Element-free Galerkin method based on Monte Carlo integration and its application in seepage analysis

Meshless methods were preponderant in dealing with problems when it was difficult to employ finite element method.And they could simplify pre-and post-processings.Element-free Galerkin method(EFG),based on moving least squares method(MLS),was one of the meshless methods.Owing to its accuracy and stability,EFG method was widely applied in structure and seepage analysis.However,EFG method was not a "truly" meshless method,since mesh was still used to conduct numerical integration.A Monte Carlo-based EFG method(MCEFG) was proposed to do the integration with Monte Carlo method.The mesh or cell was not used in MCEFG method.So it was truly a meshless method.A program based on MCEFG method was compiled and applied to seepage analysis.It was shown that the method was suitable for simulating seepage with a free surface.The idea in this study could be generally extended to other methods with integral mesh,and transformed them to be truly meshless.