Electrical resistance tomography for locating inclusions using analytical boundary element integrals and their partial derivatives

Engineering Analysis with Boundary Elements

Volumn 34, Issue 10, 2010, Pages 876-883

  Xu, Yaoyuan ^a   Dong, Feng ^a   Tan, Chao ^a  

^a TIANJIN UNIVERSITY   (China)

Author keywords

Boundary element method; Complete electrode model; Electrical resistance tomography; Levenberg Marquardt method

Indexed keywords

ANALYTICAL INTEGRATION; BOUNDARY ELEMENT INTEGRALS; COMPLETE ELECTRODE MODEL; ELECTRICAL CONDUCTIVITY DISTRIBUTION; ELECTRICAL RESISTANCE TOMOGRAPHY; FORWARD PROBLEM; HIGHER ORDER; ILL-POSED INVERSE PROBLEM; LEVENBERG-MARQUARDT METHOD; NON-INTRUSIVE TECHNIQUES; PARTIAL DERIVATIVES; QUADRATIC ELEMENT; SYSTEM MATRICES;

ELECTRIC CONDUCTIVITY; ELECTRIC NETWORK ANALYSIS; ELECTRIC RESISTANCE; INVERSE PROBLEMS; TOMOGRAPHY;

BOUNDARY ELEMENT METHOD;

EID: 77953700178     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2010.05.008     Document Type: Article

References (34)

1. Barber C.C., and Brown B.H. Imaging spatial distributions of resistivity using applied potential tomography. Electron Lett 19 (1983) 933-935
2. Dickin F., and Wang M. Electrical resistance tomography for process applications. Meas Sci Technol 7 (1996) 247-260
3. Fransolet E., Crine M., Marchot P., and Toye D. Analysis of gas holdup in bubble columns with non-Newtonian fluid using electrical resistance tomography and dynamic gas disengagement technique. Chem Eng Sci 60 (2005) 6118-6123
4. Koh C.S., Kim M.K., Jung H.K., Hahn S.Y., and Suh B.S. Electric resistivity tomography for geophysical inverse problems. IEEE Trans Magn 33 (1997) 1852-1855
5. Ikehata M. Enclosing a polygonal cavity in a two-dimensional bounded domain from Cauchy data. Inverse Probl 15 (1999) 1231-1241
6. Ikehata M., and Ohe T. A numerical method for finding the convex hull of polygonal cavities using the enclosure method. Inverse Probl 18 (2002) 111-124
7. Brühl M., and Hanke M. Numerical implementation of two noniterative methods for locating inclusions by impedance tomography. Inverse Probl 16 (2000) 1029-1042
8. Brühl M. Explicit characterization of inclusions in electrical impedance tomography. SIAM J Math Anal 32 (2001) 1327-1341
9. Bryan K. Numerical recovery of certain discontinuous electrical conductivities. Inverse Probl 7 (1991) 827-840
10. Kang H., Seo J.K., and Sheen D. Numerical identification of discontinuous conductivity coefficients. Inverse Probl 13 (1997) 113-123
11. Kress R., and Rundell W. Nonlinear integral equations and iterative solution for an inverse boundary value problem. Inverse Probl 21 (2005) 1207-1223
12. Ivanyshyn O., and Kress R. Nonlinear integral equations for solving inverse boundary value problems for inclusions and cracks. J Integral Equ Appl 18 (2006) 13-38
13. Eckel H., and Kress R. Nonlinear integral equations for the inverse electrical impedance problem. Inverse Probl 23 (2007) 475-491
14. Ito K., Kunisch K., and Li Z. Level-set function approach to an inverse interface problem. Inverse Probl 17 (2001) 1225-1242
15. Chung E.T., Chan T.F., and Tai X.C. Electrical impedance tomography using level set representation and total variational regularization. J Comput Phys 205 (2005) 357-372
16. Karageorghis A., and Lesnic D. Detection of cavities using the method of fundamental solutions. Inverse Probl Sci Eng 17 (2009) 803-820
17. Borman D., Ingham D.B., Johansson B.T., and Lesnic D. The method of fundamental solutions for detection of cavities in EIT. J Integr Equ Appl 21 (2009) 381-404
18. Lesnic D. A numerical investigation of the inverse potential conductivity problem in a circular inclusion. Inverse Probl Eng 9 (2001) 1-17
19. de Munck J.C., Faes T.J., and Heethaar R.M. The boundary element method in the forward and inverse problem of electrical impedance tomography. IEEE Trans Biomed Eng 47 (2000) 792-800
20. Babaeizadeh S., and Brooks D.H. Electrical impedance tomography for piecewise constant domains using boundary element shape-based inverse solutions. IEEE Trans Med Imaging 26 (2007) 637-647
21. Aykroyd R.G., and Cattle B.A. A boundary-element approach for the complete-electrode model of EIT illustrated using simulated and real data. Inverse Probl Sci Eng 15 (2007) 441-461
22. Tarvainen M., Vauhkonen M., Savolainen T., and Kaipio J.P. Boundary element method and internal electrodes in electrical impedance tomography. Int J Numer Meth Eng 50 (2001) 809-824
23. Mera N.S., and Lesnic D. A boundary element method for the numerical inversion of discontinuous anisotropic conductivities. Eng Anal Boundary Elem 27 (2003) 1-7
24. Duraiswami R., Sarkar K., and Chahine G.L. Boundary element techniques for efficient 2-D and 3-D electrical impedance tomography. Chem Eng Sci 52 (1997) 2185-2196
25. Duraiswami R., Sarkar K., and Chahine G.L. Efficient 2D and 3D electrical impedance tomography using dual reciprocity boundary element techniques. Eng Anal Boundary Elem 22 (1998) 13-31
26. Ingham D.B., Heggs P.J., and Manzoor M. The numerical solution of plane potential problems by improved boundary integral equation methods. J Comput Phys 42 (1981) 77-79
27. Fratantonio M., and Rencis J.J. Exact boundary element integrations for two dimensional Laplace equation. Eng Anal Boundary Elem 24 (2000) 325-342
28. Brown B.H., and Seagar A.D. The Sheffield data collection system. Clin Phys Physiol Meas 8 Suppl A (1987) 91-97
29. Cheng K.S., Isaacson D., Newell J.C., and Gisser D.G. Electrode models for electric current computed tomography. IEEE Trans Biomed Eng 36 (1989) 918-924
30. More J.J. The Levenberg-Marquardt algorithm: implementation and theory. In: Watson G.A. (Ed). Lecture Notes in Mathematics 630: Numerical Analysis (1978), Springer-Verlag, Berlin
31. Marin L., and Lesnic D.B.E.M. first-order regularisation method in linear elasticity for boundary identification. Comput Meth Appl Mech Eng 192 (2003) 2059-2071
32. Marin L., and Lesnic D. The method of fundamental solutions for the Cauchy problem associated with two-dimensional Helmholtz-type equations. Comput Struct 83 (2005) 267-278
33. Marin L. Numerical boundary identification for Helmholtz-type equations. Comput Mech 39 (2006) 25-40
34. Giguere R., Fradette L., Mignon D., and Tanguy P.A. ERT algorithms for quantitative concentration measurement of multiphase flows. Chem Eng J 141 (2008) 305-317