Differential Equations and Numerical Analysis Seminar - 21/03/2012

Wednesday, 21 March 2012, 12:00 p.m.

Lecturer: Anca-Maria Toader, CMAF - Universidade de Lisboa

Title: "The Adjoint Method in Optimization of eigenvalues and eigenmodes".

Local: Room 1.5, Edifício VII
Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: The Adjoint Method goes back to the works of Pontryagin in the framework of Ordinary Differential Equations. In the eighties, J. Cea employed the Adjoint Method in a practical way, from the perspective of Lagrange multipliers. Since then, applications of the Adjoint Method were successfully used in Shape Optimization, Topology Optimization and very recently to optimize eigenvalues and eigenmodes. Some examples will be discussed in each case and a special emphasis will be given to the Adjoint Method applied to the optimization of eigenvalues and eigenmodes. In this framework the direct problem does not involve a bilinear form and a linear form as in usual applications. However it is possible to follow the spirit of the method and deduce N adjoint problems and to obtain N adjoint states, where N is the number of eigenvalues to be optimized. This study was motivated by a real optimization problem coming from the necessity of non-destructive damage detection in concrete dams.