Related papers: A weighted scalar auxiliary variable method for so…
We develop a novel and efficient iterative scheme for solving incompressible steady Navier-Stokes equations. The method is an adaptation of the Incremental Viscosity Splitting approximation for unsteady flows to steady equations. At each…
In this study, we focus on the modelling of coupled systems of shallow water flows and solute transport with source terms due to variable topography and friction effect. Our aim is to propose efficient and accurate numerical techniques for…
In this paper, we present a linearly implicit energy-preserving scheme for the Camassa-Holm equation by using the multiple scalar auxiliary variables approach, which is first developed to construct efficient and robust energy stable schemes…
Stochastic optimization algorithms are widely used for machine learning with large-scale data. However, their convergence often suffers from non-vanishing variance. Variance Reduction (VR) methods, such as SVRG and SARAH, address this issue…
We introduce a high-order weight-adjusted discontinuous Galerkin (WADG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in anisotropic porous media. We use a coupled first-order symmetric…
We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike…
Newton-type solvers have been extensively employed for solving a variety of nonlinear system of algebraic equations. However, for some complex nonlinear system of algebraic equations, efficiently solving these systems remains a challenging…
This work considers the non-convex finite sum minimization problem. There are several algorithms for such problems, but existing methods often work poorly when the problem is badly scaled and/or ill-conditioned, and a primary goal of this…
We formulate a novel numerical method suitable for the solution of topology optimization problems in solid mechanics. The most salient feature of the new approach is that the space and time discrete equations of the numerical method can be…
Value-at-risk (VaR) has been playing the role of a standard risk measure since its introduction. In practice, the delta-normal approach is usually adopted to approximate the VaR of portfolios with option positions. Its effectiveness,…
In this paper, we develop a novel class of linear energy-preserving integrating factor methods for the 2D nonlinear Schr\"odinger equation with wave operator (NLSW), combining the scalar auxiliary variable approach and the integrating…
This paper introduces a unified framework for accelerated gradient methods through the variable and operator splitting (VOS). The operator splitting decouples the optimization process into simpler subproblems, and more importantly, the…
In this paper, a three-dimensional numerical solver is developed for suspensions of rigid and soft particles and droplets in viscoelastic and elastoviscoplastic (EVP) fluids. The presented algorithm is designed to allow for the first time…
The existing discrete variational derivative method is only second-order accurate and fully implicit. In this paper, we propose a framework to construct an arbitrary high-order implicit (original) energy stable scheme and a second-order…
Vertical equilibrium (VE) models have been introduced as computationally efficient alternatives to traditional mass and momentum balance equations for fluid flow in porous media. Since VE models are only accurate in regions where phase…
In the paper, we study the stochastic alternating direction method of multipliers (ADMM) for the nonconvex optimizations, and propose three classes of the nonconvex stochastic ADMM with variance reduction, based on different reduced…
Semi-Lagrangian (SL) schemes are known as a major numerical tool for solving transport equations with many advantages and have been widely deployed in the fields of computational fluid dynamics, plasma physics modeling, numerical weather…
The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…
This paper provides a pedagogical introduction to the classical nonlinear stability analysis of the plane Poiseuille and Couette flows. The whole procedure is kept as simple as possible by presenting all the logical steps involved in the…
We augment a thermodynamically consistent diffuse interface model for the description of line tension phenomena by multiplicative stochastic noise to capture the effects of thermal fluctuations and establish the existence of pathwise unique…