We review some of the recent advances in level-set methods and their applications. In
particular, we discuss how to impose boundary conditions at irregular domains and free …

This review paper provides an overview of different level-set methods for structural topology
optimization. Level-set methods can be categorized with respect to the level-set-function …

ChatGPT is a large language model recently released by the OpenAI company. In this
technical report, we explore for the first time the capability of ChatGPT for programming …

This review focuses on direct numerical simulations (DNS) of turbulent flows laden with
droplets or bubbles. DNS of these flows are more challenging than those of flows laden with …

An overview of the extended/generalized finite element method (GEFM/XFEM) with
emphasis on methodological issues is presented. This method enables the accurate …

This paper presents a new approach to structural topology optimization. We represent the
structural boundary by a level set model that is embedded in a scalar function of a higher …

In this paper, we review the recent development of phase-field models and their numerical
methods for multi-component fluid flows with interfacial phenomena. The models consist of a …

Direct numerical simulations of multiphase flows, using a front-tracking method, are
presented. The method is based on writing one set of governing equations for the whole …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

We propose a new multiphase level set framework for image segmentation using the
Mumford and Shah model, for piecewise constant and piecewise smooth optimal …