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Derivative-orthogonal non-uniform B-Spline wavelets

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  • Theodosiou, T.C.

Abstract

This paper attempts to merge the concept of hierarchical finite element analysis (FEA) into isogeometric analysis (IGA). The proposed methodology replaces the traditional grid refinement of IGA with custom enrichment functions. The enrichment functions are properly designed B-Spline wavelets tailored to eliminate scale-coupling terms in the stiffness matrix. In this way, the refined solution is synthesized from contributions of smaller independent problems. The proposed approach has two obvious benefits: (1) the calculations performed at each resolution are not discarded when proceeding to a finer one, and (2) it has less computational requirements since the solution is divided into smaller systems. Numerical results on an elasticity problem demonstrate superior performance and accuracy compared to traditional FEA and IGA schemes.

Suggested Citation

  • Theodosiou, T.C., 2021. "Derivative-orthogonal non-uniform B-Spline wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 368-388.
    • Handle: RePEc:eee:matcom:v:188:y:2021:i:c:p:368-388
    DOI: 10.1016/j.matcom.2021.04.012
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    References listed on IDEAS

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    1. Lamnii, A. & Mraoui, H. & Sbibih, D. & Zidna, A., 2013. "Uniform tension algebraic trigonometric spline wavelets of class C2 and order four," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 87(C), pages 68-86.
    2. Faheem, Mo & Raza, Akmal & Khan, Arshad, 2021. "Collocation methods based on Gegenbauer and Bernoulli wavelets for solving neutral delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 72-92.
    3. Behera, Ratikanta & Mehra, Mani, 2017. "Approximation of the differential operators on an adaptive spherical geodesic grid using spherical wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 120-138.
    4. Karkera, Harinakshi & Katagi, Nagaraj N. & Kudenatti, Ramesh B., 2020. "Analysis of general unified MHD boundary-layer flow of a viscous fluid - a novel numerical approach through wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 168(C), pages 135-154.
    5. Nguyen, Vinh Phu & Anitescu, Cosmin & Bordas, Stéphane P.A. & Rabczuk, Timon, 2015. "Isogeometric analysis: An overview and computer implementation aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 117(C), pages 89-116.
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