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	基于蒙特卡罗积分的无网格伽辽金法及其在渗流分析中的应用
	介玉新 ; 刘岩 ; JIE Yu-xin ; LIU Yan
	2010-06-10 ; 2010-06-10
关键词	无网格法 无单元法 蒙特卡罗方法 数值积分 渗流 meshless method element-free method Monte Carlo method numerical integration seepage O357.3
其他题名	Element-free Galerkin method based on Monte Carlo integration and its application in seepage analysis
中文摘要	无网格法在处理有限元法难以解决的问题时具有显著的优势,且前后处理比较简单。无网格伽辽金法(Element-free Galerkin method,EFG)是无网格法的一种,它采用滑动最小二乘法近似场函数,计算精度较高,且有较好的稳定性,在结构和渗流分析中受到欢迎。但EFG方法需要背景积分网格进行高斯积分,离真正的"无网格"方法还有一定距离。对其积分方法进行改进,采用蒙特卡罗方法(Monte Carlo)进行积分运算,由此提出了基于蒙特卡罗积分的无网格法(MCEFG)。从而摆脱EFG方法对背景积分网格的依赖,使之成为真正意义上的无网格方法。基于MCEFG方法的渗流分析程序对有自由面的渗流问题进行了较好模拟。该方法可以推广应用到其他需要背景积分网格的方法中,从而使无网格法真正与网格脱离。; 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.; 国家重点基础研究(973)资助项目(2007CB714102)
语种	中文 ; 中文
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/59519]
专题	清华大学
推荐引用方式 GB/T 7714	介玉新,刘岩,JIE Yu-xin,等. 基于蒙特卡罗积分的无网格伽辽金法及其在渗流分析中的应用[J],2010, 2010.
APA	介玉新,刘岩,JIE Yu-xin,&LIU Yan.(2010).基于蒙特卡罗积分的无网格伽辽金法及其在渗流分析中的应用..
MLA	介玉新,et al."基于蒙特卡罗积分的无网格伽辽金法及其在渗流分析中的应用".(2010).

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