TY - JOUR
T1 - Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation
AU - Cai , Min
AU - Kharazmi , Ehsan
AU - Li , Changpin
AU - Karniadakis , George Em
JO - Communications in Computational Physics
VL - 2
SP - 331
EP - 369
PY - 2022
DA - 2022/01
SN - 31
DO - http://doi.org/10.4208/cicp.OA-2021-0063
UR - https://global-sci.org/intro/article_detail/cicp/20209.html
KW - Variable-order fractional derivatives, FBL, wave equation.
AB - <p style="text-align: justify;">We develop fractional buffer layers (FBLs) to absorb propagating waves
without reflection in bounded domains. Our formulation is based on variable-order
spatial 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 the
domain. In particular, we first design proper FBLs for the one-dimensional one-way
and two-way wave propagation. Then, we extend our formulation to two-dimensional
problems, where we introduce a consistent variable-order fractional wave equation. In
each case, we obtain the fully discretized equations by employing a spectral collocation
method 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 show
that the proposed FBL is able to suppress reflected waves including corner reflections
in a two-dimensional rectangular domain. We also demonstrate that our formulation
is more robust and uses less number of equations.</p>