相关论文: Approximation and application of minimizing moveme…

In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…

This paper is devoted to the robust approximation with a variational phase field approach of multiphase mean curvature flows with possibly highly contrasted mobilities. The case of harmonically additive mobilities has been addressed…

Highway vehicular traffic is an inherently multi-agent problem. Traffic jams can appear and disappear mysteriously. We develop a method for traffic flow control that is applied at the vehicular level via mean-field games. We begin this work…

We suggest a finite element method for computing minimal surfaces based on computing a discrete Laplace-Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a…

Level set method has been used to capture interface motion. Narrow band algorithm is applied to localize the solving of level-set PDE on global domain to a tube around interface. Due to the unknown evolving interface, narrow band algorithm…

Brownian dynamics of colloidal particles on complex surfaces has found important applications in diverse physical, chemical and biological processes. However, current Brownian dynamics simulation algorithms mostly work for relatively simple…

The Wasserstein gradient flow structure of the PDE system governing multiphase flows in porous media was recently highlighted in [C. Canc\`es, T. O. Gallou\"et, and L. Monsaingeon, {\it Anal. PDE} 10(8):1845--1876, 2017]. The model can thus…

We introduce a new method, the Local Monge Parametrizations (LMP) method, to approximate tensor fields on general surfaces given by a collection of local parametrizations, e.g.~as in finite element or NURBS surface representations. Our goal…

This work explores an extension of machine learning-optimized piecewise polynomial approximation by incorporating energy optimization as an additional objective. Traditional closed-form solutions enable continuity and approximation targets…

The numerical simulation of realistic reactive flows is a major challenge due to the stiffness and high dimension of the corresponding kinetic differential equations. Manifold-based model reduction techniques address this problem by…

Fluid flow applications can involve a number of coupled problems. One is the simulation of free-surface flows, which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled…

Built upon previous work of the authors in (Deckelnick, Herbert, and Hinze, ESAIM: COCV 28 (2022)), we present a general shape optimisation framework based on the method of mappings in the $W^{1,\infty}$ topology together with a suitable…

Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding…

The paper addresses the numerical approximation of two variants of hyperbolic mean curvature flow of surfaces in $\mathbb R^3$. For each evolution law we propose both a finite element method, as well as a finite difference scheme in the…

The numerical computation of shortest paths or geodesics on surfaces, along with the associated geodesic distance, has a wide range of applications. Compared to Euclidean distance computation, these tasks are more complex due to the…

The computation of multiphase flows presents a subtle energetic equilibrium between potential (i.e., surface) and kinetic energies. The use of traditional interface-capturing schemes provides no control over such a dynamic balance. In the…

Mesh degeneration is a bottleneck for fluid-structure interaction (FSI) simulations and for shape optimization via the method of mappings. In both cases, an appropriate mesh motion technique is required. The choice is typically based on…

In this paper we address the convergence of stochastic approximation when the functions to be minimized are not convex and nonsmooth. We show that the "mean-limit" approach to the convergence which leads, for smooth problems, to the ODE…

Lipid vesicles appear ubiquitously in biological systems. Understanding how the mechanical and intermolecular interations deform vesicle membrane is a fundamental question in biophysics. In this article we developed a fast algorithm to…

Daily tasks require us to use our whole body to manipulate objects, for instance when our hands are unavailable. We consider the issue of providing humanoid robots with the ability to autonomously perform similar whole-body manipulation…