Towards Perfectly Matched Layers for time-dependent space fractional PDEs
Journal of Computational Physics , Volume 391 p. 59- 90
Perfectly Matched Layers (PML) are proposed for time-dependent space fractional PDEs. Within this approach, widely used powerful Fourier solvers based on FFTs can be adapted without much effort to compute Initial Boundary Value Problems (IBVP) for well-posed fractional equations with absorbing boundary layers. We analyze mathematically the method and propose some illustrating numerical experiments.
|Fourier pseudospectral approximation, Fractional partial differential equations, Perfectly matched layer, Time splitting scheme, Unbounded domain|
|Journal of Computational Physics|
|Organisation||School of Mathematics and Statistics|
Antoine, X. (Xavier), & Lorin, E. (2019). Towards Perfectly Matched Layers for time-dependent space fractional PDEs. Journal of Computational Physics, 391, 59–90. doi:10.1016/j.jcp.2019.04.025