# Sensitivity Analysis: The Direct and Adjoint Method

## Dipl.-Ing. Markus Kollmann

**Jan. 19, 2010, 3:30 p.m. P 215**

Shape optimization is widely used in practice. The typical problem is to ﬁnd the optimal shape which minimizes/maximizes a certain cost functional and satisﬁes some given constraints. Usually shape optimization problems are solved numerically, by some iterative method. But also some gradient information is needed.

There are two approaches to provide such information using shape derivatives: the direct approach and the adjoint approach.

In this talk the diﬀerent approaches, for getting gradient information of the functional, will be presented and then the focus is to compare them. It will be shown that the adjoint approach has a great advantage, but that there also exist examples, where the adjoint technique does not work in the sense we will introduce it.