Distributed shape derivative via averaged adjoint method and applications

摘要: The structure theorem of Hadamard–Zolesio states that the derivative a shape functional is distribution on boundary domain depending only normal perturbations smooth enough boundary. Actually representation, also known as distributed derivative, more general than expression it well-defined for shapes having lower regularity. It customary in optimization literature to assume regularity domains and use numerical algorithms. In this paper we describe several advantages terms generality, easiness computation implementation. We identify tensor representation study its properties show how allows recover directly. novel Lagrangian approach, which applicable large class problems, compute derivative. apply technique retrieve electrical impedance tomography. Finally explain adapt level set method framework present results.