Accurate Absorbing Boundary Conditions In Peridynamics: Part I – Scalar Waves
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The construction of absorbing boundary conditions (ABCs) for nonlocal models can be a challenging task, particularly due to the nonlocal operators that are associated with volume-constrained boundary conditions. Additionally, the application of Fourier and Laplace transforms, which are essential for the majority of available methods, can be complicated. In this talk, we will present a novel approach for constructing accurate ABCs for peridynamic (PD) scalar wave-type problems in viscous media. The proposed ABCs are constructed entirely in the time domain and are of Dirichlet-type, making their implementation considerably more streamlined as no derivatives of the wave field are required. The ABCs are derived from a semi-analytic solution of the exterior domain using harmonic exponential basis functions in space and time (wave-type modes) at the continuum level. The numerical implementation is carried out using a meshfree collocation method within a boundary layer along the truncating boundary. The modes satisfy the numerical dispersion relation of PD, resulting in a compatible solution of the interior (near field) region with that of the exterior (far field) one. The efficacy of the proposed method is demonstrated through several numerical examples in two-dimensional unbounded domains, where the high accuracy and stability of the method are highlighted.
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