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 …
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
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 …
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
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 …
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
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 …
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 …
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
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 …
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 …
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
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 …
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
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 …
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
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 …
discrete time stepping scheme, which is based on the Lagrange Multiplier approach and …