Abstract
Exact nonreflecting boundary conditions are considered for exterior three-dimensional time-dependent wave problems. These include a nonlocal condition for acoustic waves based on Kirchhoff's formula, originally proposed by L. Ting and M. J. Miksis ( J. Acoust. Soc. Am. 80, 1825 (1986), and an analogous condition for elastic waves. These conditions are computationally attractive in that their temporal nonlocality is limited to a fixed amount of past information. However, when a standard nondissipative finite difference stencil is used as the interior scheme, a long-time instability is exhibited in the numerical solution. This instability is analyzed for a simple one-dimensional model problem. it is eliminated once the standard interior scheme is replaced by the dissipative Lax-Wendroff scheme. In this case stability is demonstrated experimentally, and it is also established theoretically in the one-dimensional case.
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