本文關鍵詞：瞬態(tài)熱傳導問題的插值型無單元伽遼金方法及誤差分析　出處：《太原科技大學》2017年碩士論文　論文類型：學位論文

  更多相關文章： 插值移動最小二乘法 形函數(shù) 插值型無單元Galerkin方法 誤差估計 瞬態(tài)熱傳導問題

【摘要】：本文主要使用無網(wǎng)格方法中的插值型無單元Galerkin方法。在插值型無單元Galerkin方法中,利用插值移動最小二乘法得到形函數(shù),用Galerkin積分弱形式離散微分方程。首先討論插值移動最小二乘法及其誤差分析理論。其次利用插值移動最小二乘法建立形函數(shù),結合瞬態(tài)熱傳導的Galerkin積分弱形式,提出求瞬態(tài)熱傳導問題數(shù)值解的插值型無單元Galerkin方法,并推導出瞬態(tài)熱傳導問題的誤差估計式。用兩個數(shù)值算例驗證該方法,得出兩種類型誤差范數(shù)的收斂速度是一致的。最后利用插值移動最小二乘法建立形函數(shù),結合廣義Fisher方程的Galerkin積分弱形式,提出求廣義Fisher方程數(shù)值解的插值型無單元Galerkin方法,該方法在求解偏微分方程定解問題時可以直接施加本質(zhì)邊界條件,提高了求解效率。并給出相應的數(shù)值算例進行驗證。
[Abstract]:In this paper, we mainly use the interpolating element free Galerkin method in the meshless method. In the interpolating cell-free Galerkin method, we use the interpolation moving least square method to get the shape function. In this paper, Galerkin integral weak form discrete differential equation is used. Firstly, the interpolation moving least square method and its error analysis theory are discussed. Secondly, the shape function is established by interpolation moving least square method. Combined with the weak form of Galerkin integral of transient heat conduction, an interpolated element-free Galerkin method is proposed to solve the numerical solution of transient heat conduction problem. The error estimation formula of transient heat conduction problem is derived. Two numerical examples are used to verify the method and the convergence rate of the two kinds of error norms is obtained. Finally, the shape function is established by interpolating moving least square method. Combined with the weak form of Galerkin integral of generalized Fisher equation, an interpolation-free Galerkin method for solving the numerical solution of generalized Fisher equation is proposed. This method can directly apply essential boundary conditions to solve the definite solution of partial differential equations, and improves the efficiency of the solution, and the corresponding numerical examples are given to verify the proposed method.
【學位授予單位】：太原科技大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O241.8

【參考文獻】

相關期刊論文 前8條

1 裴凱燕;郭龍飛;任紅萍;;利用插值型無單元Galerkin方法求解KdV-B方程[J];西南民族大學學報(自然科學版);2015年06期

2 王健菲;程玉民;;New complex variable meshless method for advection-diffusion problems[J];Chinese Physics B;2013年03期

3 王聚豐;孫鳳欣;程玉民;;An improved interpolating element-free Galerkin method with a nonsingular weight function for two-dimensional potential problems[J];Chinese Physics B;2012年09期

4 白福濃;李東明;王健菲;程玉民;;An improved complex variable element-free Galerkin method for two-dimensional elasticity problems[J];Chinese Physics B;2012年02期

5 程榮軍;程玉民;;彈性力學的無單元Galerkin方法的誤差估計[J];物理學報;2011年07期

6 程榮軍;程玉民;;勢問題的無單元Galerkin方法的誤差估計[J];物理學報;2008年10期

7 ;A complex variable meshless method for fracture problems[J];Science in China(Series G:Physics,Mechanics & Astronomy);2006年01期

8 ;Boundary element-free method for elastodynamics[J];Science in China(Series G:Physics,Mechanics & Astronomy);2005年06期

相關博士學位論文 前1條

1 程榮軍;無網(wǎng)格方法的誤差估計和收斂性研究[D];上海大學;2007年

，

本文編號：1395178