Isogeometric Analysis of Boundary Integral Equations.

摘要

Isogeometric analysis is applied to boundary integral equations corresponding to boundary-value problems governed by Laplace's equation. It is shown that the smoothness of geometric parameterizations central to computer-aided design can be exploited for regularizing integral operators. As a result one obtains high-order collocation methods based on superior approximation and numerical integration schemes and well-conditioned systems of linear algebraic equations. It is demonstrated that the proposed approach allows one to solve boundary-value problems with an accuracy close to machine precision.