Shape gradients of PDE constrained shape functionals can be stated in two equivalent ways. Both rely on the solutions of two boundary value problems (BVPs), but one involves integrating their traces on the boundary of the domain, while the other evaluates integrals in the volume. Usually, the two BVPs can only be solved approximately, for instance, by finite element methods. However, when used with finite element solutions, the equivalence of the two formulas breaks down. By means of a comprehensive convergence analysis, we establish that the volume based expression for the shape gradient generally offers better accuracy in a finite element setting. The results are confirmed by several numerical experiments
This paper presents a numerical analysis method of nonparametric bound-ary shape optimization proble...
In this thesis we develop a functional analytic framework for shape optimization with elliptic parti...
Shape optimization based on analytical shape derivatives is meanwhile a well-established tool in eng...
Shape gradients of PDE constrained shape functionals can be stated in two equivalent ways. Both rely...
Shape gradients of shape differentiable shape functionals constrained to an interface problem (IP) c...
In this article, we consider the problem of optimal design of a compliant structure under a volume c...
We consider PDE constrained shape optimization in the framework of finite element discretization of ...
In this paper we investigate and compare different gradient algorithms designed for the domain expre...
A numerical analysis technique is presented for solving optimization prob-lems of geometrical domain...
We consider PDE constrained shape optimization in the framework of nite element discretizationof th...
This paper concerns the problem identifying geometrical boundary shapes of domains in which elliptic...
A general framework for calculating shape derivatives for domain optimization problems with partial ...
We present and compare two different methods for numerically solving boundary value problems of grad...
We present a variational framework for shape optimization problems that establishes clear and explic...
In the present paper we consider the minimization of gradient tracking functionals defined on a comp...
This paper presents a numerical analysis method of nonparametric bound-ary shape optimization proble...
In this thesis we develop a functional analytic framework for shape optimization with elliptic parti...
Shape optimization based on analytical shape derivatives is meanwhile a well-established tool in eng...
Shape gradients of PDE constrained shape functionals can be stated in two equivalent ways. Both rely...
Shape gradients of shape differentiable shape functionals constrained to an interface problem (IP) c...
In this article, we consider the problem of optimal design of a compliant structure under a volume c...
We consider PDE constrained shape optimization in the framework of finite element discretization of ...
In this paper we investigate and compare different gradient algorithms designed for the domain expre...
A numerical analysis technique is presented for solving optimization prob-lems of geometrical domain...
We consider PDE constrained shape optimization in the framework of nite element discretizationof th...
This paper concerns the problem identifying geometrical boundary shapes of domains in which elliptic...
A general framework for calculating shape derivatives for domain optimization problems with partial ...
We present and compare two different methods for numerically solving boundary value problems of grad...
We present a variational framework for shape optimization problems that establishes clear and explic...
In the present paper we consider the minimization of gradient tracking functionals defined on a comp...
This paper presents a numerical analysis method of nonparametric bound-ary shape optimization proble...
In this thesis we develop a functional analytic framework for shape optimization with elliptic parti...
Shape optimization based on analytical shape derivatives is meanwhile a well-established tool in eng...