Towards perfectly matched layers for time-dependent space fractional PDEs

Xavier Antoine (1, 2) , Emmanuel Lorin (3, 4)

1 IECL - Institut Élie Cartan de Lorraine
2 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
3 CRM - Centre de Recherches Mathématiques [Montréal]
4 School of Mathematics and Statistics [Ottawa]

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.

Mots clés: fractional partial differential equations; unbounded domain; perfectly matched layer; Fourier pseudospectral approximation; time splitting scheme

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Xavier Antoine, Emmanuel Lorin. Towards perfectly matched layers for time-dependent space fractional PDEs. Journal of Computational Physics, 2019, 391, pp.59-90. ⟨10.1016/j.jcp.2019.04.025⟩. ⟨hal-01962622⟩