A generalized SAV approach with relaxation for dissipative systems

Y Zhang, J Shen - Journal of Computational Physics, 2022 - Elsevier
The scalar auxiliary variable (SAV) approach [31] and its generalized version GSAV
proposed in [20] are very popular methods to construct efficient and accurate energy stable …

A new class of implicit–explicit BDFk SAV schemes for general dissipative systems and their error analysis

F Huang, J Shen - Computer Methods in Applied Mechanics and …, 2022 - Elsevier
We construct a new class of efficient implicit–explicit (IMEX) BDF k schemes combined with
a scalar auxiliary variable (SAV) approach for general dissipative systems. We show that …

Fully discrete discontinuous Galerkin numerical scheme with second-order temporal accuracy for the hydrodynamically coupled lipid vesicle model

G Zou, Z Li, X Yang - Journal of Scientific Computing, 2023 - Springer
In this paper, for the highly nonlinear hydrodynamically coupled elastic bending energy
model of vesicle membranes, based on the discontinuous Galerkin (DG) method for spatial …

A highly efficient and accurate exponential semi-implicit scalar auxiliary variable (ESI-SAV) approach for dissipative system

Z Liu, X Li - Journal of Computational Physics, 2021 - Elsevier
The scalar auxiliary variable (SAV) approach [42] is a very popular and efficient method to
simulate various phase field models. To save the computational cost, a new SAV approach …

A Second-Order, Linear, -Convergent, and Energy Stable Scheme for the Phase Field Crystal Equation

X Li, Z Qiao - SIAM Journal on Scientific Computing, 2024 - SIAM
In this paper, we present a second-order accurate and linear numerical scheme for the
phase field crystal equation and prove its convergence in the discrete sense. The key …

Step-by-step solving schemes based on scalar auxiliary variable and invariant energy quadratization approaches for gradient flows

Z Liu, X Li - Numerical Algorithms, 2022 - Springer
In this paper, we propose several novel numerical techniques to deal with nonlinear terms in
gradient flows. These step-by-step solving schemes, termed 3S-SAV and 3S-IEQ schemes …

Error analysis of the SAV Fourier-spectral method for the Cahn-Hilliard-Hele-Shaw system

N Zheng, X Li - Advances in Computational Mathematics, 2021 - Springer
In this paper, we construct several efficient scalar auxiliary variable (SAV) schemes based
on the Fourier-spectral method in space for the Cahn-Hilliard-Hele-Shaw system. The …

Phase-field based modeling and simulation for selective laser melting techniques in additive manufacturing

S Lai, Q Xia, J Kim, Y Li - … in Nonlinear Science and Numerical Simulation, 2024 - Elsevier
In this study, we develop a phase-field model to describe the solid–liquid phase changes,
heat conduction phenomena, during the selective laser melting process. This model is …

Efficient and energy stable numerical schemes for the two-mode phase field crystal equation

F Zhang, D Li, HW Sun - Journal of Computational and Applied …, 2023 - Elsevier
In this paper, we propose four time marching schemes for the two-mode phase field crystal
equation with the periodic boundary condition. The first-and second-order schemes are …

A linearly second-order, unconditionally energy stable scheme and its error estimates for the modified phase field crystal equation

S Pei, Y Hou, Q Li - Computers & Mathematics with Applications, 2021 - Elsevier
We carry out error estimates for a linear, second-order, unconditionally energy stable, semi-
discrete time stepping scheme, which is based on the Lagrange Multiplier approach and …