Sensitivity to Gauss quadrature of isogeometric boundary element method for 2D potential problems
More details
Hide details
Université de Lille, Centre National de la Recherche Scientifique, Centrale Lille
Unité Mixte de Recherche 9013-LaMcube-Laboratoire de Mécanique, Multiphysique, Multiéchelle, Lille, France
Faculté des Sciences de Gafsa, Département des Filières Technologiques, Tunisia
Submission date: 2023-02-09
Final revision date: 2023-04-20
Acceptance date: 2023-05-09
Online publication date: 2023-07-03
Publication date: 2023-07-31
Corresponding author
Ahlem Alia   

LaMcube, Université de Lille, Centre National de la Recherche Scientifique, Centrale Lille, Unité Mixte de Recherche 9013, F-59000, Lille, France
Journal of Theoretical and Applied Mechanics 2023;61(3):585-597
IsoGeometric Analysis (IGA) is widely used because it links exact geometry to analysis. When IGA is applied within the Boundary Element framework (IGBEM), and under cer- tain boundary conditions, discretization errors can be suppressed leading to an accurate estimation of the integration errors. By using the IGBEM for potential problems, the ef- fect of Gauss quadrature on the accuracy of each term arising in the IGBEM is studied for smooth geometry under constant boundary conditions. The results show that the method of computing singular integrals in the IGBEM is efficient. Results can be improved by selecting optimal numbers of Gauss points for both integrals.
Aimi A., Calabrò F., Diligenti M., Sampoli M.L., Sangalli G., Sestini A., 2018, Efficient assembly based on B-spline tailored quadrature rules for the IgA-SGBEM, Computer Methods in Applied Mechanics and Engineering, 331, 327-342.
Alia A., 2020, Ultrasonic diffraction by a circular transducer: Isogeometric analysis sensitivity to full Gauss quadrature points, Journal of the Acoustical Society of America, 147, 2, EL74-EL79.
Alia A., Khanyile N.P., Dufrénoy P., De Saxcé G., 2022, Vibration and acoustic radiation of an impacted plate: parametric study based on isogeometric analysis, International Conference on Noise and Vibration Engineering (ISMA 2022).
An Z., Yu T., Bui T.Q., Wang C., Trinh N.A., 2018, Implementation of isogeometric boundary element method for 2-D steady heat transfer analysis, Advances in Engineering Software, 116, 36-49.
Calabrò F., Falini A., Sampoli M.L., Sestini A., 2018, Efficient quadrature rules based on spline quasi-interpolation for application to IGA-BEMs, Journal of Computational and Applied Mathematics, 338, 153-167.
Chasapi M., Mester L., Simeon B., Klinkel S., 2022, Isogeometric analysis of 3D solids in boundary representation for problems in nonlinear solid mechanics and structural dynamics, International Journal for Numerical Methods in Engineering, 123, 5, 1228-1252.
Coox L., Atak O., Vandepitte D., Desmet W., 2017, An isogeometric indirect boundary element method for solving acoustic problems in open boundary domains, Computer Methods in Applied Mechanics and Engineering, 316, 186-208.
Hughes T.J.R., Cottrell J.A., Bazilevs Y., 2005, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering, 194, 39-41, 4135-4195.
Hughes T.J.R., Reali A., Sangalli G., 2010, Efficient quadrature for NURBS-based isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, 199, 5-8, 301-313.
Johnson R.W., 2005, Higher order B-spline collocation at the Greville abscissae, Applied Numerical Mathematics, 52, 1, 63-75.
Katsikadelis J.T., 2016, The Boundary Element Method for Engineers and Scientists, Theory and Applications, Academic Press.
Khanyile N.P., Alia A., Dufrénoy P., De Saxcé G., 2022, Acoustic radiation simulation of forced vibrating plates using isogeometric analysis, Journal of the Acoustical Society of America, 152, 1, 524-539.
Kostas K.V., Ginnis A.I., Politis C.G., Kaklis P.D., 2017, Shape-optimization of 2D hydrofoils using an Isogeometric BEM solver, Computer-Aided Design, 82, 79-87.
Liu Y., 2009, Fast Multipole Boundary Element Method: Theory and applications in Engineering, Cambridge University Press, New York.
Mahajerin E., 1983, Exact evaluation of ∫ dsr2 over a circular element, Applied Mathematical Modelling, 7, 4, 282-284.
Marburg S., 2002, Six boundary elements per wavelength: is that enough? Journal of Computational Acoustics, 10, 1, 25-51.
Marburg S., Nolte B. [Editors], 2008, Computational Acoustics of Noise Propagation in Fluids – Finite and Boundary Element Methods, Springer, Heiderberg.
Matzen M.E., Cichosz T., Bischoff M., 2013, A point to segment contact formulation for isogeometric, NURBS based finite elements, Computer Methods in Applied Mechanics and Engineering, 255, 27-39.
Opstal van T., Fonn E., Holdahl R., Kvamsdal T., Kvarving A.M., Mathisen K.M., Nordanger K., Okstad K.M., Rasheed A., Tabib M., 2015, Isogeometric methods for CFD and FSI-simulation of flow around turbine blades, Energy Procedia, 80, 442-449.
Peng X., Lian H., 2022, Numerical aspects of isogeometric boundary elementmethods: (nearly) singular quadrature, trimmed NURBS and surface crack modeling, Computer Modeling in Engineering and Sciences, 130, 1, 513-542.
Simpson R.N., Bordas S.P.A., Trevelyan J., Rabczuk T., 2012, A two-dimensional isogeometric boundary element method for elastostatic analysis, Computer Methods in Applied Mechanics and Engineering, 209-212, 87-100.
Temizer I., Wriggers P., Hughes T.J.R., 2011, Contact treatment in isogeometric analysis with NURBS, Computer Methods in Applied Mechanics and Engineering, 200, 9-12, 1100-1112.
Treeby B.E., Pan J., 2009, A practical examination of the errors arising in the direct collocation boundary element method for acoustic scattering, Engineering Analysis with Boundary Elements, 33, 11, 1302-1315.
Wu T.W., 2000, Boundary Element Acoustics, Fundamentals and Computer Codes, WIT Press, Southampton.
Yan J., Lin S., Bazilevs Y., Wagner G.J., 2019, Isogeometric analysis of multi-phase flows with surface tension and with application to dynamics of rising bubbles, Computers and Fluids, 179, 777-789.
Journals System - logo
Scroll to top