The use of node coordinates as design variables in shape optimization offers a larger
design space than computer-aided design (CAD)-based shape parameterizations. It also …

The phase-field method is based on the energy minimization principle which is a geometric
method for modelling diffusive cracks that are popularly implemented with irreversibility …

In the last decade, parameter-free approaches to shape optimization problems have
matured to a state where they provide a versatile tool for complex engineering applications …

We review how diffeologies complete the settings classically used from infinite dimensional
geometry to partial differential equations, based on classical settings of functional analysis …

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 …

We investigate a complex system involving multiple shapes to be optimized in a domain,
taking into account geometric constraints on the shapes and uncertainty appearing in the …

Abstract Spaces where each element describes a shape, so-called shape spaces, are of
particular interest in shape optimization and its applications. Theory and algorithms in shape …

Shape optimization models with one or more shapes are considered in this chapter. Of
particular interest for applications are problems in which a so-called shape functional is …

Airfoil shape design is a classical problem in engineering and manufacturing. In this work,
we combine principled physics-based considerations for the shape design problem with …

Deformations of the computational mesh, arising from optimization routines, usually lead to
decrease of mesh quality or even destruction of the mesh. We propose a theoretical …