A Galerkin boundary node method and its convergence analysis

摘要

The boundary node method (BNM) exploits the dimensionality of the boundary integral equation (BIE) and the meshless attribute of the moving least-square (MLS) approximations. However, since MLS shape functions lack the property of a delta function, it is difficult to exactly satisfy boundary conditions in BNM. Besides, the system matrices of BNM are non-symmetric.A Galerkin boundary node method (GBNM) is proposed in this paper for solving boundary value problems. In this approach, an equivalent variational form of a BIE is used for representing the governing equation, and the trial and test functions of the variational formulation are generated by the MLS approximation. As a result, boundary conditions can be implemented accurately and the system matrices are symmetric. Total details of numerical implementation and error analysis are given for a general BIE. Taking the Dirichlet problem of Laplace equation as an example, we set up a framework for error estimates of GBNM. Some numerical examples are also given to demonstrate the efficacity of the method.