相关论文: A Regularized Auxiliary Variable (RAV) Approach fo…
We propose a new numerical technique to deal with nonlinear terms in gradient flows. By introducing a scalar auxiliary variable (SAV), we construct efficient and robust energy stable schemes for a large class of gradient flows. The SAV…
The scalar auxiliary variable (SAV) approach is a highly efficient method widely used for solving gradient flow systems. This approach offers several advantages, including linearity, unconditional energy stability, and ease of…
We establish a general framework for developing, efficient energy stable numerical schemes for gradient flows and develop three classes of generalized scalar auxiliary variable approaches (G-SAV). Numerical schemes based on the G-SAV…
In this paper, we propose a novel family of high-order numerical schemes for the gradient flow models based on the scalar auxiliary variable (SAV) approach, which is named the high-order scalar auxiliary variable (HSAV) method. The newly…
For the past few years, scalar auxiliary variable (SAV) and SAV-type approaches became very hot and efficient methods to simulate various gradient flows. Inspired by the new SAV approach in \cite{huang2020highly}, we propose a novel…
Scalar auxiliary variable (SAV) methods are a class of linear schemes for solving gradient flows that are known for the stability of a `modified' energy. In this paper, we propose an improved SAV (iSAV) scheme that not only retains the…
In recent years, the scalar auxiliary variable (SAV) approach has become very popular and hot in the design of linear, high-order and unconditional energy stable schemes of gradient flow models. However, the nature of SAV-based numerical…
In this paper, we consider a novel auxiliary variable method to obtain energy stable schemes for gradient flows. The auxiliary variable based on energy bounded above does not limited to the hypothetical conditions adopted in previous…
Two primary scalar auxiliary variable (SAV) approaches are widely applied for simulating gradient flow systems, i.e., the nonlinear energy-based approach and the Lagrange multiplier approach. The former guarantees unconditional energy…
The scalar auxiliary variable (SAV)-type methods are very popular techniques for solving various nonlinear dissipative systems. Compared to the semi-implicit method, the baseline SAV method can keep a modified energy dissipation law but…
The scalar auxiliary variable (SAV) method was introduced by Shen et al. and has been broadly used to solve thermodynamically consistent PDE problems. By utilizing scalar auxiliary variables, the original PDE problems are reformulated into…
In this paper, we propose and analyze an efficient implicit--explicit (IMEX) second order in time backward differentiation formulation (BDF2) scheme with variable time steps for gradient flow problems using the scalar auxiliary variable…
In this paper, we present a novel investigation of the so-called SAV approach, which is a framework to construct linearly implicit geometric numerical integrators for partial differential equations with variational structure. SAV approach…
Optimizing the learning rate remains a critical challenge in machine learning, essential for achieving model stability and efficient convergence. The Vector Auxiliary Variable (VAV) algorithm introduces a novel energy-based self-adjustable…
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 present an unconditionally energy-stable scheme for approximating the incompressible Navier-Stokes equations on domains with outflow/open boundaries. The scheme combines the generalized Positive Auxiliary Variable (gPAV) approach and a…
We present an energy-stable scheme for numerically approximating the governing equations for incompressible two-phase flows with different densities and dynamic viscosities for the two fluids. The proposed scheme employs a scalar-valued…
We propose a new Lagrange Multiplier approach to design unconditional energy stable schemes for gradient flows. The new approach leads to unconditionally energy stable schemes that are as accurate and efficient as the recently proposed SAV…
We propose in this paper a new minimization algorithm based on a slightly modified version of the scalar auxiliary variable (SAV) approach coupled with a relaxation step and an adaptive strategy. It enjoys several distinct advantages over…
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…