Numerical studies of domain sampling methods for inverse boundary value problems by one measurement
Numerical studies of domain sampling methods for inverse boundary value problems by one measurement
复制标题
DOI：
10.1016/j.jcp.2023.112099
复制
发表时间：
2023-03
期刊：
影响因子：
--
通讯作者：
Shiwei Sun;Gen Nakamura;Haibing Wang
中科院分区：
文献类型：
--
作者：
Shiwei Sun;Gen Nakamura;Haibing Wang
本文考虑了拉普拉斯方程的一个边值反问题，它讨论了由一个边界测量重建背景介质中的未知目标。我们对两种域采样方法感兴趣，即，范围测试和无响应测试，其收敛性在以前的工作中理论上是合理的[17]。作为这项工作的继续，我们研究了这些方法的数值实现。提出了一些新的技术来建立有效的算法，产生相当好的数值重建。为了证明所提出的算法的性能，我们给出了几个数值例子，不同形状的未知目标的噪声测量数据。数值实现的一些关键成分进行了详细讨论。
We consider an inverse boundary value problem for the Laplace equation, which discusses the reconstruction of an unknown target inside the background medium from one boundary measurement. We are interested in two domain sampling methods, i.e., the range test and no-response test, whose convergences are justified theoretically in previous work [17]. As a continuation of this work, we study the numerical realizations of these methods. Some new techniques are proposed to set up efficient algorithms, which yield reasonably good numerical reconstructions. To demonstrate the performance of proposed algorithms, we show several numerical examples for different shapes of unknown targets with noisy measurement data. Some key ingredients of numerical implementations are discussed in detail.