A Spectral Element Solution of the Klein-Gordon Equation with High-Order Treatment of Time and Non-reflecting Boundary
Lindquist, Joseph M.
Giraldo, Francis X.
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A spectral element (SE) implementation of the GivoliÃ¢ Neta non-reflecting boundary condition (NRBC) is considered for the solution of the KleinÃ¢ Gordon equation. The infinite domain is truncated via an artificial boundary B, and a high-order NRBC is applied on B. Numerical examples, in various configurations, concerning the propagation of a pressure pulse are used to demonstrate the performance of the SE implementation. Effects of time integration techniques and long term results are discussed. Specifically, we show that in order to achieve the full benefits of high-order accuracy requires balancing all errors involved; this includes the order of accuracy of the spatial discretization method, time integrators, and boundary conditions.
Wave Motion 47 (2010) 289Ã¢ 298The article of record as published may be found at http://dx.doi.org/10.1016/j.wavemoti.2009.11.007