改进型随机无网格迦辽金法在随机热传导问题中的应用

近似方案中对移动最小二乘近似(MLS)中的基函数采用带权的正交基函数,从而形成一种改进的移动最小二乘近似(IMLS),该近似比现有的移动最小二乘近似有更高的精度和效率,且不会导致系统方程产生病态。IMLS近似与Taylor展开的随机无网格迦辽金法(SEFGM)相结合构成了一种Taylor展开的改进的随机无网格迦辽金法(TSIEFGM)。用TSIEFGM对二维随机热传导问题进行了分析。通过对含随机参数的热传导问题进行分析,算例验证该方法的正确性和有效性,为解决随机热传导问题提供了一种新方法。

Analyzing 2D stochastic heat transfer conduction problems in the Taylor expansion improved element-free Galerkin method

An improved moving least-square(IMLS) approximation is presented,in which the orthogonal function system with a weight function is used as the basis function.The IMLS approximation has a greater computational efficiency and precision than the existing moving least-squares(MLS) approximation,and does not lead to an ill-conditioned system of equations.By combining the stochastic element-free Galerkin(SEFG) method with the IMLS approximation,a Taylor expansion improved stochastic element-free Galerkin method for two-dimensional stochastic heat transfer conduction is derived.The method is correct and effective that is proved by analyzing heat transfer conduction problems with stochastic parameters.This provides a new method for solving the stochastic heat transfer conduction problems.