Removing the stiffness from interfacial flows with surface tension
Journal of Computational Physics
The NURBS book (2nd ed.)
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
An efficient numerical method for studying interfacial motion in two-dimensional creeping flows
Journal of Computational Physics
Interfacial dynamics for Stokes flow
Journal of Computational Physics
Isogeometric analysis and shape optimization via boundary integral
Computer-Aided Design
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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).