Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation (Communications in Computational Physics, 2022)
We develop fractional buffer layers (FBLs) to absorb propagating waveswithout reflection in bounded domains. Our formulation is based on variable-orderspatial fractional derivatives. We select a proper variable-order function so that dissipation is induced to absorb the coming waves in the buffer layers attached to thedomain. In particular, we first design proper FBLs for the one-dimensional one-wayand two-way wave propagation. Then, we extend our formulation to two-dimensionalproblems, where we introduce a consistent variable-order fractional wave equation. Ineach case, we obtain the fully discretized equations by employing a spectral collocationmethod in space and Crank-Nicolson or Adams-Bashforth method in time. We compare our results with a finely tuned perfectly matched layer (PML) method and showthat the proposed FBL is able to suppress reflected waves including corner reflectionsin a two-dimensional rectangular domain. We also demonstrate that our formulationis more robust and uses less number of equations.
Keywords: Variable-order fractional derivatives; FBL; wave equation.