10 citations · 10 across the 4 of their papers we have counts for
5 papers
An accurate parallel finite difference method for the variable-order fractional Laplacian in heterogeneous media
Shiping Zhou, Yanzhi Zhang
Anomalous diffusion in heterogeneous media is ubiquitous across physical and biological systems, where spatially varying microstructures give rise to distinct transport regimes. Va…
Nonlocal modeling of spatial fractional diffusion with truncated interaction domains and truncated kernel function singularity
Shiping Zhou, Yanzhi Zhang, Max Gunzburger
Parabolic partial differential equations (PDEs) are in ubiquitous, very effective use to model diffusion processes. However, there are many applications (e.g., such as in hydrology…
Moment-enhanced shallow-water equations with an effective wall closure for no-slip bottoms
Shiping Zhou, Juntao Huang, Andrew J. Christlieb
Shallow-water equations and low-order shallow-water moment models use vertically coarse representations and therefore cannot, in general, resolve the thin wall-affected region prod…
Fourier pseudospectral methods for the spatial variable-order fractional wave equations
Yanzhi Zhang, Xiaofei Zhao, Shiping Zhou
In this paper, we propose Fourier pseudospectral methods to solve the variable-order space fractional wave equation and develop an accelerated matrix-free approach for its effectiv…
A novel and simple spectral method for nonlocal PDEs with the fractional Laplacian
Shiping Zhou, Yanzhi Zhang
We propose a novel and simple spectral method based on the semi-discrete Fourier transforms to discretize the fractional Laplacian . Numerical analysis and experime…