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

TLDR: The idea in this study could be generally extended to other methods with integral mesh, and transformed them to be truly meshless.

Abstract: 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.