Simulation of Patch Field Effect in Space-Borne Gravitational Wave Detection Missions
Abstract
1. Introduction
2. Mathematical Modeling of Patch Field Simulation
2.1. Surface Subdivision and Electric Field Modeling
2.1.1. Potential and Charge Distribution
2.1.2. Calculation of Electric Field Force and Stiffness
2.1.3. Algorithm Complexity
2.2. Simulation of a Patch
3. Low-Complexity Calculation Method
3.1. The Theoretical Basis of Charge Equivalence
3.2. Building an Octree
3.3. The Operation Performed on the Octree
3.4. Main Body of the Algorithm
3.4.1. Calculating Equivalent Charges
Algorithm 1. Calculating equivalent charges | |
Input: Constructed octree, needed matrixes, triangular elements information | |
Output: The equivalent charges on two auxiliary surfaces for each node | |
1 | parfor each leaf, i |
2 | Executing the first and second steps of equivalenting source operation for i in sequence |
3 | end parfor |
4 | for i = tree_hight : 2 |
5 | parfor each node, j, in layer i of the octree |
6 | Executing up operation for j |
7 | end parfor |
11 | end for |
12 | for i = 2 : tree_height |
13 | parfor each node, j, in layer i of the octree |
14 | for each interactive node of the same layer, k, of j |
15 | Executing horizontal operation from k to j |
16 | end for |
17 | end parfor |
18 | (if it exists) of the octree |
19 | Executing down operation for j |
20 | end parfor |
24 | end for |
25 | return the equivalent charges on two auxiliary surfaces for each node |
3.4.2. Updating Expressions
3.5. Algorithm Complexity
3.5.1. Space Complexity
3.5.2. Time Complexity
4. Experiments, Results, and Discussion
4.1. Parameter Setting
4.2. Single Contaminant Patch Bulge Impact Analysis
4.2.1. Impact of Potential
4.2.2. Impact of Base Radius
4.2.3. Impact of Location
4.3. Single Planar Patch Impact Analysis
4.3.1. Impact of Potential
4.3.2. Impact of Patch Radius and Position
4.3.3. Explanation of the Curve of and
4.4. Analysis of the Metric Requirements in Space-Borne Gravitational Wave Detection Missions
4.4.1. Patch with Bulge
4.4.2. Single Planar Patch
5. Conclusions
- We established a mathematical model based on a partition of boundary elements and the GMRES method to simulate the patch field. This model can solve the charge distribution according to the potential distribution and use the charge distribution to calculate the force and stiffness on the TM. The bulges and the nonuniform distribution of the potential led by patches can also be simulated with the model.
- To overcome the difficulty of excessive computational complexity, based on existing algorithms, we made improvements according to needs, and designed an algorithm with spatiotemporal complexity for calculating potential distribution, force, and stiffness.
- With the method mentioned above, we researched what impacts single bulge forms from contaminant attachment have on force, , and stiffness, . The control variable method is adopted, and , , and location are taken as variables, respectively. The results show that both and are linear functions of , approximately proportional to to the third power. The patch which is opposite one electrode or is at one electrode has a bigger impact on than the patch in the other area. The patch at the surface of the housing has a bigger influence on than the patch at the surface of the TM.
- In addition, we also studied a single patch without a bulge and found that the relation of and to can be approximated to a quartic curve passing through the origin, which can be simplified in some cases, and both and are approximately proportional to .
- With the help of Conclusion 3~4, we respectively studied the bulges and single planar patch for space-borne gravitational wave detection missions. If we limit the stiffness caused by the patch not to exceed , we found that, under normal circumstances, the impact of a bulge can be ignored. When , the value of of a single patch should be less than 1.62 mm.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Verifying the Correctness of the Simulation Algorithm with a Parallel-Plate Capacitor
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She, M.; Peng, X.; Qiang, L.-E. Simulation of Patch Field Effect in Space-Borne Gravitational Wave Detection Missions. Sensors 2025, 25, 3107. https://doi.org/10.3390/s25103107
She M, Peng X, Qiang L-E. Simulation of Patch Field Effect in Space-Borne Gravitational Wave Detection Missions. Sensors. 2025; 25(10):3107. https://doi.org/10.3390/s25103107
Chicago/Turabian StyleShe, Mingchao, Xiaodong Peng, and Li-E Qiang. 2025. "Simulation of Patch Field Effect in Space-Borne Gravitational Wave Detection Missions" Sensors 25, no. 10: 3107. https://doi.org/10.3390/s25103107
APA StyleShe, M., Peng, X., & Qiang, L.-E. (2025). Simulation of Patch Field Effect in Space-Borne Gravitational Wave Detection Missions. Sensors, 25(10), 3107. https://doi.org/10.3390/s25103107