Dirichlet-type absorbing boundary conditions for peridynamic scalar waves in two-dimensional viscous media

被引:5
作者
Hermann, Alexander [1 ,5 ]
Shojaei, Arman [1 ]
Seleson, Pablo [2 ]
Cyron, Christian J. [1 ,3 ]
Silling, Stewart A. [4 ]
机构
[1] Helmholtz Zentrum Hereon, Inst Mat Syst Modeling, Geesthacht, Germany
[2] Oak Ridge Natl Lab, Comp Sci & Math Div, Oak Ridge, TN USA
[3] Hamburg Univ Technol, Inst Continuum & Mat Mech, Hamburg, Germany
[4] Sandia Natl Labs, Ctr Comp Res, Albuquerque, NM USA
[5] Helmholtz Zentrum Hereon, Inst Mat Syst Modeling, Max Planck Str 1, D-21502 Geesthacht, Germany
关键词
absorbing boundary conditions; nonlocal scalar waves; peridynamics; viscous medium; EXPONENTIAL BASIS FUNCTIONS; PERFECTLY MATCHED LAYERS; MESHLESS METHOD; EXTERIOR PROBLEMS; PROPAGATION; EQUATIONS; MODEL;
D O I
10.1002/nme.7260
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
Construction of absorbing boundary conditions (ABCs) for nonlocal models is generally challenging, primarily due to the fact that nonlocal operators are commonly associated with volume constrained boundary conditions. Moreover, application of Fourier and Laplace transforms, which are essential for the majority of available methods for ABCs, to nonlocal models is complicated. In this paper, we propose a simple method to construct accurate ABCs for peridynamic scalar wave-type problems in viscous media. The proposed ABCs are constructed in the time and space domains and are of Dirichlet type. Consequently, their implementation is relatively simple, since no derivatives of the wave field are required. The proposed ABCs are derived at the continuum level, from a semi-analytical solution of the exterior domain using harmonic exponential basis functions in space and time (plane-wave modes). The numerical implementation is done using a meshfree collocation approach employed within a boundary layer adjacent to the interior domain boundary. The modes satisfy the peridynamic numerical dispersion relation, resulting in a compatible solution of the interior region (near-field) with that of the exterior region (far-field). The accuracy and stability of the proposed ABCs are demonstrated with several numerical examples in two-dimensional unbounded domains.
引用
收藏
页码:3524 / 3553
页数:30
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