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Volumn , Issue , 2013, Pages 19-64

Modeling Across Scales: Discrete Geometric Structures in Homogenization and Inverse Homogenization

Author keywords

Calderon's problem; Electrical impedance; Harmonic coordinates; Homogenization; Incomplete measurements; Inverse homogenization

Indexed keywords

ELECTRIC IMPEDANCE MEASUREMENT; ELECTRIC IMPEDANCE TOMOGRAPHY; HISTOLOGY; HOMOGENIZATION METHOD; MEDICAL IMAGING; TISSUE;

EID: 84880817701     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9783527671632.ch02     Document Type: Chapter
Times cited : (8)

References (87)
  • 3
    • 0000989342 scopus 로고
    • Sulla convergenza di alcune successioni di integrali del tipo dell'aera
    • De Giorgi, E. (1975) Sulla convergenza di alcune successioni di integrali del tipo dell'aera. Rendi Conti di Mat., 8, 277-294.
    • (1975) Rendi Conti di Mat. , vol.8 , pp. 277-294
    • De Giorgi, E.1
  • 6
    • 0001083566 scopus 로고
    • Sulla convergenza di soluzioni di equazioni paraboliche ed ellittic
    • Spagnolo, S. (1968) Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche. Ann. Scuola Norm. Sup. Pisa (3), 22, 571-597, errata, ibid. (3) 22 (1968), 673.
    • (1968) Ann. Scuola Norm. Sup. Pisa , vol.3 , Issue.22 , pp. 571-597
    • Spagnolo, S.1
  • 7
    • 0017291333 scopus 로고
    • Convergence in energy for elliptic operators, Numerical solution of partial differential equations, III
    • Academic Press, New York
    • Spagnolo, S. (1976) Convergence in energy for elliptic operators, Numerical solution of partial differential equations, III. Proceedings of the Third Symposium (SYNSPADE), University of Maryland, College Park, MD, 1975, Academic Press, New York, pp. 469-498.
    • (1976) Proceedings of the Third Symposium (SYNSPADE), University of Maryland, College Park, MD , vol.1975 , pp. 469-498
    • Spagnolo, S.1
  • 10
    • 0000828256 scopus 로고
    • Generalized finite element methods: their performance and their relation to mixed methods
    • Babuška, I. and Osborn, J.E. (1983) Generalized finite element methods: their performance and their relation to mixed methods. SIAM J. Numer. Anal., 20 (3), 510-536.
    • (1983) SIAM J. Numer. Anal. , vol.20 , Issue.3 , pp. 510-536
    • Babuška, I.1    Osborn, J.E.2
  • 11
    • 0028483749 scopus 로고
    • Special finite element methods for a class of second order elliptic problems with rough coefficients
    • Babuška, I., Caloz, G., and Osborn, J.E. (1994) Special finite element methods for a class of second order elliptic problems with rough coefficients. SIAM J. Numer. Anal., 31. (4), 945-981.
    • (1994) SIAM J. Numer. Anal. , vol.31 , Issue.4 , pp. 945-981
    • Babuška, I.1    Caloz, G.2    Osborn, J.E.3
  • 13
    • 70349682431 scopus 로고    scopus 로고
    • Numerical coarsening of inhomogeneous elastic materials
    • Kharevych, L., Mullen, P., Owhadi, H., and Desbrun, M. (2009) Numerical coarsening of inhomogeneous elastic materials. ACM Trans. Graph., 28 (3), article no. 51.
    • (2009) ACM Trans. Graph. , vol.28 , Issue.3 , pp. 51
    • Kharevych, L.1    Mullen, P.2    Owhadi, H.3    Desbrun, M.4
  • 14
    • 55649097748 scopus 로고    scopus 로고
    • Homogenization of the acoustic wave equation with a continuum of scales
    • Owhadi, H. and Zhang, L. (2008) Homogenization of the acoustic wave equation with a continuum of scales. Comput. Method. Appl. Mech. Eng., 198 (3-4), 397-406.
    • (2008) Comput. Method. Appl. Mech. Eng. , vol.198 , Issue.3-4 , pp. 397-406
    • Owhadi, H.1    Zhang, L.2
  • 15
    • 34247218601 scopus 로고    scopus 로고
    • Metricbased upscaling
    • Owhadi, H. and Zhang, L. (2007) Metricbased upscaling. Comm. Pure Appl. Math., 60. (5), 675-723.
    • (2007) Comm. Pure Appl. Math. , vol.60 , Issue.5 , pp. 675-723
    • Owhadi, H.1    Zhang, L.2
  • 16
    • 55149085725 scopus 로고    scopus 로고
    • Homogenization of parabolic equations with a continuum of space and time scales
    • Owhadi, H. and Zhang, L. (2007/2008) Homogenization of parabolic equations with a continuum of space and time scales. SIAM J. Numer. Anal., 46 (1), 1-36.
    • (2007) SIAM J. Numer. Anal. , vol.46 , Issue.1 , pp. 1-36
    • Owhadi, H.1    Zhang, L.2
  • 17
    • 55249095137 scopus 로고    scopus 로고
    • George papanicolaou, and olivier pironneau, a framework for adaptive multiscale methods for elliptic problems
    • Nolen, J. (2008) George papanicolaou, and olivier pironneau, a framework for adaptive multiscale methods for elliptic problems. Multiscale Model. Simul., 7 (1), 171-196.
    • (2008) Multiscale Model. Simul. , vol.7 , Issue.1 , pp. 171-196
    • Nolen, J.1
  • 18
    • 0031161210 scopus 로고    scopus 로고
    • A multiscale finite element method for elliptic problems in composite materials and porous media
    • Hou, T.Y. and Wu, X.-H. (1997) A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys., 134 (1), 169-189.
    • (1997) J. Comput. Phys. , vol.134 , Issue.1 , pp. 169-189
    • Hou, T.Y.1    Wu, X.-H.2
  • 19
    • 34547343685 scopus 로고    scopus 로고
    • Subgrid upscaling and mixed multiscale finite elements
    • Arbogast, T. and Boyd, K.J. (2006) Subgrid upscaling and mixed multiscale finite elements. SIAM J. Numer. Anal., 44 (3), 1150-1171.
    • (2006) SIAM J. Numer. Anal. , vol.44 , Issue.3 , pp. 1150-1171
    • Arbogast, T.1    Boyd, K.J.2
  • 21
    • 58149492887 scopus 로고    scopus 로고
    • Asymptotic and numerical homogenization
    • Engquist, B. and Souganidis, P.E. (2008) Asymptotic and numerical homogenization. Acta Numerica, 17, 147-190.
    • (2008) Acta Numerica , vol.17 , pp. 147-190
    • Engquist, B.1    Souganidis, P.E.2
  • 22
    • 43149107662 scopus 로고    scopus 로고
    • Sparse second moment analysis for elliptic problems in stochastic domains
    • Harbrecht, H., Schneider, R., and Schwab, C. (2008) Sparse second moment analysis for elliptic problems in stochastic domains. Numer. Math., 109 (3), 385-414.
    • (2008) Numer. Math. , vol.109 , Issue.3 , pp. 385-414
    • Harbrecht, H.1    Schneider, R.2    Schwab, C.3
  • 23
    • 34047123580 scopus 로고    scopus 로고
    • Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients
    • Todor, R.A. and Schwab, C. (2007) Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients. IMA J. Numer. Anal., 27 (2), 232-261.
    • (2007) IMA J. Numer. Anal. , vol.27 , Issue.2 , pp. 232-261
    • Todor, R.A.1    Schwab, C.2
  • 24
    • 37649004216 scopus 로고    scopus 로고
    • A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs
    • Caffarelli, L.A. and Souganidis, P.E. (2008) A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs. Comm. Pure Appl. Math., 61 (1), 1-17.
    • (2008) Comm. Pure Appl. Math. , vol.61 , Issue.1 , pp. 1-17
    • Caffarelli, L.A.1    Souganidis, P.E.2
  • 25
    • 34547247032 scopus 로고    scopus 로고
    • Improved accuracy for alternatingdirection methods for parabolic equations based on regular and mixed finite elements
    • Arbogast, T., Huang, C.-S., and Yang, S.-M. (2007) Improved accuracy for alternatingdirection methods for parabolic equations based on regular and mixed finite elements. Math. Models Methods Appl. Sci., 17. (8), 1279-1305.
    • (2007) Math. Models Methods Appl. Sci. , vol.17 , Issue.8 , pp. 1279-1305
    • Arbogast, T.1    Huang, C.-S.2    Yang, S.-M.3
  • 26
    • 33846044694 scopus 로고    scopus 로고
    • Assessment of the cost and accuracy of the generalized FEM
    • Strouboulis, T., Zhang, L., and Babuška, I. (2007) Assessment of the cost and accuracy of the generalized FEM. Int. J. Numer. Methods Eng., 69 (2), 250-283.
    • (2007) Int. J. Numer. Methods Eng. , vol.69 , Issue.2 , pp. 250-283
    • Strouboulis, T.1    Zhang, L.2    Babuška, I.3
  • 27
    • 33751252248 scopus 로고    scopus 로고
    • Accurate multiscale finite element methods for two-phase flow simulations
    • Efendiev, Y., Ginting, V., Hou, T., and Ewing, R. (2006) Accurate multiscale finite element methods for two-phase flow simulations. J. Comput. Phys., 220 (1), 155-174.
    • (2006) J. Comput. Phys. , vol.220 , Issue.1 , pp. 155-174
    • Efendiev, Y.1    Ginting, V.2    Hou, T.3    Ewing, R.4
  • 28
    • 34247117648 scopus 로고    scopus 로고
    • Multiscale finite element methods for porous media flows and their applications
    • Efendiev, Y. and Hou, T. (2007) Multiscale finite element methods for porous media flows and their applications. Appl. Numer. Math., 57 (5-7), 577-596.
    • (2007) Appl. Numer. Math. , vol.57 , Issue.5-7 , pp. 577-596
    • Efendiev, Y.1    Hou, T.2
  • 29
    • 80051985075 scopus 로고    scopus 로고
    • Determining the anisotropic traction state in a membrane by boundary measurements
    • Alessandrini, G. and Cabib, E. (2007) Determining the anisotropic traction state in a membrane by boundary measurements. Inverse Probl. Imaging, 1 (3), 437-442.
    • (2007) Inverse Probl. Imaging , vol.1 , Issue.3 , pp. 437-442
    • Alessandrini, G.1    Cabib, E.2
  • 31
    • 0242330223 scopus 로고    scopus 로고
    • Univalent s -harmonic mappings: connections with quasiconformal mappings
    • Alessandrini, G. and Nesi, V. (2003) Univalent s -harmonic mappings: connections with quasiconformal mappings. J. Anal. Math., 90, 197-215.
    • (2003) J. Anal. Math. , vol.90 , pp. 197-215
    • Alessandrini, G.1    Nesi, V.2
  • 32
    • 85017420768 scopus 로고    scopus 로고
    • Owhadi reported in subsection 6.6.2
    • Ancona, A. (1999) Private communication between A. Ancona and H. Owhadi reported in subsection 6.6.2 of http://www. acm.caltech.edu/owhadi/publications/ phddownload.htm.
    • (1999) Private communication between A. Ancona and H
    • Ancona, A.1
  • 33
    • 0036520911 scopus 로고    scopus 로고
    • Some results and examples about the behavior of harmonic functions and Green's functions with respect to second order elliptic operators
    • Ancona, A. (2002) Some results and examples about the behavior of harmonic functions and Green's functions with respect to second order elliptic operators. Nagoya Math. J., 165, 123-158.
    • (2002) Nagoya Math. J. , vol.165 , pp. 123-158
    • Ancona, A.1
  • 34
    • 3142734882 scopus 로고    scopus 로고
    • Change of sign of the corrector's determinant for homogenization in threedimensional conductivity
    • Briane, M., Milton, G.W., and Nesi, V. (2004) Change of sign of the corrector's determinant for homogenization in threedimensional conductivity. Arch. Ration. Mech. Anal., 173 (1), 133-150.
    • (2004) Arch. Ration. Mech. Anal. , vol.173 , Issue.1 , pp. 133-150
    • Briane, M.1    Milton, G.W.2    Nesi, V.3
  • 37
    • 3042755624 scopus 로고    scopus 로고
    • Optimal Delaunay triangulations
    • Chen, L. and Xu, J. (2004) Optimal Delaunay triangulations. J. Comput. Math., 22. (2), 299-308.
    • (2004) J. Comput. Math. , vol.22 , Issue.2 , pp. 299-308
    • Chen, L.1    Xu, J.2
  • 38
    • 84950826016 scopus 로고
    • Computing discrete minimal surfaces and their conjugates
    • Pinkall, U. and Polthier, K. (1993) Computing discrete minimal surfaces and their conjugates. Exp. Math., 2 (1), 15-36.
    • (1993) Exp. Math. , vol.2 , Issue.1 , pp. 15-36
    • Pinkall, U.1    Polthier, K.2
  • 40
    • 37249009184 scopus 로고    scopus 로고
    • A monotonicity property for weighted Delaunay triangulations
    • Glickenstein, D. (2007) A monotonicity property for weighted Delaunay triangulations. Discrete Comp. Geom., 38. (4), 651-664.
    • (2007) Discrete Comp. Geom. , vol.38 , Issue.4 , pp. 651-664
    • Glickenstein, D.1
  • 42
    • 85017419483 scopus 로고    scopus 로고
    • version 3.3.1
    • CGAL, Computational Geometry Algorithms Library, version 3.3.1, http:// www.cgal.org. (accessed August 2007.).
    • (2007)
  • 44
    • 0002338788 scopus 로고
    • Effective characteristics of composite materials and the optimal design of structural elements
    • Lurie, K.A. and Cherkaev, A.V. (1986) Effective characteristics of composite materials and the optimal design of structural elements. Adv. Mech., 9 (2), 3-81.
    • (1986) Adv. Mech. , vol.9 , Issue.2 , pp. 3-81
    • Lurie, K.A.1    Cherkaev, A.V.2
  • 47
    • 0004181511 scopus 로고
    • Mathematical Concepts and Methods in Science and Engineering, Plenum Press, New York
    • Lurie, K.A. (1993) Applied Optimal Control Theory of Distributed Systems, Mathematical Concepts and Methods in Science and Engineering, Vol. 43, Plenum Press, New York.
    • (1993) Applied Optimal Control Theory of Distributed Systems , vol.143
    • Lurie, K.A.1
  • 51
    • 33846472514 scopus 로고    scopus 로고
    • Optimization of composite structures subject to local stress constraints
    • Lipton, R. and Stuebner, M. (2006) Optimization of composite structures subject to local stress constraints. Comput. Methods Appl. Mech. Eng., 196 (1-3), 66-75.
    • (2006) Comput. Methods Appl. Mech. Eng. , vol.196 , Issue.1-3 , pp. 66-75
    • Lipton, R.1    Stuebner, M.2
  • 52
    • 85017435136 scopus 로고    scopus 로고
    • (Progress in Nonlinear Differential Equations and their Applications), Birkhäuser Boston Inc., Boston, MA
    • Cherkaev, A. and Kohn, R. (eds) (1997) Topics in the Mathematical Modelling of Composite Materials, (Progress in Nonlinear Differential Equations and their Applications), Vol. 31, Birkhäuser Boston Inc., Boston, MA.
    • (1997) Topics in the Mathematical Modelling of Composite Materials , vol.31
    • Cherkaev, A.1    Kohn, R.2
  • 55
    • 67649545051 scopus 로고    scopus 로고
    • 2D EIT reconstructions using Calderón's method
    • MR 2375322 (2009c:35469)
    • Bikowski, J. and Mueller, J.L. (2008) 2D EIT reconstructions using Calderón's method. Inverse Probl. Imaging, 2 (1), 43-61. MR 2375322 (2009c:35469).
    • (2008) Inverse Probl. Imaging , vol.2 , Issue.1 , pp. 43-61
    • Bikowski, J.1    Mueller, J.L.2
  • 56
    • 21844471512 scopus 로고    scopus 로고
    • Lipschitz stability for the inverse conductivity problem
    • Alessandrini, G. and Vessella, S. (2005) Lipschitz stability for the inverse conductivity problem. Adv. Appl. Math., 35, 207-241.
    • (2005) Adv. Appl. Math. , vol.35 , pp. 207-241
    • Alessandrini, G.1    Vessella, S.2
  • 57
    • 0040817437 scopus 로고
    • Uniqueness and stability in multi-dimensional inverse problems
    • Isakov, V. (1993) Uniqueness and stability in multi-dimensional inverse problems. Inverse Probl., 9, 579-621.
    • (1993) Inverse Probl. , vol.9 , pp. 579-621
    • Isakov, V.1
  • 58
    • 84990583776 scopus 로고
    • Determining conductivity by boundary measurements
    • Kohn, R.V. and Vogelius, M. (1984) Determining conductivity by boundary measurements. Commun. Pure Appl. Math., 37, 113-123.
    • (1984) Commun. Pure Appl. Math. , vol.37 , pp. 113-123
    • Kohn, R.V.1    Vogelius, M.2
  • 59
    • 0001110912 scopus 로고
    • A global uniqueness theorem for an inverse boundary value problem
    • Sylvester, J. and Uhlmann, G. (1987) A global uniqueness theorem for an inverse boundary value problem. Ann. Math., 125, 153-169.
    • (1987) Ann. Math. , vol.125 , pp. 153-169
    • Sylvester, J.1    Uhlmann, G.2
  • 60
    • 0742323755 scopus 로고    scopus 로고
    • On nonuniqueness for Calderón's inverse problem
    • Greenleaf, A., Lassas, M., and Uhlmann, G. (2003) On nonuniqueness for Calderón's inverse problem. Math. Res. Lett., 10 (5), 685.
    • (2003) Math. Res. Lett. , vol.10 , Issue.5 , pp. 685
    • Greenleaf, A.1    Lassas, M.2    Uhlmann, G.3
  • 61
    • 17444429256 scopus 로고    scopus 로고
    • Calderon's inverse problem for anisotropic conductivity in the plane
    • Astala, K., Lassas, M., and Paivarinta, L. (2005) Calderon's inverse problem for anisotropic conductivity in the plane. Commun. Part. Diff. Eq., 30 (2), 207-224.
    • (2005) Commun. Part. Diff. Eq. , vol.30 , Issue.2 , pp. 207-224
    • Astala, K.1    Lassas, M.2    Paivarinta, L.3
  • 62
    • 0038439643 scopus 로고    scopus 로고
    • Anisotropic conductivities that cannot be detected by EIT
    • Greenleaf, A., Lassas, M., and Uhlmann, G. (2003) Anisotropic conductivities that cannot be detected by EIT. Physiol. Meas., 24, 412-420.
    • (2003) Physiol. Meas. , vol.24 , pp. 412-420
    • Greenleaf, A.1    Lassas, M.2    Uhlmann, G.3
  • 63
    • 0030550779 scopus 로고
    • Global uniqueness for a two-dimensional inverse boundary value problem
    • Nachman, A.I. (1995) Global uniqueness for a two-dimensional inverse boundary value problem. Ann. Math., 142, 71-96.
    • (1995) Ann. Math. , vol.142 , pp. 71-96
    • Nachman, A.I.1
  • 64
    • 84990586454 scopus 로고
    • An anisotropic inverse boundary value problem
    • Sylvester, J. (1990) An anisotropic inverse boundary value problem. Commun. Pure Appl. Math., 43, 201-232.
    • (1990) Commun. Pure Appl. Math. , vol.43 , pp. 201-232
    • Sylvester, J.1
  • 65
    • 33645778239 scopus 로고    scopus 로고
    • The inverse conductivity problem with an imperfectly known boundary
    • Kolehmainen, V., Lassas, M., and Ola, P. (2005) The inverse conductivity problem with an imperfectly known boundary. SIAM J. Appl. Math., 66 (2), 365-383.
    • (2005) SIAM J. Appl. Math. , vol.66 , Issue.2 , pp. 365-383
    • Kolehmainen, V.1    Lassas, M.2    Ola, P.3
  • 66
    • 34547282631 scopus 로고    scopus 로고
    • D-bar method for electrical impedance tomography with discontinuous conductivities
    • Knudsen, K., Lassas, M., Mueller, J.L., and Siltanen, S. (2007) D-bar method for electrical impedance tomography with discontinuous conductivities. SIAM J. Appl. Math., 67 (3), 893-913.
    • (2007) SIAM J. Appl. Math. , vol.67 , Issue.3 , pp. 893-913
    • Knudsen, K.1    Lassas, M.2    Mueller, J.L.3    Siltanen, S.4
  • 67
    • 29444435881 scopus 로고    scopus 로고
    • A remark on a paper by Alessandrini and Vessella
    • Rondi, L. (2006) A remark on a paper by Alessandrini and Vessella. Adv. Appl. Math., 36, 67-69.
    • (2006) Adv. Appl. Math. , vol.36 , pp. 67-69
    • Rondi, L.1
  • 68
    • 84957378692 scopus 로고    scopus 로고
    • Simulated annealing with asymptotic convergence for nonlinear constrained global optimization, in Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming, London, Lecture Notes in Computer Science, Vol
    • Wah, B.W. and Wang, T. (1999) Simulated annealing with asymptotic convergence for nonlinear constrained global optimization, in Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming, London, Lecture Notes in Computer Science, Vol. 1713, Springer, pp. 461-475.
    • (1999) 1713, Springer, pp. , pp. 461-475
    • Wah, B.W.1    Wang, T.2
  • 69
    • 44449098058 scopus 로고    scopus 로고
    • Electrical impedance tomography with resistor networks
    • Borcea, L., Druskin, V., and Vasquez, F.G. (2008) Electrical impedance tomography with resistor networks. Inverse Probl., 24. (3), 035013.
    • (2008) Inverse Probl. , vol.24 , Issue.3 , pp. 035013
    • Borcea, L.1    Druskin, V.2    Vasquez, F.G.3
  • 70
    • 0025448414 scopus 로고
    • Determining the resistors in a network
    • Curtis, E.B. and Morrow, J.A. (1990) Determining the resistors in a network. SIAM J. Appl. Math., 50 (3), 931-941.
    • (1990) SIAM J. Appl. Math. , vol.50 , Issue.3 , pp. 931-941
    • Curtis, E.B.1    Morrow, J.A.2
  • 73
    • 36149030663 scopus 로고
    • Analysis of bounded variation penalty methods for illposed problems
    • Acar, R. and Vogel, C.R. (1994) Analysis of bounded variation penalty methods for illposed problems. Inverse Probl., 10, 1217-1229.
    • (1994) Inverse Probl. , vol.10 , pp. 1217-1229
    • Acar, R.1    Vogel, C.R.2
  • 74
    • 1042279262 scopus 로고    scopus 로고
    • Penalized triograms: Total variation regularization for bivariate smoothing
    • Koenker, R. and Mizera, I. (2004) Penalized triograms: Total variation regularization for bivariate smoothing. J. Roy. Stat. Soc. B, 66 (1), 145-163.
    • (2004) J. Roy. Stat. Soc. B , vol.66 , Issue.1 , pp. 145-163
    • Koenker, R.1    Mizera, I.2
  • 75
    • 74349086162 scopus 로고    scopus 로고
    • On the regularization of the inverse conductivity problem with discontinuous conductivities
    • Rondi, L. (2008) On the regularization of the inverse conductivity problem with discontinuous conductivities. Inverse Probl. Imaging, 2 (3), 397-409.
    • (2008) Inverse Probl. Imaging , vol.2 , Issue.3 , pp. 397-409
    • Rondi, L.1
  • 77
    • 85017466867 scopus 로고    scopus 로고
    • GNU Linear Programming Kit (2009) http://www.gnu.org/software/glpk/.
    • (2009)
  • 79
    • 0142062405 scopus 로고    scopus 로고
    • Variationally constrained numerical solution of electrical impedance tomography
    • Borcea, L., Gray, G.A., and Zhang, Y. (2003) Variationally constrained numerical solution of electrical impedance tomography. Inverse Probl., 19, 1159-1184.
    • (2003) Inverse Probl. , vol.19 , pp. 1159-1184
    • Borcea, L.1    Gray, G.A.2    Zhang, Y.3
  • 80
    • 0026841764 scopus 로고
    • Convergence of a reconstruction method for the inverse conductivity problem
    • Dobson, D.C. (1992) Convergence of a reconstruction method for the inverse conductivity problem. SIAM J. Appl. Math., 52. (2), 442-458.
    • (1992) SIAM J. Appl. Math. , vol.52 , Issue.2 , pp. 442-458
    • Dobson, D.C.1
  • 81
    • 85017439684 scopus 로고    scopus 로고
    • version 3.2.4
    • IpOpt, Interior Point Optimizer, version 3.2.4 (2009) https://projects.coin-or.org/ Ipopt.
    • (2009)
  • 82
    • 33745160014 scopus 로고    scopus 로고
    • Imaging cardiac activity by the D-bar method for electrical impedance tomography
    • Isaacson, D.,Mueller, J.L., Newell, J.C., and Siltanen, S. (2006) Imaging cardiac activity by the D-bar method for electrical impedance tomography. Physiol. Meas., 27, S43-S50.
    • (2006) Physiol. Meas. , vol.27 , pp. S43-S50
    • Isaacson, D.1    Mueller, J.L.2    Newell, J.C.3    Siltanen, S.4
  • 83
    • 2342566028 scopus 로고    scopus 로고
    • Numerical solution method for the dbar-equation in the plane
    • Knudsen, K., Mueller, J.L., and Siltanen, S. (2004) Numerical solution method for the dbar-equation in the plane. J. Comput. Phys., 198, 500-517.
    • (2004) J. Comput. Phys. , vol.198 , pp. 500-517
    • Knudsen, K.1    Mueller, J.L.2    Siltanen, S.3
  • 85
    • 77950549009 scopus 로고    scopus 로고
    • Circular resistor networks for electrical impedance tomography with partial boundary measurements
    • Borcea, L., Druskin, V., and Mamonov, A.V. (2010) Circular resistor networks for electrical impedance tomography with partial boundary measurements. Inverse Probl., 26 (4), 045010.
    • (2010) Inverse Probl. , vol.26 , Issue.4 , pp. 045010
    • Borcea, L.1    Druskin, V.2    Mamonov, A.V.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.