Leseprobe
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Applications of the Topological Derivative Method
Jan Sokołowski, Antonio André Novotny, Antoni Żochowski, et al.
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Springer International Publishing 
Naturwissenschaften, Medizin, Informatik, Technik / Elektronik, Elektrotechnik, Nachrichtentechnik
Beschreibung
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.
Kundenbewertungen
Topological Derivative Method, Topological Derivatives for Optimal Control Problems, Newton-Type Method and Applications, Steklov-Poincare´ Operator for Helmholtz Equation, Singularly Perturbed Geometrical Domains