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Finite Element Mesh Refinement for EM-Field Solvers Modeling using Genetic Algorithm

by Kiptoo Lelon, Waweru Njeri, Joseph Muguro
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 186 - Number 52
Year of Publication: 2024
Authors: Kiptoo Lelon, Waweru Njeri, Joseph Muguro
10.5120/ijca2024924189

Kiptoo Lelon, Waweru Njeri, Joseph Muguro . Finite Element Mesh Refinement for EM-Field Solvers Modeling using Genetic Algorithm. International Journal of Computer Applications. 186, 52 ( Dec 2024), 14-23. DOI=10.5120/ijca2024924189

@article{ 10.5120/ijca2024924189,
author = { Kiptoo Lelon, Waweru Njeri, Joseph Muguro },
title = { Finite Element Mesh Refinement for EM-Field Solvers Modeling using Genetic Algorithm },
journal = { International Journal of Computer Applications },
issue_date = { Dec 2024 },
volume = { 186 },
number = { 52 },
month = { Dec },
year = { 2024 },
issn = { 0975-8887 },
pages = { 14-23 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume186/number52/finite-element-mesh-refinement-for-em-field-solvers-modeling-using-genetic-algorithm/ },
doi = { 10.5120/ijca2024924189 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-12-07T02:20:16+05:30
%A Kiptoo Lelon
%A Waweru Njeri
%A Joseph Muguro
%T Finite Element Mesh Refinement for EM-Field Solvers Modeling using Genetic Algorithm
%J International Journal of Computer Applications
%@ 0975-8887
%V 186
%N 52
%P 14-23
%D 2024
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Electromagnetic field solvers are pivotal in numerous engineering and scientific applications, ranging from antenna design to medical imaging. Achieving accurate and efficient solutions to complex electromagnetic (EM) field problems often necessitates a refined finite element (FE) mesh. This study explored using genetic algorithms (GA) as a robust optimization tool to enhance the quality of FE meshes for EM field simulations. The proposed approach not only automates the mesh refinement process but also significantly improves the convergence and accuracy of numerical simulations. The initial mesh on a problem domain was generated using the Delaunay triangulation algorithm (DTA), and the developed mesh was then refined using a more flexible GA that could handle regions of the problem domain containing several local extrema. The aspect ratio and the maximum angle at each node of the triangular mesh were used to select the fitness function to be optimized in the GA. The GA was tested and validated for various test cases covering multiple complex geometry applications. The results showed a significant change in the quality of the refined meshes, a shift of fitness value ranges from (0.1-0.50) to (0.60-1.0), and the ability to handle nonconvex regions. Results of mesh refinement and modeling EM field solvers were validated and accomplished through a series of tests and comparisons of the GA and the DTA mesh quality results and by observing the effect of E-fields and H-fields on the computed results.

References
  1. M. A. AL-Amoudi, “STUDY, DESIGN, AND SIMULATION FOR MICROSTRIP PATCH ANTENNA,” International Journal of Applied Science and Engineering Review, vol. 02, no. 02, pp. 01–29, 2021, Doi: 10.52267/ijaser.2021.2201.
  2. M. KURYLA, “Introduction to Finite Element Analysis (FEA) or finite element method (FEM),” Freak Weather, 2018.
  3. L. B. W. and R. E. White, “An Introduction to the Finite Element Method with Application to Nonlinear Problems.,” Math Comput, vol. 50, no. 181, 1988, doi: 10.2307/2007936.
  4. M. BERN and D. EPPSTEIN, “MESH GENERATION AND OPTIMAL TRIANGULATION,” 1992. doi: 10.1142/9789814355858_0002.
  5. D. Schillinger and M. Ruess, “The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models,” Archives of Computational Methods in Engineering, vol. 22, no. 3, 2015, doi: 10.1007/s11831-014-9115-y.
  6. J. C. Heinrich, D. R. Poirier, and D. F. Nagelhout, “Mesh generation and flow calculations in highly contorted geometries,” Comput Methods Appl Mech Eng, vol. 133, no. 1–2, 1996, doi: 10.1016/0045-7825(96)01021-3.
  7. K. Key and J. Ovall, “A parallel goal-oriented adaptive finite element method for 2.5-D electromagnetic modeling,” Geophys J Int, vol. 186, no. 1, 2011, doi: 10.1111/j.1365-246X.2011.05025.x.
  8. Alhijawi, B., & Awajan, A. (2023). Genetic algorithms: theory, genetic operators, solutions, and applications. Evolutionary Intelligence. https://doi.org/10.1007/s12065-023-00822-6
  9. Chong, C. S., Lee, H. P., & Kumar, A. S. (2006). Genetic algorithms in mesh optimization for visualization and finite element models. Neural Computing and Applications, 15(3–4), 366–372. https://doi.org/10.1007/s00521-006-0041-2
  10. M. J. Aftosmis, J. E. Melton, and M. J. Berger, “Adaptation and surface modeling for cartesian mesh methods,” in 12th Computational Fluid Dynamics Conference, 1995. doi: 10.2514/6.1995-1725.
  11. D. J. Mavriplis, “Unstructured Mesh Generation and Adapativity,” 1995.
  12. X.-H. Wang, “Automatic Mesh Generation,” in Finite Element Methods for Nonlinear Optical Waveguides, 2019. doi: 10.1201/9780203756027-4.Spector, A. Z. 1989. Achieving application requirements. In Distributed Systems, S. Mullender.
  13. A. C. Polycarpou, “Introduction to the finite element method in electromagnetics,” Synthesis Lectures on Computational Electromagnetics, vol. 4, 2006, doi: 10.2200/S00019ED1V01Y200604CEM004.
  14. D. J. Mavriplis, “Unstructured mesh generation and adaptivity. 26th Computational Fluid Dynamics Lecture Series, Rhode-Saint-Genese, March 1995,” 1995.
  15. G. Meunier, The Finite Element Method for Electromagnetic Modeling. 2010. doi: 10.1002/9780470611173.
  16. D. J. Mavriplis, “An advancing front Delaunay triangulation algorithm designed for robustness,” J Comput Phys, vol. 117, no. 1, 1995, doi: 10.1006/jcph.1995.1047.
  17. C. B. Barber, D. P. Dobkin, and H. Huhdanpaa, “The Quickhull Algorithm for Convex Hulls,” ACM Transactions on Mathematical Software, vol. 22, no. 4, 1996, doi: 10.1145/235815.235821.
  18. D. T. Lee and B. J. Schachter, “Two algorithms for constructing a Delaunay triangulation,” International Journal of Computer & Information Sciences, vol. 9, no. 3, 1980, doi: 10.1007/BF00977785.
  19. A. Rassineux, “Generation and optimization of tetrahedral meshes by advancing front technique,” Int J Numer Methods Eng, vol. 41, no. 4, 1998, doi: 10.1002/(SICI)1097-0207(19980228)41:4<651::AID-NME304>3.0.CO;2-P.
  20. S. H. Chen, “Geometrical Description and Discretization of Hydraulic Structures,” in Springer Tracts in Civil Engineering, 2019. doi: 10.1007/978-981-10-8135-4_3.
  21. T. Wan, B. Tang, and M. Li, “An Iteration-Free Domain Decomposition Method for the Fast Finite Element Analysis of Electromagnetic Problems,” IEEE Trans Antennas Propag, vol. 68, no. 1, 2020, doi: 10.1109/TAP.2019.2943352.
  22. M. N. O. Sadiku, “Simple introduction to finite element analysis of electromagnetic problems,” IEEE Transactions on Education, vol. v, no. n, 1992.
  23. J. T. Hwang and J. R. R. A. Martins, “An unstructured quadrilateral mesh generation algorithm for aircraft structures,” Aerosp Sci Technol, vol. 59, 2016, doi: 10.1016/j.ast.2016.10.010.
  24. D. A. Field, “Laplacian smoothing and Delaunay triangulations,” Communications in Applied Numerical Methods, vol. 4, no. 6, 1988, doi: 10.1002/cnm.1630040603.
  25. J. Y. Kang and B. S. Lee, “Optimisation of pipeline route in the presence of obstacles based on a least cost path algorithm and laplacian smoothing,” International Journal of Naval Architecture and Ocean Engineering, vol. 9, no. 5, 2017, doi: 10.1016/j.ijnaoe.2017.02.001.
  26. S. A. Canann, M. B. Stephenson, and T. Blacker, “Optismoothing: An optimization-driven approach to mesh smoothing,” Finite Elements in Analysis and Design, vol. 13, no. 2–3, 1993, doi: 10.1016/0168-874X(93)90056-V.
  27. C. O. Lori A. Freitag, “A Comparison of Tetrahedral Mesh Improvement Techniques,” Fifth International Meshing Roundtable, 1996.
  28. N. Amenta, M. Bern, and D. Eppstein, “Optimal point placement for mesh smoothing,” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 1997.
  29. S. A. Canann, J. J. R. Tristano, and M. M. L. Staten, “An Approach to Combined Laplacian and Optimization-Based Smoothing for Triangular, Quadrilateral, and Quad-Dominant Meshes,” in 7th International Meshing Roundtable, 1998.
  30. C. Cervellera and M. Muselli, “Deterministic Learning and an Application in Optimal Control,” 2006. doi: 10.1016/S1076-5670(05)40002-6.
  31. M. Salama, A. Abdo Ali, and E. H. Atta, “A Genetic Algorithm Approach for Optimizing Unstructured Meshes.”
  32. Prieto, F. G., Lahtinen, J., Samavaki, M., & Pursiainen, S. (2023). Multi-compartment head modeling in EEG: Unstructured boundary-fitted tetra meshing with subcortical structures. PLoS ONE, 18(9), e0290715. https://doi.org/10.1371/journal.pone.0290715
  33. Li, H., Kondoh, T., Jolivet, P., Nakayama, N., Furuta, K., Zhang, H., Zhu, B., Izui, K., & Nishiwaki, S. (2022). Topology optimization for lift–drag problems incorporated with distributed unstructured mesh adaptation. Structural and Multidisciplinary Optimization, 65(8). https://doi.org/10.1007/s00158-022-03314-w
  34. Lam, S. (2016). A Methodology for the Optimization of Autonomous Public Transportation [Thesis]. In UNSW Sydney, The School of Mechanical and Manufacturing Engineering, The University of New South Wales. https://doi.org/10.13140/RG.2.2.33767.91046
Index Terms

Computer Science
Information Sciences
Meshing Algorithms
Magnetostatics

Keywords

Mesh Generation Mesh Refinement Delaunay Triangulation Genetic Algorithm.

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