Isogemetric analysis and symmetric Galerkin BEM: A 2D numerical study

Isogeometric approach applied to Boundary Element Methods is an emerging research area (see e.g. Simpson et al. (2012) [33]). 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 (de Boor (2001) [9]). We mainly compare this approach, which we call IGA-SGBEM, with a curvilinear SGBEM (Aimi et al. (1999) [2]), 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 (Aimi et al. (1997) [1]), 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.