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Miscellaneous Topics

In: Numerical Methods for Inverse Scattering Problems

Author

Listed:
  • Jingzhi Li

    (Southern University of Science and Technology, Department of Mathematics)

  • Hongyu Liu

    (City University of Hong Kong, Department of Mathematics)

Abstract

In this chapter, two enhanced techniques are discussed for the multilevel linear sampling method in Chap. 3 in order to avoid the breakage cells. Inverse acoustic obstacle scattering problem is considered as a model problem for the development of the two enhanced multilevel linear sampling methods. On the one hand, the discussed two methods, expanding MLSM and searching MLSM, are shown to possess the same optimal computational complexity as the original MLSM. On the other hand, the enhanced methods can defeat the breakage cells problem and produce very fine reconstructions. Numerical experiments are conducted to illustrate the effectiveness of our methods. Since the techniques are mainly some computational strategies, they could be straightforwardly extended to MLSM for inverse medium scattering problem and inverse electromagnetic scattering problems. Our discussion follows the treatment in [25, 26] In their original paper [12], Colton and Kirsch developed a ‘simple’ method for the shape reconstruction in inverse scattering problem which is nowadays known as the linear sampling method (LSM). The method has been extensively studied and extended in several directions, and we refer to [28] for a comprehensive review. These works are mainly concerned with an implementation technique with LSM.

Suggested Citation

  • Jingzhi Li & Hongyu Liu, 2023. "Miscellaneous Topics," Springer Books, in: Numerical Methods for Inverse Scattering Problems, chapter 0, pages 269-314, Springer.
    • Handle: RePEc:spr:sprchp:978-981-99-3772-1_8
    DOI: 10.1007/978-981-99-3772-1_8
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