Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation

Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation

Year:    2022

Author:    Min Cai, Ehsan Kharazmi, Changpin Li, George Em Karniadakis

Communications in Computational Physics, Vol. 31 (2022), Iss. 2 : pp. 331–369

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2021-0063

Communications in Computational Physics, Vol. 31 (2022), Iss. 2 : pp. 331–369

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    39

Keywords:    Variable-order fractional derivatives FBL wave equation.

Author Details

Min Cai

Ehsan Kharazmi

Changpin Li

George Em Karniadakis

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