4 papers
A Universal Fractional Model of Wall-Turbulence
Fangying Song, George Em Karniadakis
Modeling of wall-bounded turbulent flows is still an open problem in classical physics, with only modest progress made in the last few decades beyond the so-called `log law', which…
A fast solver for spectral element approximation applied to fractional differential equations using hierarchical matrix approximation
Xianjuan Li, Zhiping Mao, Fangying Song +2
We develop a fast solver for the spectral element method (SEM) applied to the two-sided fractional diffusion equation on uniform, geometric and graded meshes. By approximating the…
Fractional Gray-Scott Model: Well-posedness, Discretization, and Simulations
Tingting Wang, Fangying Song, Hong Wang +1
The Gray-Scott (GS) model represents the dynamics and steady state pattern formation in reaction-diffusion systems and has been extensively studied in the past. In this paper, we c…
What Is the Fractional Laplacian?
Anna Lischke, Guofei Pang, Mamikon Gulian +8
The fractional Laplacian in R^d has multiple equivalent characterizations. Moreover, in bounded domains, boundary conditions must be incorporated in these characterizations in math…