相关论文: Highly efficient norm preserving numerical schemes…

The scalar auxiliary variable (SAV) approach of Shen et al. (2018), which presents a novel way to discretize a large class of gradient flows, has been extended and improved by many authors for general dissipative systems. In this work we…

This paper continues to study linear and unconditionally modified-energy stable (abbreviated as SAV-GL) schemes for the gradient flows. The schemes are built on the SAV technique and the general linear time discretizations (GLTD) as well as…

A highly efficient energy-preserving scheme for univariate conservative or dissipative systems was recently proposed in [Comput. Methods Appl. Mech. Engrg. 425 (2024) 116938]. This scheme is based on a grid-point partitioned averaged vector…

In this paper, we develop a novel staggered mesh (SM) approach for general nonlinear dissipative systems with arbitrary energy distributions (including cases with known or unknown energy lower bounds). Based on this framework, we propose…

We present two novel classes of fully discrete energy-preserving algorithms for the sine-Gordon equation subject to Neumann boundary conditions. The cosine pseudo-spectral method is first used to develop structure-preserving spatial…

In this paper, we design a novel class of arbitrarily high-order structure-preserving numerical schemes for the time-dependent Gross-Pitaevskii equation with angular momentum rotation in three dimensions. Based on the idea of the scalar…

Implicit-explicit (IMEX) time integration schemes are well suited for nonlinear structural dynamics because of their low computational cost and high accuracy. However, stability of IMEX schemes cannot be guaranteed for general nonlinear…

A conforming finite element scheme with mixed explicit-implicit time discretization for quasi-incompressible Navier-Stokes-Maxwell-Stefan systems in a bounded domain with periodic boundary conditions is presented. The system consists of the…

The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one and two-body reduced density matrices (RDM) instead of many-electron…

In this paper, we generalize the idea in our previous work for the Vlasov-Amp\`{e}re (VA) system \cite{cheng_va} and develop energy-conserving discontinuous Galerkin (DG) methods for the Vlasov-Maxwell (VM) system. The VM system is a…

To address the magnetization dynamics in ferromagnetic materials described by the Landau-Lifshitz-Gilbert equation under large damping parameters, a third-order accurate numerical scheme is developed by building upon a second-order method…

In this paper, we focus on constructing numerical schemes preserving the averaged energy evolution law for nonlinear stochastic wave equations driven by multiplicative noise. We first apply the compact finite difference method and the…

This paper introduces a novel paradigm for constructing linearly implicit and high-order unconditionally energy-stable schemes for general gradient flows, utilizing the scalar auxiliary variable (SAV) approach and the additive Runge-Kutta…

Parametric finite element discretizations of constrained geometric flows must simultaneously address high-order geometric stiffness, mesh degeneration, and nonlinear global constraints. This paper develops a stabilized dual-SAV (scalar…

Computational material modeling using advanced numerical techniques speeds up the design process and reduces the costs of developing new engineering products. In the field of multiscale modeling, huge computation efforts are expected for…

The classic second-order average vector field (AVF) method can exactly preserve the energy for Hamiltonian ordinary differential equations and partial differential equations. However, the AVF method inevitably leads to fully-implicit…

We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate the objective function and variable sample size strategy…

In this paper, we consider numerical approximations for solving the micropolar Navier-Stokes (MNS) equations, that couples the Navier-Stokes equations and the angular momentum equation together. By combining the scalar auxiliary variable…

A novel numerical strategy is introduced for computing approximations of solutions to a Cahn-Hilliard model with degenerate mobilities. This model has recently been introduced as a second-order phase-field approximation for surface…

In this paper, we analyze two classes of spectral volume (SV) methods for one-dimensional hyperbolic equations with degenerate variable coefficients. The two classes of SV methods are constructed by letting a piecewise $k$-th order ($k\ge…