{"title":"Numerical Solution of the Inverse Problem of Electrical\nImpedance Tomography Using the Iteration Method","authors":"A. A. Afanasyeva, A. V. Starchenko","doi":"10.1134/S199047892404001X","DOIUrl":null,"url":null,"abstract":"<p> A computational algorithm has been developed for solving the inverse problem of electrical\nimpedance tomography in a complete electrode model, which is an inverse coefficient problem for\na difference scheme built on unstructured grids for an elliptic equation with integro-differential\nboundary conditions. The iteration algorithm is based on the iterative regularized Gauss–Newton\nmethod in which the inverse matrix of the main matrix of the system of linear equations is\ncalculated; the derivatives of the main matrix whose coefficients depend linearly on conductivity\nare found analytically. The implementation of the computational algorithm is performed for the\ntwo-dimensional case of a 16-electrode disk model with one insert. The influence of the choice of\nthe initial approximation and the error in the input data on the convergence of the iteration\nprocess has been studied.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 4","pages":"631 - 642"},"PeriodicalIF":0.5800,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S199047892404001X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
A computational algorithm has been developed for solving the inverse problem of electrical
impedance tomography in a complete electrode model, which is an inverse coefficient problem for
a difference scheme built on unstructured grids for an elliptic equation with integro-differential
boundary conditions. The iteration algorithm is based on the iterative regularized Gauss–Newton
method in which the inverse matrix of the main matrix of the system of linear equations is
calculated; the derivatives of the main matrix whose coefficients depend linearly on conductivity
are found analytically. The implementation of the computational algorithm is performed for the
two-dimensional case of a 16-electrode disk model with one insert. The influence of the choice of
the initial approximation and the error in the input data on the convergence of the iteration
process has been studied.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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