An isogeometric BEM for exterior potential-flow problems in the plane

In this paper, the isogeometric concept introduced by Hughes, in the context of Finite Element Method, is applied to Boundary Element Method (BEM), for solving an exterior planar Neumann problem. The developed isogeometric-BEM concept is based on NURBS, for representing the exact body geometry and employs the same basis for representing the potential and/or the density of the single layer. In order to examine the accuracy of the scheme, numerical results for the case of a circle and a free-form body are presented and compared against analytical solutions. This enables performing a numerical error analysis, verifying the superior convergence rate of the isogeometric BEM versus low-order BEM. When starting from the initial NURBS representation of the geometry and then using knot insertion for refinement of the NURBS basis, the achieved rate of convergence is O(DoF-4). This rate may be further improved by using a degree-elevated initial NURBS representation of the geometry (kh-refinement).