This review presents developments in structural shape optimization post 2000 from
perspective of numerical analysis techniques. Traditional shape optimization with FEM has …

DOLFINx is the next generation problem solving environment from the FEniCS Project; it
provides an expressive and performant environment for solving partial differential equations …

We present a novel isogeometric method, namely the Immersed Boundary-Conformal
Method (IBCM), that features a layer of discretization conformal to the boundary while …

In this article, we propose a shape optimization algorithm which is able to handle large
deformations while maintaining a high level of mesh quality. Based on the method of …

We consider shape optimization problems subject to elliptic partial differential equations. In
the context of the finite element method, the geometry to be optimized is represented by the …

We introduce Fireshape, an open-source and automated shape optimization toolbox for the
finite element software Firedrake. Fireshape is based on the moving mesh method and …

In this article we propose a scalable shape optimization algorithm which is tailored for large
scale problems and geometries represented by hierarchically refined meshes. Weak …

The multimesh finite element method is a technique for solving partial differential equations
on multiple non-matching meshes by enforcing interface conditions using Nitsche's method …

We analyze a new framework for expressing finite element methods on arbitrarily many
intersecting meshes: multimesh finite element methods. The multimesh finite element …