## NUMERICAL APPROXIMATION AND ANALYSIS OF BLOCK-CENTERED FINITE VOLUME ELEMENT METHOD FOR ELECTRICAL IMPEDANCE TOMOGRAPHY

Published: 2016-11-11

Page: 130-149

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

#### How to Cite

LI, J., YUAN, Y., LI, C., & SUN, T. (2016). NUMERICAL APPROXIMATION AND ANALYSIS OF BLOCK-CENTERED FINITE VOLUME ELEMENT METHOD FOR ELECTRICAL IMPEDANCE TOMOGRAPHY. Asian Journal of Mathematics and Computer Research, 14(2), 130–149. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/682