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.

Additional Metadata
Keywords Fourier pseudospectral approximation, Fractional partial differential equations, Perfectly matched layer, Time splitting scheme, Unbounded domain
Persistent URL dx.doi.org/10.1016/j.jcp.2019.04.025
Journal Journal of Computational Physics
Citation
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