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**Boundary meshfree methods based on the boundary point interpolation methods.**
*(English)*
Zbl 1130.74466

Summary: A group of meshfree methods based on boundary integral equation have been developed in order to overcome drawbacks in the conversional boundary element method (BEM) that requires boundary elements in constructing shape functions. In this paper, the radial basis point interpolation is firstly used to formulate the boundary radial point interpolation method (BRPIM). Two boundary meshfree methods: the boundary point interpolation method (BPIM) using the polynomial PIM and the BRPIM, are then examined in detail. The numerical implementations of these two methods are studied to address several technical issues, including the size of the compact support domain, the convergence, the performance, and so on. These two boundary-type meshfree methods are also compared with the boundary node method and the conventional BEM in terms of both efficiency and performance. Several numerical examples of 2D elastostatics are analyzed using BPIM and BRPIM. It is found that BPIM and BRPIM are very easy to implement, and very robust for obtaining numerical solutions for problems of computational mechanics with very good accuracy. Key issues related the future development of boundary meshfree methods are also discussed.

### MSC:

74S15 | Boundary element methods applied to problems in solid mechanics |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

### Keywords:

Meshless methods; Mesh free method; Boundary Integral Equation; Boundary Element Method; Numerical Analysis
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\textit{G. R. Liu} and \textit{Y. T. Gu}, Eng. Anal. Bound. Elem. 28, No. 5, 475--487 (2004; Zbl 1130.74466)

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