一维分层Boussinesq方程反问题的设计与求解  

Design and Solution of Inverse Problem of One-Dimensional Layered Boussinesq Equation

作　　者：金裕红[1] 左雷浩 

机构地区：[1]海军工程大学基础部,湖北武汉

出　　处：《理论数学》2019年第5期563-567,共5页Pure Mathematics

摘　　要：在均匀地质中,渗透系数通常是一个常数,与空间位置无关。在非均匀地质中,渗透系数就是一个与所在空间位置相关的函数,随着空间位置的变化而变化。但是在实际处理非均匀地质的问题时,我们可以将非均匀地质近似为多层均匀地质构成,相应地,渗透系数通常可以近似为一个分段常数函数,即在每一个时空网格单元中,都可以视之为一个常数值。本文将给出分层Boussinesq方程的描述、实例设计、反问题离散化求解方法、实例数值验证等给出反问题的解决过程,并验证算法的有效性。In homogeneous geology,the permeability coefficient is usually a constant,independent of spatial location.In heterogeneous geology,the permeability coefficient is a function related to the spatial position and changes with the spatial position.However,when dealing with the problem of hetero-geneous geology in practice,we can approximate the heterogeneous geology as a multi-layer uni-form geological composition.Correspondingly,the permeability coefficient can generally be ap-proximated as a piecewise constant function,that is,in each space-time grid unit,it can be regarded as a constant value.This paper will give the description of layered Boussinesq equation,instance design,discretization solution method of inverse problem,numerical verification of instance,and give the solution process of inverse problem,and verify the effectiveness of the algorithm.

关 键 词：反问题 BOUSSINESQ方程 分层 

分 类 号：G6[文化科学—教育学]