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逆散射問題的數值方法(英文版)(精)

  • 作者：李景治//劉宏宇
  • 出版社：科學
  • ISBN：9787030762481
  • 出版日期：2023/01/01
  • 裝幀：精裝
  • 頁數：364
人民幣：RMB 198 元      售價：元
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    《逆散射問題的數值方法》致力於聲學、電磁學和彈性動力學中出現的反散射問題的數值研究。在物理問題中，發送入射波來確定一個未知或不可訪問的對象——散射體，以產生散射波場。然後，通過收集／測量被編碼成稱作遠場模式的散射數據，人們將推斷散射體的幾何／介質性質。這種逆散射問題出現在各種具有實際重要性的工業應用中，包括雷達和聲納、遙感、地球物理勘探、醫療成像和無損檢測。我們主要關注異常散射體的幾何／拓撲信息的恢復和識別，包括其位置和形狀，立於其介質性質，通過相關的遠場測量。事實上，在許多波成像的實際場景中，人們主要對反常散射體的可視化感興趣，如果需要，將根據成像效果進一步探索介質性質。我們將把聲散射、電磁散射和彈性散射納入我們的研究，並主要在時間諧波範圍內工作。
作者介紹
李景治//劉宏宇
目錄
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
Book list of the Series in Information and Computational Science

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