TOPOLOGICAL DERIVATIVE METHOD FOR ELECTRICAL IMPEDANCE TOMOGRAPHY PROBLEMS

Allaire G., de Gournay F., Jouve F., Toader A.M.: Structural optimization using topological and shape sensitivity via a level set method. Control and Cybernetics 34(1), 2005, 59–80.
  Google Scholar

Allaire G., Jouve F., Van Goethem N.: Damage and fracture evolution in brittle materials by shape optimization methods. Journal of Computational Physics 230(12), 2011, 5010–5044.
  Google Scholar

Ammari H., Garnier J., Jugnon V., Kang H.: Stability and resolution analysis for a topological derivative based imaging functional. SIAM Journal on Control and Optimization 50(1), 2012, 48–76.
  Google Scholar

Ammari H., Kang H.: High-order terms in the asymptotic expansions of the steady-state voltage potentials in the presence of inhomogeneities of small diameter. SIAM Journal on Mathematical Analysis 34(5), 2003, 1152–1166.
  Google Scholar

Ammari H., Kang H.: Reconstruction of small inhomogeneities from boundary measurements. Lectures Notes in Mathematics vol. 1846. Springer-Verlag, Berlin 2004.
  Google Scholar

Amstutz S.: Sensitivity analysis with respect to a local perturbation of the material property. Asymptotic Analysis 49(1–2), 2006, 87–108.
  Google Scholar

Amstutz S.: A penalty method for topology optimization subject to a pointwise state constraint. ESAIM: Control, Optimisation and Calculus of Variations 16(3), 2010, 523–544.
  Google Scholar

Amstutz S., Andrä H.: A new algorithm for topology optimization using a level-set method. Journal of Computational Physics 216(2), 2006, 573–588.
  Google Scholar

Amstutz S., Giusti S.M., Novotny A.A., de Souza Neto E.A.: Topological derivative for multiscale linear elasticity models applied to the synthesis of microstructures. International Journal for Numerical Methods in Engineering 84, 2010, 733–756.
  Google Scholar

Amstutz S., Horchani I., Masmoudi M.: Crack detection by the topological gradient method. Control and Cybernetics 34(1), 2005, 81–101.
  Google Scholar

Amstutz S., Novotny A.A.: Topological optimization of structures subject to von Mises stress constraints. Structural and Multidisciplinary Optimization 41(3), 2010, 407–420.
  Google Scholar

Amstutz S., Novotny A.A., de Souza Neto E.A.: Topological derivative-based topology optimization of structures subject to Drucker-Prager stress constraints. Computer Methods in Applied Mechanics and Engineering 233–236, 2012, 123–136 [DOI: 10.1016/j.cma.2012.04.004].
  Google Scholar

Auroux D., Masmoudi M., Belaid L.: Image restoration and classification by topological asymptotic expansion. Variational formulations in mechanics: theory and applications. Spain, Barcelona 2007.
  Google Scholar

Belaid L.J., Jaoua M., Masmoudi M., Siala L.: Application of the topological gradient to image restoration and edge detection. Engineering Analysis with Boundary Elements 32, 2008, 891–899.
  Google Scholar

Bojczuk D., Mróz Z.: Topological sensitivity derivative and finite topology modications: application to optimization of plates in bending. Structural and Multidisciplinary Optimization 39, 2009, 1–15.
  Google Scholar

Bonnet M.: Higher-order topological sensitivity for 2-D potential problems. International Journal of Solids and Structures 46(11–12), 2009, 2275–2292.
  Google Scholar

Burger M., Hackl B., Ring W.: Incorporating topological derivatives into level set methods. Journal of Computational Physics 194(1), 2004, 344–362.
  Google Scholar

Calderón A.P.: On an inverse boundary value problem. Computational and Applied Mathematics 25(2–3), 2006. Reprinted from the Seminar on Numerical Analysis and its Applications to Continuum Physics, Sociedade Brasileira de Matemática, Rio de Janeiro, 1980.
  Google Scholar

Canelas A., Laurain A., Novotny A.A.: A new reconstruction method for the inverse potential problem. Journal of Computational Physics 268, 2014, 417–431.
  Google Scholar

Canelas A., Laurain A., Novotny A.A.: A new reconstruction method for the inverse source problem from partial boundary measurements. Inverse Problems 31(7), 2015, 075009.
  Google Scholar

Canelas A., Novotny A.A., Roche J.R.: A new method for inverse electromagnetic casting problems based on the topological derivative. Journal of Computational Physics 230, 2011, 3570–3588.
  Google Scholar

de Faria J.R., Novotny A.A.: On the second order topological asymptotic expansion. Structural and Multidisciplinary Optimization 39(6), 2009, 547–555.
  Google Scholar

Feijóo G.R.: A new method in inverse scattering based on the topological derivative. Inverse Problems 20(6), 2004, 1819–1840.
  Google Scholar

Feijáo R.A., Novotny A.A., Taroco E., Padra C.: The topological derivative for the Poisson's problem. Mathematical Models and Methods in Applied Sciences 13(12), 2003, 1825–1844.
  Google Scholar

Garreau S., Guillaume Ph., Masmoudi M.: The topological asymptotic for PDE systems: the elasticity case. SIAM Journal on Control and Optimization 39(6), 2001, 1756–1778.
  Google Scholar

Giusti S.M., Novotny A.A., de Souza Neto E.A.: Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions. Proceeding of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, 2010, 1703–1723.
  Google Scholar

Giusti S.M., Novotny A.A., de Souza Neto E.A., Feijóo R.A.: Sensitivity of the macroscopic elasticity tensor to topological microstructural changes. Journal of the Mechanics and Physics of Solids 57(3), 2009, 555–570.
  Google Scholar

Giusti S.M., Novotny A.A., de Souza Neto E.A., Feijóo R.A.: Sensitivity of the macroscopic thermal conductivity tensor to topological microstructural changes. Computer Methods in Applied Mechanics and Engineering 198(5–8), 2009, 727–739, [DOI: 10.1016/j.cma.2008.10.005].
  Google Scholar

Giusti S.M., Novotny A.A., Sokołowski J.: Topological derivative for steady-state orthotropic heat diffusion problem. Structural and Multidisciplinary Optimization 40(1), 2010, 53–64.
  Google Scholar

Guzina B.B., Bonnet M.: Small-inclusion asymptotic of misfit functionals for inverse problems in acoustics. Inverse Problems 22(5), 2006, 1761–1785.
  Google Scholar

Hintermüller M.: Fast level set based algorithms using shape and topological sensitivity. Control and Cybernetics 34(1), 2005, 305–324.
  Google Scholar

Hintermüller M., Laurain A.: Electrical impedance tomography: from topology to shape. Control and Cybernetics 37(4), 2008, 913–933.
  Google Scholar

Hintermüller M., Laurain A.: Multiphase image segmentation and modulation recovery based on shape and topological sensitivity. Journal of Mathematical Imaging and Vision 35, 2009, 1–22.
  Google Scholar

Hintermüller M., Laurain A., Novotny A.A.: Second-order topological expansion for electrical impedance tomography. Advances in Computational Mathematics 36(2), 2012, 235–265.
  Google Scholar

Hlaváček I., Novotny A.A., Sokołowski J., Żochowski A.: On topological derivatives for elastic solids with uncertain input data. Journal of Optimization Theory and Applications 141(3), 2009, 569–595.
  Google Scholar

Jackowska-Strumiłło L., Sokołowski J., Żochowski A., Henrot A.: On numerical solution of shape inverse problems. Computational Optimization and Applications 23(2), 2002, 231–255.
  Google Scholar

Khludnev A.M., Novotny A.A., Sokołowski J., Żochowski A.: Shape and topology sensitivity analysis for cracks in elastic bodies on boundaries of rigid inclusions. Journal of the Mechanics and Physics of Solids 57(10), 2009, 1718–1732.
  Google Scholar

Kobelev V.: Bubble-and-grain method and criteria for optimal positioning inhomogeneities in topological optimization. Structural and Multidisciplinary Optimization 40(1–6), 2010, 117–135.
  Google Scholar

Larrabide I., Feijóo R.A., Novotny A.A., Taroco E.: Topological derivative: a tool for image processing. Computers & Structures 86(13–14), 2008, 1386–1403.
  Google Scholar

Leugering G., Sokołowski J.: Topological derivatives for elliptic problems on graphs. Control and Cybernetics 37, 2008, 971–998.
  Google Scholar

Lewinski T., Sokołowski J.: Energy change due to the appearance of cavities in elastic solids. International Journal of Solids and Structures 40(7), 2003, 1765–1803.
  Google Scholar

Masmoudi M., Pommier J., Samet B.: The topological asymptotic expansion for the Maxwell equations and some applications. Inverse Problems 21(2), 2005, 547–564.
  Google Scholar

Nazarov S.A., Sokołowski J.: Asymptotic analysis of shape functionals. Journal de Mathématiques Pures et Appliquées 82(2), 2003, 125–196.
  Google Scholar

Nazarov S.A., Sokołowski J.: Self-adjoint extensions of differential operators in application to shape optimization. Comptes Rendus Mecanique 331, 2003, 667–672.
  Google Scholar

Nazarov S.A., Sokołowski J.: Singular perturbations in shape optimization for the Dirichlet Laplacian. Comptes rendus - Mécanique 333(4), 2005, 305–310.
  Google Scholar

Nazarov S.A., Sokołowski J.: Self-adjoint extensions for the Neumann laplacian and applications. Acta Mathematica Sinica (English Series) 22(3), 2006, 879–906.
  Google Scholar

Nazarov S.A., Sokołowski J.: On asymptotic analysis of spectral problems in elasticity. Latin American Journal of Solids and Structures 8, 2011, 27–54.
  Google Scholar

Novotny A.A., Feijóo R.A., Padra C., Taroco E.: Topological sensitivity analysis. Computer Methods in Applied Mechanics and Engineering 192(7–8), 2003, 803–829.
  Google Scholar

Novotny A.A., Feijóo R.A., Padra C., Taroco E.: Topological derivative for linear elastic plate bending problems. Control and Cybernetics 34(1), 2005, 339–361.
  Google Scholar

Novotny A.A., Feijóo R.A., Taroco E., Padra C.: Topological sensitivity analysis for three dimensional linear elasticity problem. Computer Methods in Applied Mechanics and Engineering 196(41–44), 2007, 4354–4364.
  Google Scholar

Novotny A.A., Sokołowski J.: Topological derivatives in shape optimization. Interaction of Mechanics and Mathematics. Springer-Verlag, Berlin, Heidelberg 2013.
  Google Scholar

Novotny A.A., Sokołowski J., de Souza Neto E.A.: Topological sensitivity analysis of a multiscale constitutive model considering a cracked microstructure. Mathematical Methods in the Applied Sciences 33(5), 2010, 676–686.
  Google Scholar

Sankowski D., Sikora J.: Electrical Capacitance Tomography: Theoretical Basis and Applications. Electrotechnical Institute, Poland, Miedzylesie 2010.
  Google Scholar

Sikora J.: Boundary Element Method for Impedance and Optical Tomography. Oficyna Wydawnicza Politechniki Warszawskiej, Poland, Warsaw 2007.
  Google Scholar

Sikora J., Wójtowicz S.: Industrial and Biological Tomography: Theoretical Basis and Applications. Electrotechnical Institute, Poland, Miedzylesie 2010.
  Google Scholar

Sokołowski J., Żochowski A.: On the topological derivative in shape optimization. SIAM Journal on Control and Optimization 37(4), 1999, 1251–1272.
  Google Scholar

Sokołowski J., Żochowski A.: Optimality conditions for simultaneous topology and shape optimization. SIAM Journal on Control and Optimization 42(4), 2003, 1198–1221.
  Google Scholar

Sokołowski J., Żochowski A.: Modelling of topological derivatives for contact problems. Numerische Mathematik 102(1), 2005, 145–179.
  Google Scholar

Turevsky I., Gopalakrishnan S.H., Suresh K.: An ecient numerical method for computing the topological sensitivity of arbitrary-shaped features in plate bending. International Journal for Numerical Methods in Engineering 79(13), 2009, 1683–1702.
  Google Scholar

Van Goethem N., Novotny A.A.: Crack nucleation sensitivity analysis. Mathematical Methods in the Applied Sciences 33(16), 2010, 1978–1994.
  Google Scholar