Nonsingular isogeometric boundary element method for Stokes flows in 3D

Isogeometric analysis (IGA) is emerging as a technology bridging computer aided geometric design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2014-01, Vol.268, p.514-539
Main Authors: Heltai, Luca, Arroyo, Marino, DeSimone, Antonio
Format: Article
Language:English
Subjects:
65D Aproximació numèrica i geometria computacional
Anàlisi numèrica
Boundaries
Boundary element method
Integral equations
Iron
Isogeometric analysis
Matemàtiques i estadística
Mathematical analysis
Mathematical models
Mètodes en elements finits
Numerical analysis
NURBS
Stokes flow
Stokes flows
Three dimensional
Àrees temàtiques de la UPC
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Summary:Isogeometric analysis (IGA) is emerging as a technology bridging computer aided geometric design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that describe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of boundary integral equations, leading to boundary element isogeometric analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. (2012) [27] to IGA-BEM.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2013.09.017