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首页> 美国政府科技报告 >On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions
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On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions

机译：关于波动方程在外域中的精确长时解：渐近展开和修正边界条件

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摘要

We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.

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