Research On Genetic Algorithm Of The Inverse Problem For Two-Dimensional Partial Differential Equation

Inverse problem of partial differential equation is an interdisciplinary and frontier science. It has great significance not only in theory but also in practice. In this paper a systematic research is made on the theory, solution, analytical approach and engineering application of two-dimensional partial differential equation inverse problem, specifically including the following aspects:(1) The paper puts forth a general descriptive concept of inverse problem of partial differential equation as well as an exact definition and offers a classification of differential equation inverse problem.(2) Practical examples of partial differential equation inverse problem are provided in the paper. The paper points out inverse problem's wide application, its variety and complexity as well as the significance of its solution in the field of practical application. A general introduction of the most recent achievements on inverse problem is also given in the paper.(3) The high nonlinear and ill-posed inverse problems are also discussed in the paper. Study the traditional methods' pros and cons, we can make aconclusion: If we do not choose the special methods, we cannot get the rational result to such a problem. According to the numerous characteristics of the genetic algorithm, It is being used to solve inverse problem of differential equation. Research shows that genetic algorithms are very suitable for solving a great many inverse problem of partial differential equation. It opens up a new approach for solving inverse problem of differential equation.(4) In order to solve the inverse problem, we must go on the solving of corresponding direct problem at first. In this paper, numerous calculations for solving differential equation are being compared. Meanwhile, the ADI method and finite element are used for solving parabolic and elliptic equation, respectively. Both of the equations are two-Dimensional.(5) A numerical calculation program is written up for the various solution methods in this paper and the program is being used in various aspects of inverse problem of practical application, including the inverse problem of the source of convection-diffusion, identification of the steady-state permeability for two dimensional isotropic medium, two-dimensional steady inverse problem of convection-diffusion and parameter identification inverse problem for two-dimensional parabolic equation, etc.