【摘要】 针对偏微分方程参数反演问题,提出了小波多尺度-正则化反演方法,用小波变换将参数反演问题转化为小波域中有限维系数的反演问题,基于多尺度分析思想,有效改进了局部极小和计算量大的问题,结合正则化方法克服了反问题的不适定性。数值模拟试验表明了该方法的有效性。更多还原

【Abstract】 A wavelet - multilevel - regularization method is proposed for the parameter estimation problems of partial differential equation. The inverse problem is transformed to the inversion of finite wavelet coefficient in wavelet domain.By combining with the idea of multilevel, the problem of local minimization is overcomed, and the computational cost is reduced. The regularization method is introduced to overcome the ill -posedness. The results of numerical tests indicate the method’s effectiveness.更多还原