Energy quadratization Runge–Kutta scheme for the conservative Allen–Cahn equation with a nonlocal Lagrange multiplier

Lee, Hyun Geun; Shin, Jeeyoung; Lee, June-Yub

doi:10.1016/j.aml.2022.108161

Cited by 11 publications

(1 citation statement)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finite difference [18][19][20], finite element [21][22][23], and finite volume [24][25][26] methods have been investigated to solve space-fractional models. In this paper, we employ the Fourier spectral method [27][28][29][30][31][38][39][40][41] for the spatial discretization, which gives a full diagonal representation of the fractional operator and achieves spectral convergence regardless of the fractional power. And we present a linear, energy stable, and second-order method that can be combined with the Fourier spectral method directly.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of a Space-Fractional Molecular Beam Epitaxy Model without Slope Selection

Lee

2023

Fractal Fract

Self Cite

View full text Add to dashboard Cite

In this paper, we introduce a space-fractional version of the molecular beam epitaxy (MBE) model without slope selection to describe super-diffusion in the model. Compared to the classical MBE equation, the spatial discretization is an important issue in the space-fractional MBE equation because of the nonlocal nature of the fractional operator. To approximate the fractional operator, we employ the Fourier spectral method, which gives a full diagonal representation of the fractional operator and achieves spectral convergence regardless of the fractional power. And, to combine with the Fourier spectral method directly, we present a linear, energy stable, and second-order method. Then, it is possible to simulate the dynamics of the space-fractional MBE equation efficiently and accurately. By using the numerical method, we investigate the effect of the fractional power in the space-fractional MBE equation.

show abstract