一维抛物型偏微分方程的多重网格解法和模型问题分析

A Multigrid Method for Solutions of One-Dimensional Parabolic Partial Differential Equations and Model Problem Analysis

具体构造了一维抛物型偏微分方程的多重网格解法。就模型方程分析了光滑因子,建立了不变子空间,并给出校正算子和二重网格方法算子的矩阵表示。导出了二重网格方法算子的谱半径——收敛因子,解决了收敛问题。

In this paper, a new multigrid method for solutions of one-dimensional partial differential equations is developed. For the model equation, the smoothing factor is analysed, the invariant subspaces structured and the matrixes representing the correction and two-grid operators, respectively, are obtained. The spectral radius, the convergent factor of two grid method is deduced, thus solving the convergenee problem of the two grid method.