地下水环境对解逆问题的数学模型及其优化分析

Analysis of The Mathematic Method and Value Solution With the Combination of Groundwater Environment

研究了偏微分方程定解问题的逆问题分类,结合地下水流,建立了解逆问题的数学模型,归纳了逆问题的特点,并较全面的分析了逆问题的数值解法,对试估校正法、高斯牛顿法、数学规化法等做了深入分析,同时讨论了目前国内外流行的3种全局优化方法:模拟退火法、模拟进化法和神经网络法.对不同方法的优缺点及适用情况做了分析,阐述了各种数值方法的合理性和优越性.研究结果表明,无论是直接方法还是间接方法都各有利弊,各有使用条件,可根据具体情况具体分析,选取哪种方法与所求参数个数、观测资料多少、计算机计算时长,以及优化后结果可靠性等因素来确定.另外,笔者分析的数值解法与优化,可在类似地下水资源评估和地下水流场计算中推广应用.

This article studies the classification of the inverse problem with partial differential equation and creates the mathematic model of the solution to the inverse problem with ground water flow, analyzes the value solution to the inverse problem and, Gauss-Newton method, deeply. It also debates three global optimize methods-stimulated annealing algorithm,stimulated evolution and neural network, which are prevalent at present. It makes an analysis of the advantages and disadvantages, application and elaborates the rationality and superiority of all kinds of value solutions. In the addition, the value solution and optimize method analyzed in this article can be extended to the application of the evaluation of the analogous groundwater resource and the calculation of groundwater flow field.