配点型无网格法及其迭代求解在导热微分方程中的应用

COLLOCATION MESHLESS AND ITERATION METHOD FOR SOLVING HEAT CONDUCTION DIFFERENTIAL EQUATIONS

对配点型无网格法在求解导热微分方程中的应用进行研究,提出配点型无网格法的迭代求解算法,并同有限元法进行对比。结果表明,配点型无网格及其迭代方法易于编程实现,且精度与有限元法相当。采用迭代求解法甚至可以不用形成系数矩阵,求解逐点进行,占用内存空间少。选择适当的松弛因子,松弛迭代相对于 Gauss-Seidel迭代可减少迭代次数。研究表明配点型无网格法及其迭代求解方法在求解大规模工程问题时具有优势。

Collocation meshless method is applied to solve the heat conduction differential equations and an iterative meshless technique is proposed. The results show that the collocation meshless and iteration method is convenient in the implementation of programming, and the computation accuracy is almost the same as that of FEM. The iterative meshless method is free of assembling the interpolation matrix, and it only occupies a little storage space because of point iteration. By properly selecting a relaxation factor, the number of iterations can be decreased for the relaxation iterative method compared with the Gauss-Seidel iteration. The preliminary study indicates that collocation meshless and iteration method has advantage for solving large scale engineering problems.