The determination of inhomogeneous permeability coefficient was studied as a parameter-control inverse problem for parabolic-type equation in this paper. By virtue of PST, the solution of the inverse problem is conver...The determination of inhomogeneous permeability coefficient was studied as a parameter-control inverse problem for parabolic-type equation in this paper. By virtue of PST, the solution of the inverse problem is converted into an iteration procedure of solving a direct problem and solving a Fredholm integral equation of the first kind. Besides, Tikhonov normalization method is introduced to treat the uncertainty caused by the integral equation. Thus an algorithm for determining inhomogeneous permeability coefficient has been formulated and implemented. Numerical results show: (1) The algorithm presented in the paper is suitable to strongly inhomogeneous seepagel; (2) The additional information needed for solution is merely the seepage velocity on partical boundary, so that drill works can be reduced remarkably; (3) The algorithm is applicable to determining inhomogeneous transmission coefficients in groundwater engineering or other engineering.展开更多
文摘The determination of inhomogeneous permeability coefficient was studied as a parameter-control inverse problem for parabolic-type equation in this paper. By virtue of PST, the solution of the inverse problem is converted into an iteration procedure of solving a direct problem and solving a Fredholm integral equation of the first kind. Besides, Tikhonov normalization method is introduced to treat the uncertainty caused by the integral equation. Thus an algorithm for determining inhomogeneous permeability coefficient has been formulated and implemented. Numerical results show: (1) The algorithm presented in the paper is suitable to strongly inhomogeneous seepagel; (2) The additional information needed for solution is merely the seepage velocity on partical boundary, so that drill works can be reduced remarkably; (3) The algorithm is applicable to determining inhomogeneous transmission coefficients in groundwater engineering or other engineering.
