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Applications of the topological deri...

Novotny, Antonio Andre.

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Applications of the topological derivative method

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Applications of the topological derivative method/ by Antonio Andre Novotny, Jan Sokolowski, Antoni Zochowski.
作者:	Novotny, Antonio Andre.
其他作者:	Sokolowski, Jan.
出版者:	Cham :Springer International Publishing : : 2019.,
面頁冊數:	xiv, 212 p. :ill., digital ;24 cm.
內容註:	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
標題:	Topological dynamics. -
電子資源:	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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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.
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