Singular boundary method:A novel,simple,meshfree,boundary collocation numerical method
The fundamental solution of governing equations in physics and mechanics encounters so-called singularity at origin. Not surprisingly, the traditional view is that the fundamental solution can not be used as the basis function in the numerical solution of a partial differential equation, except that the source nodes are placed on the fictitious boundary outside the physical domain and are separated from the collocation nodes on the physical boundary, which underlies the method of fundamental solution, a popular method in recent years. In this paper, a breakthrough on this traditional view is made in that we simply uses the fundamental solution as the interpolation basis function while keeping the same source and collocation nodes on the physical boundary. The fundamental assumption of this research is the existence of the origin intensity factor (OIF) upon the singularity of the coincident source-collocation nodes. By employing a simple known solution of the governing equation of interest, we present a numerical approach to evaluate OIF. Our findings are that OIF does exist and its value is of a finite value, depending on the distribution of discrete boundary knots and respective boundary conditions. Based on the above findings, this paper proposes a novel numerical method for partial differential equations, called the singular boundary method. The method is mathematically simple, easy-to-program, and truly meshfree. Our preliminary numerical experiments show that the method is highly accurate and fast convergent. But mathematical physics underlying this method remains an open issue.
Singular boundary method fundamental solution singularity at origin origin intensity factor meshfree
W.Chen
Department of Engineering Mechanics,Hohai University,Nanjing,210098 China
国际会议
南京
英文
1
2009-10-18（万方平台首次上网日期，不代表论文的发表时间）