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Applications of the topological deri...

Novotny, Antonio Andre.

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Applications of the topological derivative method

Record Type:	Electronic resources : Monograph/item
Title/Author:	Applications of the topological derivative method/ by Antonio Andre Novotny, Jan Sokolowski, Antoni Zochowski.
Author:	Novotny, Antonio Andre.
other author:	Sokolowski, Jan.
Published:	Cham :Springer International Publishing : : 2019.,
Description:	xiv, 212 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction -- Theory in Singularly Perturbed Geometrical Domains -- Steklov-Poincare' Operator for Helmholtz Equation -- Topological Derivatives for Optimal Control Problems -- Optimality Conditions with Topological Derivatives -- A Gradient-Type Method and Applications -- Synthesis of Compliant Thermomechanical Actuators -- Synthesis of Compliant Piezomechanical Actuators -- Asymptotic Analysis of Variational Inequalities -- A Newton-Type Method and Applications -- The Electrical Impedance Tomography Problem.
Contained By:	Springer eBooks
Subject:	Topological dynamics. -
Online resource:	https://doi.org/10.1007/978-3-030-05432-8
ISBN:	9783030054328

Applications of the topological derivative method
Novotny, Antonio Andre.

Applications of the topological derivative method[electronic resource] /by Antonio Andre Novotny, Jan Sokolowski, Antoni Zochowski. - Cham :Springer International Publishing :2019. - xiv, 212 p. :ill., digital ;24 cm. - Studies in systems, decision and control,v.1882198-4182 ;. - Studies in systems, decision and control ;v.188..

Introduction -- Theory in Singularly Perturbed Geometrical Domains -- Steklov-Poincare' Operator for Helmholtz Equation -- Topological Derivatives for Optimal Control Problems -- Optimality Conditions with Topological Derivatives -- A Gradient-Type Method and Applications -- Synthesis of Compliant Thermomechanical Actuators -- Synthesis of Compliant Piezomechanical Actuators -- Asymptotic Analysis of Variational Inequalities -- A Newton-Type Method and Applications -- The Electrical Impedance Tomography Problem.

The book presents new results and applications of the topological derivative method in control theory, topology optimization and inverse problems. It also introduces the theory in singularly perturbed geometrical domains using selected examples. Recognized as a robust numerical technique in engineering applications, such as topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena, the topological derivative method is based on the asymptotic approximations of solutions to elliptic boundary value problems combined with mathematical programming tools. The book presents the first order topology design algorithm and its applications in topology optimization, and introduces the second order Newton-type reconstruction algorithm based on higher order topological derivatives for solving inverse reconstruction problems. It is intended for researchers and students in applied mathematics and computational mechanics interested in the mathematical aspects of the topological derivative method as well as its applications in computational mechanics.

ISBN: 9783030054328

Standard No.: 10.1007/978-3-030-05432-8doiSubjects--Topical Terms:

621854
Topological dynamics.

LC Class. No.: QA611.5 / .N686 2019

Dewey Class. No.: 512.55

Applications of the topological derivative method
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100 1 $a Novotny, Antonio Andre. $3 3383398
245 1 0 $a Applications of the topological derivative method $h [electronic resource] / $c by Antonio Andre Novotny, Jan Sokolowski, Antoni Zochowski.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a xiv, 212 p. : $b ill., digital ; $c 24 cm.
490 1 $a Studies in systems, decision and control, $x 2198-4182 ; $v v.188
505 0 $a Introduction -- Theory in Singularly Perturbed Geometrical Domains -- Steklov-Poincare' Operator for Helmholtz Equation -- Topological Derivatives for Optimal Control Problems -- Optimality Conditions with Topological Derivatives -- A Gradient-Type Method and Applications -- Synthesis of Compliant Thermomechanical Actuators -- Synthesis of Compliant Piezomechanical Actuators -- Asymptotic Analysis of Variational Inequalities -- A Newton-Type Method and Applications -- The Electrical Impedance Tomography Problem.
520 $a The book presents new results and applications of the topological derivative method in control theory, topology optimization and inverse problems. It also introduces the theory in singularly perturbed geometrical domains using selected examples. Recognized as a robust numerical technique in engineering applications, such as topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena, the topological derivative method is based on the asymptotic approximations of solutions to elliptic boundary value problems combined with mathematical programming tools. The book presents the first order topology design algorithm and its applications in topology optimization, and introduces the second order Newton-type reconstruction algorithm based on higher order topological derivatives for solving inverse reconstruction problems. It is intended for researchers and students in applied mathematics and computational mechanics interested in the mathematical aspects of the topological derivative method as well as its applications in computational mechanics.
650 0 $a Topological dynamics. $3 621854
650 1 4 $a Control and Systems Theory. $3 3381515
650 2 4 $a Vibration, Dynamical Systems, Control. $3 893843
650 2 4 $a Systems Theory, Control. $3 893834
700 1 $a Sokolowski, Jan. $3 3383399
700 1 $a Zochowski, Antoni. $3 3383400
710 2 $a SpringerLink (Online service) $3 836513
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830 0 $a Studies in systems, decision and control ; $v v.188. $3 3383401
856 4 0 $u https://doi.org/10.1007/978-3-030-05432-8
950 $a Intelligent Technologies and Robotics (Springer-42732)