SIMULATION AND ANALYSIS OF FINITE VOLUME METHOD FOR 3-DIMENSIONAL ELECTRICAL IMPEDANCE TOMOGRAPHY
三维电阻抗成像的体积元方法的数值模拟和分析

Electrical impedance tomography is an inverse problem of elliptic differential equations, numerical simulation and analysis for it in 3-dimensional domain are presented.In this paper a modified symmetric finite volume element method is proposed,positive semi-definiteness and existence of solution for this scheme are proved;element geometry matrix is introduced, which is helpful for simplifying the calculation of coefficient matrix;patch approximation for electrical resistivity is present to lower the scale of this inverse problem;the computational formula of Jacobian matrix of error functional is obtained,a class of electrical current pat- terns is proposed,under which the number of direct problems to be solved at each iteration can be reduced to the least.A series of numerical experiments verify the reliability of its mathematical model and the feasibility of the algorithm.These methods have been applied successfully in practical simulation of electrical impedance tomography.