TOPOLOGICAL DERIVATIVE - THEORY AND APPLICATIONS

Katarzyna Szulc

doi:10.5604/20830157.1148040

Open full text

pdf (Język Polski)

Published: Mar 31, 2015

DOI: https://doi.org/10.5604/20830157.1148040

Issue Vol. 5 No. 1 (2015)

Articles

BIAŁYSTOK UNIVERSITY OF TECHNOLOGY, FACULTY OF ELECTRICAL ENGINEERING - DEVELOPMENT AND NEW CHALLENGES
Bogusław Butryło

3-6
TOPOLOGICAL DERIVATIVE - THEORY AND APPLICATIONS
Katarzyna Szulc

7-13
EXAMINATION OF EMERGENCY LIGHTING SYSTEM FOR PASSENGER SHIPS AND FERRIES
Małgorzata Zalesińska, Krzysztof Wandachowicz

14-19
AN INTERVAL TYPE-2 FUZZY SYSTEMS IN THE MANAGEMENT OF EMISSIONS OF NITROGEN OXIDES
Marcin Kacprowicz

20-23
FUZZY EVALUATION OF VISUAL CONNECTEDNESS IN THERMOGRAPHY IMAGES OF CYLINDRICAL SURFACE
Tomasz Jaworski, Jacek Kucharski

24-28
OBJECT-RELATIONAL MAPPING TECHNOLOGIES IN PHP APPLICATIONS
Beata Pańczyk, Arkadiusz Sławiński

29-32
IMPLEMENTATION OF FUZZY CONTROL ALGORITHM FOR PHOTOVOLTAIC ARRAY MAXIMUM POWER POINT TRACKING
Stefan Wójtowicz, Maciej Zawistowski

33-36
BENCHMARKING OF POWER DISTRIBUTION SYSTEMS
Mirosław Dechnik, Szczepan Moskwa

37-44
IMPLEMENTATION OF BASIC INTEGRATION METHODS IN APP INVENTOR ENVIRONMENT AND THEIR EFFICIENCY
Kamil Żyła

45-48
MOBILE DEVICES AS ACCELERATION RECORDERS
Jakub Smołka, Maria Skublewska-Paszkowska, Marcin Badurowicz, Edyta Łukasik

49-52
POSSIBILITIES OF STAND-OFF DETECTION OF ALCOHOL IN CAR CABINS WITH WINDOWS
Jarosław Młyńczak, Krzysztof Kopczyński, Jan Kubicki, Jadwika Mierczyk

53-58
AUTOMATIC IDENTIFICATION METHOD OF BLURRED IMAGES
Mikolaj Karpinski, Nazarii Piontko, Volodymyr Karpinskyi

59-61
EXAMINATION OF HEATING PROCESS OF FILTERS PROTECTING AGAINST HAZARDOUS INFRARED RADIATION
Grzegorz Gralewicz, Grzegorz Owczarek, Janusz Kubrak

62-65
INFORMATION TECHNOLOGY IMPLEMENTATIONS AND LIMITATIONS IN MEDICAL RESEARCH
Marcin Maciejewski

66-72
RELIABILITY ANALYSIS OF PWR REACTOR PROTECTION SYSTEM
Karol Kowal, Mieczysław Borysiewicz

73-79
USING THE GPU TO DETERMINING THE AREA THE FLAME IN THE VISION DIAGNOSTIC SYSTEM
Daniel Sawicki

80-85
AUTOMATED SYSTEM TO CONTROL A ROBOT’S MOVEMENT ON COMPLEX TRAJECTORY WITH AVOIDING OBSTACLES BASED ON FUZZY LOGIC
Oksana Radion

86-92
ALGORITHMIC REALIZATION IMPACTS ASSESSMENT FOR RENEWABLE SOURCES ELECTRIC POWER ON RELIABILITY ELECTRICAL NETWORKS
Dymitr Sobczuk

93-100

DOI

https://doi.org/10.5604/20830157.1148040

Authors

Katarzyna Szulc

Katarzyna.Szulc@ibspan.waw.pl

Polish Academy of Sciences, Systems Research Institute, Poland

Abstract

The paper is devoted to present some mathematical aspects of the topological derivative and its applications in different fields of sciences such as shape optimization and inverse problems. First the definition of the topological derivative is given and the shape optimization problem is formulated. Next the form of the topological derivative is evaluated for a mixed boundary value problem defined in a geometrical domain. Finally, an example of an application of the topological derivative in the electric impedance tomography is presented.

Keywords:

Topological derivative, shape optimization, electrical impedance tomography

References

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.

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.

Hintermüller M., Laurain A.: Electrical inpedance tomography: from topology to shape, Control and Cybernetics 37(4), 2008, 913-933.

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.

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.

Leugering G., Sokołowski J.: Topological derivative for elliptic problems on graphs, Control and Cybernetics 37, 2008, 917-998.

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.

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.

Nazarov S.A., Sokołowski J.: Asymptotic analysis of shape functionals, Journal de Mathématiques pures et appliquées, 2003, Vol. 82, 125-196.

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.

Novotny A. A., Sokołowski J.: Topological Derivatives in Shape Optimization, Interaction of Mechanics and Mathematics, Springer, 2013.

Sokołowski J., Zolésio J.-P.: Introduction to shape optimization. Shape sensitivity analysis. Springer-Verlag, 1992, New York.

Sokołowski J., Zochowski A.: On topological derivative in shape optimization, SIAM Journal on Control and Optimization, 1999, Vol. 37, No. 4, 1251-1272.

Sokołowski J., Zochowski A.: Topological derivatives of shape functionals for elasticity systems, Mechanics of Structures and Machines, 2001, Vol. 29, 333-351.

Sokołowski J., Zochowski A.: Modeling of Topological Derivatives for Contact Problems, Numerische Mathematik, 2003, Vol. 102, No. 1, 145-179.

Szulc K.: Quelques méthode numérique en optimisation de formes, Ph.D. Thesis, 2010.

Szulc, K. (2015). TOPOLOGICAL DERIVATIVE - THEORY AND APPLICATIONS. Informatyka, Automatyka, Pomiary W Gospodarce I Ochronie Środowiska, 5(1), 7–13. https://doi.org/10.5604/20830157.1148040

TOPOLOGICAL DERIVATIVE - THEORY AND APPLICATIONS

Issue Vol. 5 No. 1 (2015)

Archives

DOI

Authors

Abstract

Keywords:

References

License

Article Sidebar

Issue Vol. 5 No. 1 (2015)

Archives

Main Article Content

DOI

Authors

Abstract

Keywords:

References

Article Details

License