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Conference Papers Year : 2021

Unlocking the power of unstructured Isogeometric Analysis: a unified framework and some applications to wave propagation and elasticity

Abstract

Isogeometric Analysis (IGA) [1] is enjoying a prosperous career in numerical analysis, having been applied with success to many engineering applications and for the solution of many types of partial differential equations. Based on the use of B-splines and NURBS functions as basis for the Finite Elements Method (FEM), its numerical advantages include an almost perfect representation of the problem geometry, less numerical noise and dispersion, longer simulation timesteps and better stability, among others. In two or more dimensions, multivariate bases are usually obtained via a simple tensor product. This approach, convenient in engineering, is impractical for applications where no Computer Aided Design (CAD) model is available and the problem topology is complex and/or unknown, limiting the penetration of the technology in fields outside engineering, such as geophysics. REFERENCES [1] J. A. Cottrell, T. J. Hughes, and Y. Bazilevs. “Isogeometric analysis: toward integration of CAD and FEA”. John Wiley & Sons, 2009. [2] M. Neamtu. “Delaunay configurations and multivariate splines: A generalization of a result of B.N. Delaunay”, Transactions of the AMS., 359(7), pp.2993-3004. [3] Y. Liu and J. Snoeyink. “Quadratic and cubic B-splines by generalizing higher-order Voronoi diagrams”. 23rd annual symposium on Comp. Geom.. ACM. 2007, pp. 150–157. [4] H. Barucq, H. Calandra, J. Diaz, and S. Frambati, “Polynomial-reproducing spline spaces from fine zonotopal tilings “, arXiv preprint arXiv:2006.10307 (2020), under review for publication. [5] H. Barucq, J. Diaz, H. Calandra, S. Frambati,“Unstructured multi-patch DG-IGA formulation for wave propagation”, WCCM-ECCOMAS 2020 congress, Jan 2021
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Dates and versions

hal-03520492 , version 1 (11-01-2022)

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  • HAL Id : hal-03520492 , version 1

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Hélène Barucq, Henri Calandra, Julien Diaz, Stefano Frambati. Unlocking the power of unstructured Isogeometric Analysis: a unified framework and some applications to wave propagation and elasticity. IX International Conference on Isogeometric Analysis, Sep 2021, Lyon, France. ⟨hal-03520492⟩
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