Related papers: Stiffness Mitigation in Stochastic Particle Flow F…
In this work, we study shape optimization problems in the Stokes flows. By phase-field approaches, the resulted total objective function consists of the dissipation energy of the fluids and the Ginzburg--Landau energy functional as a…
We consider stochastic optimal control of linear dynamical systems with additive non-Gaussian disturbance. We propose a novel, sampling-free approach, based on Fourier transformations and convex optimization, to cast the stochastic optimal…
In this work we propose, {analyze}, and validate a stabilized finite element method for a flow problem arising from the assessment of {4D Flow Magnetic Resonance Imaging quality}. Starting from the Navier-Stokes equation and splitting its…
A Cahn-Hilliard equation with stochastic multiplicative noise and a random convection term is considered. The model describes isothermal phase-separation occurring in a moving fluid, and accounts for the randomness appearing at the…
Filters that act by adsorbing contaminant onto their pore walls will experience a decrease in porosity over time, and may eventually block. As adsorption will generally be larger towards the entrance of a filter, where the concentration of…
We study the Wasserstein Hamiltonian flow with a common noise on the density manifold of a finite graph. Under the framework of stochastic variational principle, we first develop the formulation of stochastic Wasserstein Hamiltonian flow…
Hamiltonian dynamics of a thin vortex filament in ideal incompressible fluid near a flat fixed boundary is considered at the conditions that at any point of the curve determining shape of the filament the angle between tangent vector and…
We investigate stationary solutions of a thin-film model for liquid two-layer flows in an energetic formulation that is motivated by its gradient flow structure. The goal is to achieve a rigorous understanding of the contact-angle…
Modulating the number of particles in a region is key to accurately capturing the nuances in compressible flows with Smoothed Particle Hydrodynamics (SPH). This paper presents a volume-based adaptive refinement and derefinement procedure,…
We propose a sequential homotopy method for the solution of mathematical programming problems formulated in abstract Hilbert spaces under the Guignard constraint qualification. The method is equivalent to performing projected backward Euler…
Many problems of theoretical and practical interest involve finding a convex or concave function. For instance, optimization problems such as finding the projection on the convex functions in $H^k(\Omega)$, or some problems in economics. In…
The considered optimal control problem of a stochastic power system, is to select the set of power supply vectors which infimizes the probability that the phase-angle differences of any power flow of the network, endangers the transient…
Particle filters (PFs), which are successful methods for approximating the solution of the filtering problem, can be divided into two types: weighted and unweighted PFs. It is well known that weighted PFs suffer from the weight degeneracy…
A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…
We study a fictitious domain approach with Lagrange multipliers to discretize Stokes equations on a mesh that does not fit the boundaries. A mixed finite element method is used for fluid flow. Several stabilization terms are added to…
The smoothed particle hydrodynamics (SPH) method has been widely used to simulate incompressible and slightly compressible fluid flows. Adaptive refinement strategies to dynamically increase the resolution of the particles to capture sharp…
We consider multiscale stochastic systems that are partially observed at discrete points of the slow time scale. We introduce a particle filter that takes advantage of the multiscale structure of the system to efficiently approximate the…
This paper proposes a computational framework for the design optimization of stable structures under large deformations by incorporating nonlinear buckling constraints. A novel strategy for suppressing spurious buckling modes related to…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
We propose two new alternating direction methods to solve "fully" nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and…