求解快速振荡系数的抛物型方程的新方法

New Method for Parabolic Equations with Rapidly Oscillating Coefficients

提出了小波变换数值均匀化方法,并将其用于求解快速振荡系数的抛物型方程。小波变换数值均匀化方法基于小波的多分辨分析,在细尺度空间上得到原方程的半离散方程,然后利用小波变换得到粗尺度空间的数值均匀化方程,即可在粗尺度上求解原方程,有效地减小了计算量。计算结果表明:小波数值均匀化方法与精细剖分的有限体积法相比较,既大大地节省了计算时间又获得了较好的精度。

Wavelet transform numerical homogenization is proposed for parabolic equations with rapidly oscillating coefficients.Based on MRA,muhiscale numerical homogenization obtains semi-discrete equations in fine scale space,and transforms to numerical homogenization equations in coarse scale space by wavelet transform.Then wavelet transform numerical homogenization gets numerical results at a low cost for solving the original equation in coarse scale space. The numerical results show that the proposed method is better than the finite volume method,not only in calculation but also in accuracy.