...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>SIAM Journal on Mathematical Analysis >Wave-number-explicit bounds in time-harmonic scattering
【24h】

Wave-number-explicit bounds in time-harmonic scattering

机译：时谐散射中的波数显式边界

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

In this paper we consider the problem of scattering of time-harmonic acoustic waves by a bounded, sound soft obstacle in two and three dimensions, studying dependence on the wave number in two classical formulations of this problem. The first is the standard weak formulation in the part of the exterior domain contained in a large sphere, with an exact Dirichlet-to-Neumann map applied on the boundary. The second formulation is as a second kind boundary integral equation in which the solution is sought as a combined single- and double-layer potential. For the variational formulation we obtain, in the case when the obstacle is starlike, explicit upper and lower bounds which show that the inf-sup constant decreases like k(-1) as the wave number k increases. We also give an example where the obstacle is not starlike and the inf-sup constant decreases at least as fast as k(-2). For the boundary integral equation formulation, if the boundary is also Lipschitz and piecewise smooth, we show that the norm of the inverse boundary integral operator is bounded independently of k if the coupling parameter is chosen correctly. The methods we use also lead to explicit bounds on the solution of the scattering problem in the energy norm when the obstacle is starlike. The dependence of these bounds on the wave number and on the geometry is made explicit.
机译：在本文中，我们研究了时谐声波在二维和三维中被有界声软障碍物散射的问题，研究了该问题的两种经典表示形式对波数的依赖性。第一个是在大球体中包含的外部区域部分中的标准弱公式，并在边界上应用了精确的Dirichlet-to-Neumann映射。第二种形式是作为第二类边界积分方程，其中将解作为组合的单层和双层电势来寻找。对于变分公式，我们获得了障碍物为星形的情况下的明确上下边界，这表明随着波数k的增加，INF常数像k（-1）一样下降。我们还给出了一个例子，其中障碍物不是星形的，并且insup常数减小的速度至少与k（-2）一样快。对于边界积分方程式，如果边界也是Lipschitz且分段光滑，则表明，如果正确选择了耦合参数，则逆边界积分算子的范数与k无关。当障碍物为星形时，我们使用的方法还导致能量范数中散射问题的解决方案有明确的界限。这些界限对波数和几何形状的依赖性是明确的。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号