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 …

In this article we consider shape optimization problems as optimal control problems via the
method of mappings. Instead of optimizing over a set of admissible shapes, a reference …

We introduce a Monte Carlo method for computing derivatives of the solution to a partial
differential equation (PDE) with respect to problem parameters (such as domain geometry or …

Immersed finite element (IFE) methods are a group of long-existing numerical methods for
solving interface problems on unfitted meshes. A core argument of the methods is to avoid a …

We propose in this paper two kinds of continuity preserving discrete shape gradients of
boundary type for PDE-constrained shape optimizations. First, a modified boundary shape …

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 …

In this paper, we present a method that combines the Boundary Element Method (BEM) with
IsoGeometric Analysis (IGA) for numerically solving the system of Boundary Integral …

We study the iterated quasi-reversibility method to regularize ill-posed elliptic and parabolic
problems: data completion problems for Poisson's and heat equations. We define an …

This article presents a finite element method on a fixed mesh for solving a group of inverse
geometric problems for recovering the material interface of a linear elasticity system. A …

We investigate the reconstruction of an unknown cavity inside a heat conductor with only
single boundary measurement, which is a typical non-destructive testing of defects in …