Mixed unsplit-field perfectly matched layers for transient simulations of scalar waves in heterogeneous domains |
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| Authors: | Jun Won Kang Loukas F Kallivokas |
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| Institution: | (1) Department of Mechanical Engineering, University of Colorado at Boulder, Boulder, CO 80309, USA;(2) Department of Aerospace Science and Engineering, University of Colorado at Boulder, Boulder, CO 80309, USA; |
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| Abstract: | We discuss a new formulation for transient scalar wave simulations in heterogeneous semi-infinite domains. To deal with the
semi-infinite extent of the physical domains, we introduce truncation boundaries and adopt perfectly matched layers (PMLs)
as the boundary wave absorbers. Within this framework, we develop a new mixed displacement-stress (or stress memory) finite
element formulation based on unsplit-field PMLs. We use, as typically done, complex-coordinate stretching transformations
in the frequency domain, and recover the governing partial differential equations in the time-domain through the inverse Fourier
transform. Upon spatial discretization, the resulting equations lead to a mixed semi-discrete form, where both displacements
and stresses (or stress histories/memories) are treated as independent unknowns. We propose approximant pairs, which, numerically,
are shown to be stable. The resulting mixed finite element scheme is relatively simple and straightforward to implement, when
compared against split-field PML techniques. It also bypasses the need for complicated time integration schemes that arise
when recent displacement-based formulations are used. We report numerical results for 1D and 2D scalar wave propagation in
semi-infinite domains truncated by PMLs. We also conduct parametric studies and report on the effect the various PML parameter
choices have on the simulation error. |
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