Topological Derivatives in Shape Optimization

• Domain Derivation in Continuum Mechanics.- Material and Shape Derivatives for Boundary Value Problems.- Singular Perturbations of Energy Functionals.- Configurational Perturbations of Energy Functionals.- Topological Derivative Evaluation with Adjoint States.- Topological Derivative for Steady-State Orthotropic Heat Diffusion Problems.- Topological Derivative for Three-Dimensional Linear Elasticity Problems.- Compound Asymptotic Expansions for Spectral Problems.- Topological Asymptotic Analysis for Semilinear Elliptic Boundary Value Problems.- Topological Derivatives for Unilateral Problems.

From the reviews: "The main aim of the presented book is the presentation of topological derivatives for a wide class of elliptic problems with the applications in numerical methods of shape and topology optimization. This volume is primarily addressed to applied mathematicians working in the field of partial differential equations and their applications, especially those concerned with numerical aspects. However, the book will also be useful for applied scientists from engineering and physics." (Jan Lovisek, zbMATH, Vol. 1276, 2014) "The book under review concerns new methods of solving a class of shape optimization problems appearing in continuum mechanics, mainly in solid mechanics, composites and plate-like bodies. ... The theoretical results are illustrated by numerical examples. Moreover, carefully selected exercises are provided. This valuable book fills a gap in the literature on topology optimization." (Tomasz Lewinski, Mathematical Reviews, August, 2013)