基于Landweber迭代重构河流污染物初值

Reconstruction of the Initial Value of River Pollutant with Landweber Iteration

采用Landweber迭代建立了一维河流水体污染物非恒定输运逆问题模型,通过某时刻实测值来反演污染物初始浓度分布,应用Landweber迭代算法反演了一维纯扩散和对流-扩散过程两个算例。结果表明:Landweber迭代能准确重构污染物的初始分布,并且该方法具有良好的抗干扰性;当测量误差较大时,该算法仍能较好地反演污染物初始浓度,即Landweber迭代可以较精确地反演一些非连续的污染物初始浓度,可以较好地解决一些连续污染物初值和污染源项的识别问题。

In order to reconstruct the initial value of non-constant transport one-dimensional river water pollutant, Landweber iteration was designed to inverse the initial value of pure diffusion and convection-diffusion examples, appending several measured values. The results show that the proposed algorithm can reconstruct the initial distribution of the pollutant effectively with good robustness. When the measured value consists of a larger measurement error, the algorithm can still reconstruct the numerical results with high precision, which shows that Land- weber iterative algorithm can effectively reconstruct the discontinuous initial concentration of river pollution. Furthermore, Landweber iteration can also be applied to the continuous pollutants initial reconstruction issues.