NUMERICAL APPROXIMATION AND ANALYSIS OF BLOCK-CENTERED FINITE VOLUME ELEMENT METHOD FOR ELECTRICAL IMPEDANCE TOMOGRAPHY
JIUPING LI
Institute of Mathematics, Shandong University, 250100, Jinan, P.R.China
YIRANG YUAN *
Institute of Mathematics, Shandong University, 250100, Jinan, P.R.China
CHANGFENG LI
Institute of Mathematics, Shandong University, 250100, Jinan, P.R.China
TONGJUN SUN
Institute of Mathematics, Shandong University, 250100, Jinan, P.R.China
*Author to whom correspondence should be addressed.
Abstract
Electrical impedance tomography is described by an inverse problem of an elliptic equation, which is simulated numerically on three-dimensional region. For the elliptic equation with Neumann boundary value condition, a conservative block-centered finite volume element scheme is discussed in this paper. This procedure is semi-positive definite and its numerical solution exists. Error functional computational formula of Jacobi matrix is concluded, and direct problems can be computed in a minimum number by the collecting usage of the symmetry of finite volume element scheme and the special base vectors of the electric current. A series of numerical experimental tests are given to illustrate the reliability of mathematical model and the algorithmic feasibility. These methods have been applied in actual numerical simulations of multi-dimensional electrical impedance tomography.
Keywords: Multi-dimensional electric impedance tomography, finite volume element, stability, numerical simulation, graph reestablishment