Related papers: A provably efficient monotonic-decreasing algorith…
We consider the numerical approximations for a phase field model consisting of incompressible Navier--Stokes equations with a generalized Navier boundary condition, and the Cahn-Hilliard equation with a dynamic moving contact line boundary…
The numerical solution of the Stokes equations on an evolving domain with a moving boundary is studied based on the arbitrary Lagrangian-Eulerian finite element method and a second-order projection method along the trajectories of the…
We propose a partitioned method for the monolithic formulation of the Stokes-Biot system that incorporates Lagrange multipliers enforcing the interface conditions. The monolithic system is discretized using finite elements, and we establish…
This paper addresses a distributed optimization problem in a communication network where nodes are active sporadically. Each active node applies some learning method to control its action to maximize the global utility function, which is…
This contribution describes the implementation of a data--driven shape optimization pipeline in a naval architecture application. We adopt reduced order models (ROMs) in order to improve the efficiency of the overall optimization, keeping a…
In this paper, a semi-Lagrangian gas-kinetic scheme is developed for smooth flows based on the Bhatnagar-Gross-Krook (BGK) equation. As a finite-volume scheme, the evolution of the average flow variables in a control volume is under the…
We introduce a novel dynamic learning-rate scheduling scheme grounded in theory with the goal of simplifying the manual and time-consuming tuning of schedules in practice. Our approach is based on estimating the locally-optimal stepsize,…
Gradient-flow (GF) viewpoints unify and illuminate optimization algorithms, yet most GF analyses focus on unconstrained settings. We develop a geometry-respecting framework for constrained problems by (i) reparameterizing feasible sets with…
In this paper we study obstacles immerged in a Stokes flow with Navier boundary conditions. We prove the existence and regularity of an obstacle with minimal drag, among all shapes of prescribed volume and controlled surface area, taking…
We present a component-based model order reduction procedure to efficiently and accurately solve parameterized incompressible flows governed by the Navier-Stokes equations. Our approach leverages a non-overlapping optimization-based domain…
Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…
We propose a new least squares finite element method to solve the Stokes problem with two sequential steps. The approximation spaces are constructed by patch reconstruction with one unknown per element. For the first step, we reconstruct an…
Consider a polynomial optimisation problem, whose instances vary continuously over time. We propose to use a coordinate-descent algorithm for solving such time-varying optimisation problems. In particular, we focus on relaxations of…
Various methods for numerically solving Stokes Flow, where a small Reynolds number is assumed to be zero, are investigated. If pressure, horizontal velocity, and vertical velocity can be decoupled into three different equations, the…
We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…
Optimization problems with continuous data appear in, e.g., robust machine learning, functional data analysis, and variational inference. Here, the target function is given as an integral over a family of (continuously) indexed target…
The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid density on the phase-field order parameter. Driven by…
An algorithm is presented for momentum gradient descent optimization based on the first-order differential equation of the Newtonian dynamics. The fictitious mass is introduced to the dynamics of momentum for regularizing the adaptive…
In this paper, we study the convergence analysis for a robust stochastic structure-preserving Lagrangian numerical scheme in computing effective diffusivity of time-dependent chaotic flows, which are modeled by stochastic differential…
We formulate a general shape and topology optimization problem in structural optimization by using a phase field approach. This problem is considered in view of well-posedness and we derive optimality conditions. We relate the diffuse…