We present a coupling of the reduced basis methods and free-form deformations for shape
optimization and design of systems modelled by elliptic PDEs. The free-form deformations …

Recent progress in PDE constrained optimization on shape manifolds is based on the
Hadamard form of shape derivatives, ie, in the form of integrals at the boundary of the shape …

We compare surface metrics for shape optimization problems with constraints, consisting
mainly of partial differential equations (PDE), from a computational point of view. In …

This article introduces a novel method for the implementation of shape optimisation with
Lipschitz domains. We propose to use the shape derivative to determine deformation fields …

We develop a mathematical foundation for shape optimization problems under state
equation constraints where both state and control are discretized by B-splines or NURBS. In …

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

In this paper, we present an isogeometric analysis framework for design space exploration.
While the methodology is presented in the setting of structural mechanics, it is applicable to …

Shapes do not define a linear space. This paper explores the linear structure of
deformations as a representation of shapes. This transforms shape optimization to a variant …

As a specific type of shape gradient descent algorithm, shape gradient flow is widely used
for shape optimization problems constrained by partial differential equations. In this …

Shape optimization is of interest in many fields of application. In particular, shape
optimization problems arise frequently in technological processes which are modelled by …