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Journal of Discrete Mathematical Sciences and Cryptography cover

Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

CiteScore 2025: 2.7 (Q1)

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Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

Enhancing computational engineering : Wavelet transforms in finite element meshing

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pp. 1753–1764Vol. 29Issue 4April 2026DOI: 10.47974/JDMSC-2565 Crossmark XML
Received:
01 May 2025
Published Online:
08 Apr 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2565
Pages:
1753–1764

Abstract

This study presents a hybrid computational approach integrating Discrete Wavelet Transforms (DWT) with the Finite Element Method (FEM) to achieve adaptive mesh refinement and improve simulation efficiency. Traditional FEM incurs high computational costs when uniformly fine meshes are required for localized phenomena. Wavelet transforms enable localized, multi-resolution analysis, allowing targeted mesh refinement in critical regions while maintaining coarser meshes elsewhere. The method is validated through two case studies—a vibrating beam and turbulent flow around a bluff body—showing up to 40% reduction in mesh elements and 30% faster computation, without sacrificing accuracy. Although wavelet-enhanced FEM introduces modest memory overhead and requires integration effort in commercial software, it offers significant benefits for large-scale, multi-scale problems. Beyond meshing, wavelet coefficients could also serve as features for data mining, enabling intelligent analysis and pattern discovery in simulation results. This framework lays the groundwork for future applications in biomechanics, aerospace engineering, and environmental modeling.

Keywords

Wavelet transformFinite element method (FEM)Computational engineeringMeshing techniquesStructural dynamicsFluid dynamicsData mining

Subject Classifications

65T6065N5065P99

References

[1] W. K. Liu, S. Li, and H. S. Park, “Eighty years of the finite element method: Birth, evolution, and future,” Arch. Comput. Methods Eng., vol. 29, no. 6, pp. 4431–4453 (2022).
[2] M. Baccouch, “A brief summary of the finite element method for differential equations,” Finite Element Methods Appl., pp. 1–42 (2021).
[3] M. V. Reddy, B. Hemasunder, S. V. Ramana, P. R. Babu, P. Thejasree, and J. Joseph, “State of art on FEM approach in inverse heat transfer problems for different materials,” Mater. Today Proc. (2023).
[4] J. P. Wolf, The Scaled Boundary Finite Element Method. Hoboken, NJ, USA: Wiley (2003).
[5] M. Ayari, A. Gharbi, Y. El Touati, Z. Klai, and M. S. Elsayed, “Advanced numerical methods in electromagnetics: Techniques and applications,” Lett. High Energy Phys., pp. 791–803 (2024).
[6] A. M. Alshoaibi and Y. A. Fageehi, “Advances in finite element modeling of fatigue crack propagation,” Appl. Sci., vol. 14, no. 20, pp. 9297 (2024).
[7] S. Dan, P. Tarafder, and S. Ghosh, “Adaptive wavelet-enhanced cohesive zone phase-field FE model for crack evolution in piezoelectric composites,” Comput. Methods Appl. Mech. Eng., vol. 392, pp. 114636 (2022).
[8] M. A. Alkhonaini, E. Gemeay, F. M. Z. Mahmood, M. Ayari, F. A. Alenizi and S. Lee, “A new encryption algorithm for image data based on two-way chaotic maps and iterative cellular automata,” Sci. Rep., vol. 14, no. 1, pp. 16701 (2024).
[9] C. M. Akujuobi, Wavelets and Wavelet Transform Systems and Their Applications. Cham, Switzerland: Springer (2022).
[10] M. L. Duc, P. Bilik, and R. Martinek, “Harmonics signal feature extraction techniques: A review,” Mathematics, vol. 11, no. 8, pp. 1877 (2023).
[11] H. Zuo, Y. Chen, and F. Jia, “Thermo-mechanical coupling analysis of laminated composite plates using wavelet finite element method,” Thin-Walled Struct., vol. 172, pp. 108911 (2022).
[12] N. H. Abu-Hamdeh, K. Daqrouq, and F. Mebarek-Oudina, “Simulation and analysis with wavelet transform technique and the vibration characteristics for early revealing of cracks in structures,” Math. Probl. Eng., vol. 2021, pp. 6626232 (2021).
[13] R. A. de Sá, G. Gomes, and R. Silva, “Development and application of wavelet-based algorithms for damage localization in two-dimensional structures,” J. Build. Pathol. Rehabil., vol. 10, no. 1, pp. 71 (2025).
[14] D. Sinha and A. Sethi, “An algorithmic characterization of sigraphs whose second iterated line sigraphs and common-edge sigraphs are switching equivalent,” J. Discrete Math. Sci. Cryptogr., vol. 18, no. 5, pp. 581–603 (2015).
[15] A. Alameri, “F-coindex of some corona products of graphs,” J. Discrete Math. Sci. Cryptogr., vol. 24, no. 8, pp. 2443–2459 (2021).
[16] O. R. Shahin and R. El Rwelli, “Part-of-speech tagging for Arabic text based on radial basis function,” J. Discrete Math. Sci. Cryptogr., vol. 24, no. 8, pp. 2443–2459 (2021).
[17] S. H. Kulkarni, V. V. Deshmukh, R. K. Moje, and S. H. Lavate, “Applied discrete mathematics in developing efficient cryptographic algorithms for enhancing information security in WSN,” J. Discrete Math. Sci. Cryptogr., vol. 28, no. 5-A, pp. 1733–1742 (2025).
[18] M. Affaf, L. Susilowati, Y. Wahyuni, and K. Dliou, “Central edge metric dimension of joint graph,” J. Discrete Math. Sci. Cryptogr., vol. 29, no. 1, pp. 97–110 (2026).

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