An efficient framework is described for the shape and topology optimization of realistic three-
dimensional, weakly-coupled fluid-thermal-mechanical systems. At the theoretical level, the …

We introduce a novel method for Gaussian process (GP) modeling of massive datasets
called globally approximate Gaussian process (GAGP). Unlike most large-scale supervised …

This chapter is an introduction to shape and topology optimization, with a particular
emphasis on the method of Hadamard for appraising the sensitivity of quantities of interest …

A new level set method is developed for multi-material structural topology optimization. The
method features in using the discontinuous Galerkin finite-element method for discretization …

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 energy dissipation minimization constrained by steady Navier–Stokes
flows. The nonlinearity of the Navier–Stokes equation causes its numerical solver …

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 …

The optimization of shape functionals under convexity, diameter or constant width
constraints shows numerical challenges. The support function can be used in order to …

We discuss automating the calculation of weak shape derivatives in the Unified Form
Language (ACM TOMS 40 (2): 9: 1–9: 37 2014) by introducing an appropriate additional …

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 …