This is a book on Optimal Control Problems (OCPs): how to formulate them, how to set up a
suitable mathematical framework for their analysis, how to approximate them numerically …

This paper discusses the topology optimization of unsteady incompressible Navier–Stokes
flows. An optimization problem is formulated by adding the artificial Darcy frictional force into …

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 …

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 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 …

We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the
Navier--Stokes equations. Inside a holdall container we use a phase field approach using …

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 …

Recent research has used deep learning to develop partial differential equation (PDE)
models in science and engineering. The functional form of the PDE is determined by a …

Shape gradients have been widely used in numerical shape gradient descent algorithms for
shape optimization. The two types of shape gradients, ie, the distributed one and the …

In this paper we present a method for estimating unknown parameters that appear on an
avascular, spheric tumor growth model. The model for the tumor is based on nutrient driven …