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Isogemetric analysis and symmetric Galerkin BEM: a 2D numerical study. (English) Zbl 1410.65468
Summary: Isogeometric approach applied to boundary element methods is an emerging research area (see, e.g., [R. N. Simpson et al., Comput. Methods Appl. Mech. Eng. 209–212, 87–100 (2012; Zbl 1243.74193)]). In this context, the aim of the present contribution is that of investigating, from a numerical point of view, the symmetric Galerkin boundary element method (SGBEM) devoted to the solution of 2D boundary value problems for the Laplace equation, where the boundary and the unknowns on it are both represented by B-splines [C. De Boor, A practical guide to splines. Rev. ed. New York, NY: Springer (2001; Zbl 0987.65015)]. We mainly compare this approach, which we call IGA-SGBEM, with a curvilinear SGBEM [A. Aimi et al., Int. J. Numer. Methods Eng. 45, No. 12, 1807–1830 (1999; Zbl 0958.65122)], which operates on any boundary given by explicit parametric representation and where the approximate solution is obtained using Lagrangian basis. Both techniques are further compared with a standard (conventional) SGBEM approach [A. Aimi et al., ibid. 40, No. 11, 1977–1999 (1997; Zbl 0886.73074)], where the boundary of the assigned problem is approximated by linear elements and the numerical solution is expressed in terms of Lagrangian basis. Several examples will be presented and discussed, underlying benefits and drawbacks of all the above-mentioned approaches.

MSC:
65N38 Boundary element methods for boundary value problems involving PDEs
65D17 Computer-aided design (modeling of curves and surfaces)
Software:
BEAN; ISOGAT
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