Related papers: Global constraints preserving SAV schemes for grad…
We prove quantitative estimates on flows of ordinary differential equations with vector field with gradient given by a singular integral of an $L^1$ function. Such estimates allow to prove existence, uniqueness, quantitative stability and…
An algorithm for simulating self-gravitating cosmological astrophysical fluids is presented. The advantages include a large dynamic range, parallelizability, high resolution per grid element and fast execution speed. The code is based on a…
We consider a kind of differential equations d/dt y(t) = R(y(t))y(t) + f(y(t)) with energy conservation. Such conservative models appear for instance in quantum physics, engineering and molecular dynamics. A new class of energy-preserving…
Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two of the central Hamiltonian systems encountered in…
We propose novel algorithms combining accelerated gradient flows with linearized projection-free treatments of non-convex constraints and BDF pseudo-temporal discretization for quadratic energy minimization. A general framework is developed…
The robustness and accuracy of marginally resolved discontinuous Galerkin spectral element computations are evaluated for the standard formulation and a kinetic energy conserving split form on complex flow problems of physical and…
We consider a family of steady free-surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable…
We introduce a novel and efficient algorithm called the stochastic approximate gradient descent (SAGD), as an alternative to the stochastic gradient descent for cases where unbiased stochastic gradients cannot be trivially obtained.…
We present a numerical formulation for the solution of non-isothermal, compressible, Navier-Stokes equations with thermal fluctuations to describe mesoscale transport phenomena in multispecies fluid mixtures. The novelty of our numerical…
We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion…
The numerical approximation of incompressible fluid-structure interaction problems with Lagrange multiplier is generally based on strongly coupled schemes. This delivers unconditional stability but at the expense of solving a…
In this work we study the convergence of gradient methods for nonconvex optimization problems -- specifically the effect of the problem formulation to the convergence behavior of the solution of a gradient flow. We show through a simple…
We propose a novel Skew Gradient Embedding (SGE) framework for systematically reformulating thermodynamically consistent partial differential equation (PDE) models-capturing both reversible and irreversible processes-as generalized gradient…
We construct a numerical scheme based on the scalar auxiliary variable (SAV) approach in time and the MAC discretization in space for the Cahn-Hilliard-Navier-Stokes phase field model, and carry out stability and error analysis. The scheme…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
We present in this paper construction and analysis of a block-centered finite difference method for the spatial discretization of the scalar auxiliary variable Crank-Nicolson scheme (SAV/CN-BCFD) for gradient flows, and show rigorously that…
Accurate and efficient prediction of multi-scale flows remains a formidable challenge. Constructing theoretical models and numerical methods often involves the design and optimization of parameters. While gradient descent methods have been…
Recently, a new class of non-convex optimization problems motivated by the statistical problem of learning an acyclic directed graphical model from data has attracted significant interest. While existing work uses standard first-order…
The scalar auxiliary variable (SAV) approach \cite{shen2018scalar} and its generalized version GSAV proposed in \cite{huang2020highly} are very popular methods to construct efficient and accurate energy stable schemes for nonlinear…
We propose finite-volume schemes for the Cahn-Hilliard equation which unconditionally and discretely preserve the boundedness of the phase field and the dissipation of the free energy. Our numerical framework is applicable to a variety of…