The isogeometric Nyström method

Abstract

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

A Review of Trimming in Isogeometric Analysis: Challenges, Data Exchange and Simulation Aspects

“…It is also noteworthy that the coupling procedure may be neglected in certain simulation methods. For example, the boundary element method and the Nyström method do not require certain continuity between elements or patches, see e.g., [ 218 , 223 , 225 , 319 ].…”

Patch coupling in isogeometric analysis of solids in boundary representation using a mortar approach

“…Figure depicts the geometry and boundary conditions. The geometry is adopted from the literature . The system is fixed along the Dirichlet boundary ∂ u Ω and loaded with a constant traction along the Neumann boundary ∂ t Ω as shown in Figure .…”

A robust solver for elliptic PDEs in 3D complex geometries

“…Most relevant to this work, IGA has recently been applied to singular and hypersingular boundary integral equations with a collocation discretization [TRH16] with great success. A Nyström IGA method along with a regularized quadrature scheme is detailed in [ZMBF16].…”