Isogeometric approach applied to Boundary Element Methods is an emerging research area. 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. We mainly compare this approach, which we call IGA-SGBEM, with a curvilinear SGBEM, 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, 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.

翻译：对边界要素方法应用的测地法是一个新兴的研究领域,在这方面,目前的贡献的目的是从数字角度调查用于解决2D拉普尔方程式边界值问题的对称加列金边界要素法(Symit Galerkin Element 方法),在这个方程式中,边界和边界上的未知物都以B-splines为代表,我们主要比较这个方法,我们称之为IGA-SGBEM,与一个卷线性SGBEM,该方程式以明确的参数表示方式在任何边界上运作,并使用Lagrangian为基础获得近似解决办法,这两种技术都与标准(常规)SGBEM方法进一步比较,在标准(SGBEM方法)中,指定问题的边界以线性要素为近似值,数字解决办法以Lagrangian为基础表示,将提出和讨论若干例子,说明所有上述方法的潜在好处和缺点。