Isogeometric Boundary Element Method for Avoiding Singular Integrals with External Source Points

（How we can avoid singular coefficient matrix）

Abstract

Recently, the isogeometric boundary element method (IGABEM), which combines isogeometric analysis and the boundary element method, has been proposed. IGABEM is a method that combines the use of the same geometric representation as CAD and Isogeometric Analysis (IGA), with the boundary-only discretization characteristic of the Boundary Element Method. This approach is expected to eliminate the need for mesh generation, allowing CAD models to be directly used as analysis models. However, the implementation of IGABEM requires proper handling computations known as singular integrals. In this study, a method is proposed to eliminate the need for handling singular integrals by placing source points exterior of the domain of geometry. Numerical analysis was performed for a two-dimensional elasticity problem, and the accuracy was evaluated by comparing it with the exact solution of linear elasticity. The results show that by even placing the source points outside the domain, the analysis can be performed accurately.