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Isogeometric analysis in BIE for 3-D potential problem. (English) Zbl 1352.65585
Summary: The isogeometric analysis is introduced in the Boundary Integral Equation (BIE) for solution of 3-D potential problems. In the solution, B-spline basis functions are employed not only to construct the exact geometric model but also to approximate the boundary variables. And a new kind of B-spline function, i.e., local bivariate B-spline function, is deducted, which is further applied to reduce the computation cost for analysis of some special geometric models, such as a sphere, where large number of nearly singular and singular integrals will appear. Numerical tests show that the new method has good performance in both exactness and convergence.

65N38 Boundary element methods for boundary value problems involving PDEs
65D07 Numerical computation using splines
65D17 Computer-aided design (modeling of curves and surfaces)
Full Text: DOI
[1] Hughes, T.J.R.; Cottrell, J.A.; Bazilevs, Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput methods appl mech eng, 194, 4135-4195, (2005) · Zbl 1151.74419
[2] Cottrell, J.A.; Hughes, T.J.R.; Reali, A., Studies of refinement and continuity in isogeometric analysis, Comput methods appl mech eng, 196, 4160-4183, (2007) · Zbl 1173.74407
[3] Cottrell, J.A.; Reali, A.; Bazilevs, Y.; Hughes, T.J.R., Isogeometric analysis of structural vibrations, Comput methods appl mech eng, 195, 5257-5296, (2006) · Zbl 1119.74024
[4] Bazilevs, Y.; Calo, V.M.; Zhang, Y.; Hughes, T.J.R., Isogeometric fluid – structure interaction analysis with applications to arterial blood flow, Comput methods appl mech eng, 38, 310-322, (2006) · Zbl 1161.74020
[5] Bazilevs, Y.; Beirao de Veiga, L.; Cottrell, J.A.; Hughes, T.J.R.; Sangalli, G., Isogeometric analysis: approximation, stability and error estimates for h-refined meshes, Math models methods appl sci, 16, 1031-1090, (2006) · Zbl 1103.65113
[6] Zhang, Y.; Bazilevs, Y.; Goswami, S.; Bajaj, C.; Hughes, T.J.R., Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow, Comput methods appl mech eng, 196, 2943-2959, (2007) · Zbl 1121.76076
[7] Sederberg, T.W.; Zheng, J.; Bakenov, A.; Nasri, A., T-splines and T-nurccss, ACM trans graph, 22, 477-484, (2003)
[8] Brebbia, C.A.; Wrobel, L.C., Boundary element method for fluid flow, Adv water res, 2, 83-89, (1979)
[9] Cabral, J.J.S.P.; Wrobel, L.C.; Brebbia., C.A., A BEM formulation using B-splines: II-multiple knots and non-uniform blending functions, Eng anal boundary elem, 8, 51-55, (1991)
[10] Kitagawa, Koichi; Brebbia, Carlos A.; Luiz, C.Wrobel; Tanaka, Masataka, Boundary element analysis of viscous flow by penalty function formulation, Eng anal boundary elem, 3, 194-200, (1986)
[11] DeFigueiredo, T.G.B.; Brebbia., C.A., A new variational boundary element model for potential problems, Eng anal boundary elem, 8, 45-50, (1991)
[12] Gavankar, P.; Henderson, M.R., Graph-based extraction of protrusions and depressions from boundary representation, Comput-aided des, 22, 7, 442-450, (1990)
[13] Falcidieno, B.; Giannini, F., Automatic recognition and representation of shape-based features in a geometric modeling system, Comput vision graphics image process, 48, 93-123, (1989)
[14] Zhang, J.M.; Qin, X.Y.; Han, X.; Li, G.Y., A boundary face method for potential problems in three dimensions, Int J numer methods eng, 80, 320-337, (2009) · Zbl 1176.74212
[15] Bazilevs, Y.; Calo, V.M.; Cottrell, J.A.; Evans, J.A.; Hughes, T.J.R.; Lipton, S., Isogeometric analysis using T-splines, Comput methods appl mech eng, 199, 229-263, (2010) · Zbl 1227.74123
[16] Sederberg, T.W.; Zheng, J.; Bakenov, A.; Nasri, A., T-splines and T-nurccss, ACM trans graph, 22, 3, 477-484, (2003)
[17] Chati, M.K.; Mukherjee, S., The boundary node method for three-dimensional problems in potential theory, Int J numer methods eng, 47, 1523-1547, (2000) · Zbl 0961.65100
[18] Zhang, J.M.; Tanaka, M.; Endo, M., The hybrid boundary node method accelerated by fast multipole method for 3D potential problems, Int J numer methods eng, 63, 660-680, (2005) · Zbl 1085.65115
[19] Zhang, J.M.; Tanaka, M., Fast hdbnm for large-scale thermal analysis of CNT-reinforced composites, Comput mech, 41, 777-787, (2008) · Zbl 1210.74171
[20] Zhang, J.M.; Tanaka, M., Adaptive spatial decomposition in fast multipole method, J comput phys, 226, 17-28, (2007) · Zbl 1124.65115
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