Solving an inverse problem for the wave equation by using a minimization algorithm and time-reversed measurements
Solving an inverse problem for the wave equation by using a minimization algorithm and time-reversed measurements
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使用最小化算法和时间反演测量来求解波动方程的反问题
DOI：
10.3934/ipi.2011.5.731
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
L. Oksanen
中科院分区：
文献类型：
--
作者：
L. Oksanen
本文研究了紧致黎曼流形上或$\R^n$中有界区域上波动方程的反问题，推广了影响域的概念。我们提出了一个有效的最小化算法来计算使用边界测量和时间反演边界测量的影响域的体积。此外，我们表明，如果流形是简单的，那么体积的影响域确定的流形。对于流形边界上的连续真实的值函数$\tau$，影响域是流形上那些点的集合，从这些点到某个边界点$y$的旅行时间小于$\tau（y）$。
We consider the inverse problem for the wave equation on a compact Riemannian manifold or on a bounded domain of $\R^n$, and generalize the concept of {\em domain of influence}. We present an efficient minimization algorithm to compute the volume of a domain of influence using boundary measurements and time-reversed boundary measurements. Moreover, we show that if the manifold is simple, then the volumes of the domains of influence determine the manifold. For a continuous real valued function $\tau$ on the boundary of the manifold, the domain of influence is the set of those points on the manifold from which the travel time to some boundary point $y$ is less than $\tau(y)$.
通过改进的时间反转迭代聚焦未知介质中的波
影响因子：
2.2
作者：
Dahl M
通讯作者：
Dahl M