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- research-articleApril 2020
A fast Galerkin finite element method for a space–time fractional Allen–Cahn equation
Journal of Computational and Applied Mathematics (JCAM), Volume 368, Issue Chttps://doi.org/10.1016/j.cam.2019.112482AbstractIn this paper, a space–time fractional Allen–Cahn equation is investigated to account for the memory effect of certain materials or the anomalous diffusion processes in heterogeneous distributed media for the mixture of two immiscible ...
- articleAugust 2018
A Fast Discontinuous Galerkin Method for a Bond-Based Linear Peridynamic Model Discretized on a Locally Refined Composite Mesh
Journal of Scientific Computing (JSCI), Volume 76, Issue 2Pages 913–942https://doi.org/10.1007/s10915-018-0645-6We develop a family of fast discontinuous Galerkin (DG) finite element methods for a bond-based linear peridynamic (PD) model in one space dimension. More precisely, we develop a preconditioned fast piecewise-constant DG scheme on a geometrically graded ...
- research-articleOctober 2017
A spacetime fractional phase-field model with tunable sharpness and decay behavior and its efficient numerical simulation
Journal of Computational Physics (JOCP), Volume 347, Issue CPages 20–38https://doi.org/10.1016/j.jcp.2017.06.036We present a spacetime fractional AllenCahn phase-field model that describes the transport of the fluid mixture of two immiscible fluid phases. The space and time fractional order parameters control the sharpness and the decay behavior of the interface ...
- research-articleOctober 2015
A preconditioned fast finite volume scheme for a fractional differential equation discretized on a locally refined composite mesh
Journal of Computational Physics (JOCP), Volume 299, Issue CPages 842–862https://doi.org/10.1016/j.jcp.2015.06.028Numerical methods for fractional differential equations generate full stiffness matrices, which were traditionally solved via Gaussian type direct solvers that require O ( N 3 ) of computational work and O ( N 2 ) of memory to store where N is the ...