Research On Numerical Solution Of Electrical Impedance Tomography

The theoretical research of electrical impedance imaging(EIT)has important research significance in engineering and natural sciences.It belongs to the multidisciplinary application theory category,and it is particularly widely applied in natural sciences such as resource exploration,pipeline industry,and medical diagnosis.In fact,such problems can be attributed to the solution of elliptic partial differential equations.Due to the non-linearity and ill-posedness of this type of equation,it is difficult to find its exact solution.Therefore,it is very important to find an effective numerical solution method.This paper mainly uses the elliptic equation of electrical impedance imaging as the research background,combined with the finite element method,Spectral methods,regularized Gaussian Newton iteration method,Seek Optimization Algorithm,in-depth analysis and research on the numerical solutions of its positive and negative problems.The main research work carried out in this paper is as follows:(1)Based on the analysis of the background,significance and the research status of electrical impedance imaging technology at home and abroad,the current research status and research significance of the positive problem of the electrical impedance imaging elliptic equation and the inverse problem of parameter identification are analyzed.(2)Solve the positive problem of the elliptic equation by using the spectral method,perform the parameter inversion by the Seek Optimization Algorithm(SOA),and enumerate the numerical simulation of different types of parameters.compare and analyze the results,and verify that the proposed algorithm is effective and feasible;(3)The finite element method and the regularized Gauss-Newton method is used to solve the positive problem of electrical impedance imaging and its inverse problem.And it chose different regularization parameters are selected for numerical simulation and result analysis.