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Applications of the Topological Derivative Method

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Applications of the Topological Derivative Method/ by Antonio André Novotny, Jan Sokołowski, Antoni Żochowski.
Author:	Novotny, Antonio André.
other author:	Sokołowski, Jan.
Description:	XIV, 212 p. 62 illus., 9 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Control engineering. -
Online resource:	https://doi.org/10.1007/978-3-030-05432-8
ISBN:	9783030054328

Applications of the Topological Derivative Method
Novotny, Antonio André.

Applications of the Topological Derivative Method[electronic resource] /by Antonio André Novotny, Jan Sokołowski, Antoni Żochowski. - 1st ed. 2019. - XIV, 212 p. 62 illus., 9 illus. in color.online resource. - Studies in Systems, Decision and Control,1882198-4182 ;. - Studies in Systems, Decision and Control,27.

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:

1249728
Control engineering.

LC Class. No.: TJ212-225

Dewey Class. No.: 629.8

Applications of the Topological Derivative Method
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