Applications of the Topological Derivative Method

• 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 is well written, and the examples treated are carefully motivated. The references are up-to-date. The material presented in the book requires good mathematical background, so that the book could be used, as usefull reference, for researchers and graduate students that are working in the optimization theory.”(Teodor Atanacković, zbMATH 1460.74001, 2021)“The book under review provides an excellent overview of historical and current developments in the field and, at the same time, is a very good introduction to readers familiar with linear elliptic equations and variational inequalities. … In all chapters, a thorough literature discussion is provided along with a detailed discussion of open problems.” (Guenter Leugering, Mathematical Reviews, October, 2019)