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.

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Keywords Fourier pseudospectral approximation, Fractional partial differential equations, Perfectly matched layer, Time splitting scheme, Unbounded domain
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Journal Journal of Computational Physics
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/