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《Mathematica Numerica Sinica》 2008-01
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SIMULATION AND ANALYSIS OF FINITE VOLUME METHOD FOR 3-DIMENSIONAL ELECTRICAL IMPEDANCE TOMOGRAPHY

Li Jiuping Yuan Yirang (School of Mathematics and System Sciences,Shandong University,Jinan 250100,China)  
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.
【Fund】: 国家重点基础研究专项经费(G1999032803);; 国家自然科学基金(10372052,10271066);; 教育部博士点基金(20030422047)资助项目
【CateGory Index】: O241
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