TOPOLOGICAL DERIVATIVE - THEORY AND APPLICATIONS

Belaid L.J., Jaoua M., Masmoudi M., Siala L.: Application of the topological gradient to image restoration and edge detection, Engineering Analysis with Boundary Element 32(11), 2008, 891-899.
  Google Scholar

Fulmanski P., Lauraine A., Scheid J.-F., Sokołowski J.: A level set method in shape and topology optimization for variational inequalities, Int. J. Appl. Math. Comput. Sci., 2007, Vol. 17, No. 3, 413-430.
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Hintermüller M., Laurain A.: Electrical inpedance tomography: from topology to shape, Control and Cybernetics 37(4), 2008, 913-933.
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Hintermüller M., Laurain A., Novotny A.A.: Second-order topological expansion for electrical impedance tomography, Advances in Computational Mathematics, February 2012, Vol. 36, Issue 2, 235-265.
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Iguernane M., Nazarov S.A., Roche J.-R., Sokolowski J., Szulc K.: Topological derivatives for semilinear elliptic equations, Int. J. Appl. Math. Comput. Sci., 2009, Vol. 19, No. 2, 191-205.
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Leugering G., Sokołowski J.: Topological derivative for elliptic problems on graphs, Control and Cybernetics 37, 2008, 917-998.
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Mazja V.G., Nazarov S.A., Plomenevskii B.A.: Asymptotic theory of elliptic boundary value problems in singularly perturbed domains, Vol. 1, Basel: Birkhäuser Verlag, 2000.
  Google Scholar

Nazarov S. A.: The damage tensor and measures. 1. Asymptotic analysis of anisotropic media with defects, Mekh. Tverd. Tela, Vol. 3, 2000, 113–124, in Russian; English transl.: Mech. Solids 35, Vol. 3, 2000, 96–105.
  Google Scholar

Nazarov S.A., Sokołowski J.: Asymptotic analysis of shape functionals, Journal de Mathématiques pures et appliquées, 2003, Vol. 82, 125-196.
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Nazarov S.A., Sokołowski J.: Self-adjoint Extensions for the Neumann Laplacian and Applications, Acta Math. Sin. (Engl. Ser.), 2006, Vol. 22, No. 3, 879-906.
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Novotny A. A., Sokołowski J.: Topological Derivatives in Shape Optimization, Interaction of Mechanics and Mathematics, Springer, 2013.
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Sokołowski J., Zolésio J.-P.: Introduction to shape optimization. Shape sensitivity analysis. Springer-Verlag, 1992, New York.
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Sokołowski J., Zochowski A.: On topological derivative in shape optimization, SIAM Journal on Control and Optimization, 1999, Vol. 37, No. 4, 1251-1272.
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Sokołowski J., Zochowski A.: Topological derivatives of shape functionals for elasticity systems, Mechanics of Structures and Machines, 2001, Vol. 29, 333-351.
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Sokołowski J., Zochowski A.: Modeling of Topological Derivatives for Contact Problems, Numerische Mathematik, 2003, Vol. 102, No. 1, 145-179.
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Szulc K.: Quelques méthode numérique en optimisation de formes, Ph.D. Thesis, 2010.
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