The present monograph is intended to provide a comprehensive and accessible introduction
to the optimization of elliptic systems. This area of mathematical research, which has many …

Three-dimensional modeling and numerical analysis utilizing computers are conducted on a
day-to-day basis in product design, and there is a growing interest in the optimization of …

Probability functions depending upon parameters are represented as integrals over sets
given by inequalities. New derivative formulas for the intergrals over a volume are …

This paper is concerned with the computation of the drag T associated with a body traveling
at uniform velocity in a fluid governed by the stationary Navier--Stokes equations. It is …

We present a review of known results in shape optimization from the point of view of
Geometric Analysis. This paper is devoted to the mathematical aspects of the shape …

In shape optimization problems, each computation of the cost function by the finite element
method leads to an expensive analysis. The use of the second order derivative can help to …

In this paper, we present a framework for automated shape differentiation in the finite
element software NGSolve. Our approach combines the mathematical Lagrangian approach …

We are interested in the question of stability in the field of shape optimization, with focus on
the strategy using second order shape derivative. More precisely, we identify structural …

The paper is concerned with the solution of nonlinear ill-posed problems by methods that
utilize the second derivative. A general predictor-corrector approach is developed; one …

The object of this paper is to study the shape Hessian of a shape functional by the velocity
(speed) method. It contains a review and an extension of the velocity method and its …