On the reconstruction of a Riemannian manifold from boundary data: the theory and plan of a numerical experiment
On the reconstruction of a Riemannian manifold from boundary data: the theory and plan of a numerical experiment
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从边界数据重建黎曼流形：数值实验的理论和计划
DOI：
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发表时间：
2011
期刊：
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通讯作者：
M. Belishev
中科院分区：
文献类型：
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作者：
M. Belishev
本文讨论由边界数据重建黎曼流形的反问题。这个问题已经解决了边界控制方法，目前有几个变种解决it.In文件中，一个版本的过程中，恢复的流形从标量谱或动力学数据，提出。这个版本是关于用途：几何光学、算子的极坐标表示等的最简单的版本，并且仅应用相关动力系统的可控性。没有实质性的变化，这个版本是适用于一个更复杂的（矢量）的电动力学问题的麦克斯韦系统。所提出的程序的简单性提供了额外的机会，其数值实现。最后，本文讨论了数值试验方案。提请注意这些新的备选办法是本文件的主要目的之一。参考书目：9种。
The paper deals with the inverse problem of reconstructing a Riemannian manifold from its boundary data. This problem has been solved by the boundary control method, and at the moment there are several variants of solving it. In the paper, one more version of the procedure, which recovers the manifold from scalar spectral or dynamical data, is proposed. This version is the simplest one in regard to the devices in use: geometrical optics, polar representation of operators, etc. are not employed and only a controllability property of a relevant dynamical system is applied. Without substantial changes, this version is applicable to a more complicated (vector) problem of electrodynamics for the Maxwell system. The simplicity of the procedure proposed provides additional chances for its numerical realizability. At the end of the paper, a plan of numerical experiment is discussed. To draw attention to such new options is one of the main aims of the paper. Bibliography: 9 titles.