Isogeometric Analysis of the Dual Boundary Element Method for the Laplace Problem With a Degenerate Boundary

Abstract

In this paper, we develop the isogeometric analysis of the dual boundary element method (IGA-DBEM) to solve the potential problem with a degenerate boundary. The non-uniform rational B-Spline (NURBS) based functions are employed to interpolate the geometry and physical function. To deal with the rank-deficiency problem due to the degenerate boundary, the hypersingular integral equation is introduced to promote the full rank for the influence matrix in the dual BEM. Finally, three numerical examples are given to verify the accuracy of our proposed method. Both circular and square domains subjected to the Dirichlet boundary condition are considered. The engineering problem containing a degenerate boundary is considered, e.g., a seepage flow problem with a sheet pile. Numerical results of the IGA-DBEM agree well with these of the exact solution and the original dual boundary element method.