | −20.5–20.5 | 0–7 | 1 | 0.09 | 15661877 | 15816485 | 442 | 3 min 56 s |
−27.5–27.5 | 7–55 | 2 | 1 | 154608 | ||||
MR2 | −20.5–20.5 | 0–7 | 1 | 0.2 | 1470875 | 1625483 | 354 | 31 s |
−27.5–27.5 | 7–55 | 2 | 1 | 154608 | ||||
MR3 | −20.5–20.5 | 0–7 | 1 | 0.33 | 317709 | 472317 | 261 | 14 s |
−27.5–27.5 | 7–55 | 2 | 1 | 154608 | ||||
SG1 | −27.5–27.5 | 0–7 | 0.09 | 221445125 | 221445125 | 1654 | 20 h 3 min 29 s | |
SG2 | −27.5–27.5 | 7–55 | 1 | 1 | 166375 | 166375 | 184 | 3.02 s |
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Duan, L.; Feng, X.; Li, R.; Li, T.; Di, Y.; Hao, T. A Discrete Resistance Network Based on a Multiresolution Grid for 3D Ground-Return Current Forward Modeling. Mathematics 2024, 12, 2392. https://doi.org/10.3390/math12152392
Duan L, Feng X, Li R, Li T, Di Y, Hao T. A Discrete Resistance Network Based on a Multiresolution Grid for 3D Ground-Return Current Forward Modeling. Mathematics. 2024; 12(15):2392. https://doi.org/10.3390/math12152392
Chicago/Turabian StyleDuan, Lijun, Xiao Feng, Ruiheng Li, Tianyang Li, Yi Di, and Tian Hao. 2024. "A Discrete Resistance Network Based on a Multiresolution Grid for 3D Ground-Return Current Forward Modeling" Mathematics 12, no. 15: 2392. https://doi.org/10.3390/math12152392