The isogeometric Nyström method

The isogeometric Nyström method is presented in this paper. The important features of the method are: it allows the analysis of domains described by many different geometry descriptions in computer aided geometric design and it requires only pointwise function evaluations similar to isogeometric collocation methods. The analysis of the computational domain is carried out by means of boundary integral equations, therefore a boundary representation only is required. The method is thoroughly integrated into the isogeometric framework. For example, the regularization of the singular integrals arising is performed with local correction and also the interpolation of the pointwise results is carried out by means of Bézier elements. The isogeometric Nyström method is applied to practical problems solved by the Laplace and the Lamé-Navier equation. Numerical tests show a higher order convergence in two and three dimensions. It is concluded that the approach presented provides a simple and flexible alternative to the methods currently used for solving boundary integral equations, although it does have some limitations.