- 逆散射问题的数值方法(英文版)(精)
- - 作者：李景治//刘宏宇
  - 出版社：科学
  - ISBN：9787030762481
  - 出版日期：2023/01/01
  - 页数：364
- 售价：79.2

内容大纲
《逆散射问题的数值方法》致力于声学、电磁学和弹性动力学中出现的反散射问题的数值研究。在物理问题中，发送入射波来确定一个未知或不可访问的对象——散射体，以产生散射波场。然后，通过收集／测量被编码成称作远场模式的散射数据，人们将推断散射体的几何／介质性质。这种逆散射问题出现在各种具有实际重要性的工业应用中，包括雷达和声纳、遥感、地球物理勘探、医疗成像和无损检测。我们主要关注异常散射体的几何／拓扑信息的恢复和识别，包括其位置和形状，立于其介质性质，通过相关的远场测量。事实上，在许多波成像的实际场景中，人们主要对反常散射体的可视化感兴趣，如果需要，将根据成像效果进一步探索介质性质。我们将把声散射、电磁散射和弹性散射纳入我们的研究，并主要在时间谐波范围内工作。
作者介绍
目录
1 Introduction
  References
2 Direct Acoustic Scattering Problems
  2.1  Acoustic Scattering From Obstacles
  2.2  Acoustic Scattering From Mediums
  2.3  Acoustic Scattering From Complex Scatterers
  2.4  Green’s Formula and Linear Potential Theory for Scattering Problems
  2.5  Numerical Methods for Acoustic Scattering Problems
    2.5.1  Nystxom Method
    2.5.2  Finite Element Method with Perfectly Matched Layer (PML)
  References
3 Numerical Inverse Acoustic Scattering Problems
  3.1  Overview
  3.2  Strengthened Linear Sampling Methods
    3.2.1  Strengthened Linear Sampling Method with a   Reference Ball
    3.2.2  Numerical Experiments and Discussion
    3.2.3  Conclusion
  3.3  Single-Shot Method for Multiple Multiscale Scatterers
    3.3.1  Locating Small Scatterers
    3.3.2  Locating Scatterers of Regular Size
    3.3.3  Locating Scatterers of Multiple Scales
  3.4  Reconstruction by Phaseless Backscattering Measurements
    3.4.1  Physical Optics Approximation
    3.4.2  Recovery Scheme
    3.4.3  Numerical Experiments and Discussions
    3.4.4  Concluding Remarks
  References
4 Direct Electromagnetic Scattering Problems
  4.1  Electromagnetic Scattering From Obstacles
  4.2  Electromagnetic Scattering From Mediums
  4.3  Electromagnetic Scattering From Complex Scatterers
  4.4  Green’s Theorem and Representation Formulas
  4.5  Numerical Methods for Electromagnetic Scattering Problems
  References
5 Numerical Inverse Electromagnetic Scattering Problems
  5.1  Overview
  5.2  Strengthened Linear Sampling Methods
  5.3  Single-shot Method for Multiple Multiscale Scatterers
    5.3.1  The Locating Schemes
    5.3.2  Proofs of Theorems 5.3.1 and 5.3.2
    5.3.3  Numerical Experiments and Discussions
    5.3.4  Concluding Remarks
  5.4  Scatterers
    5.4.1  Multi-scale EM Scatterers and Two Locating Schemes
    5.4.2  Scheme R with Augmented   Reference Spaces
    5.4.3  Locating Multiple Multi-scale Scatterers
    5.4.4  Numerical Experiments and Discussions
    5.4.5  Discussions
  References
6 Direct Elastic Scattering Problems

  6.1  Elastic Scattering from Obstacles
  6.2  Elastic Scattering from Mediums
  6.3  Elastic Scattering from Complex Scatterers
  6.4  Green’s Theorems and Representation Formulas
  6.5  Numerical Methods for Elastic Scattering Problems
  References
7 Numerical Inverse Elastic Scattering Problems
  7.1  Overview
  7.2  Single-Shot Method for Multiple Multiscale Scatterers
    7.2.1  Locating Multiple Small Scatterers
    7.2.2  Locating Multiple Extended Scatterers
    7.2.3  Locating Multiple Multiscale Scatterers
    7.2.4  Numerical Examples
    7.2.5  Concluding Remarks
  7.3  Traction Free Case
    7.3.1  Elastic Scattering From Multiscale Scatterers
    7.3.2  Locating Multiple Multiscale Elastic Scatterers
  7.4  Reconstructing Multiple Small Scatterers
  7.5  Reconstructing Multiple Extended Scatterers
  7.6  Reconstructing Multiple Multiscale Scatterers
  7.7  Two-Stage Fast Imaging of Multiple Multiscale Scatterers
  References
8 Miscellaneous Topics
  8.1  Multilevel Linear Sampling Methods
    8.1.1  Multilevel Linear Sampling Method
    8.1.2  Numerical Experiments and Some Discussions
  8.2  EMLSM
    8.2.1  Inverse Acoustic Obstacle Scattering Problem
    8.2.2  Review of LSM and MLSM
    8.2.3  Enhanced Multilevel-LSMs
    8.2.4  Numerical Experiments
  References
9 Others
  9.1  Ground Detection by a Single Electromagnetic Far-Field Measurement
    9.1.1  Scattering from Multiscale Ground Objects
    9.1.2  Locating Multiscale Ground Objects
    9.1.3  Numerical Experiments and Discussions
  9.2  Recovering Multiscale Buried Anomalies in a Two-Layered Medium
    9.2.1  Mathematical Formulation
    9.2.2  Results on Direct Scattering Problem
    9.2.3  Recovery Scheme
    9.2.4  Numerical Experiments
  References
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