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Volume 31, Issue 2
Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation

Min Cai, Ehsan Kharazmi, Changpin Li & George Em Karniadakis

Commun. Comput. Phys., 31 (2022), pp. 331-369.

Published online: 2022-01

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  • 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.

  • AMS Subject Headings

35L05, 26A33, 76M22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-31-331, author = {Cai , MinKharazmi , EhsanLi , Changpin and Karniadakis , George Em}, title = {Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation}, journal = {Communications in Computational Physics}, year = {2022}, volume = {31}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0063}, url = {http://global-sci.org/intro/article_detail/cicp/20209.html} }
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 -

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.

Min Cai, Ehsan Kharazmi, Changpin Li & George Em Karniadakis. (2022). Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation. Communications in Computational Physics. 31 (2). 331-369. doi:10.4208/cicp.OA-2021-0063
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