论文标题
使用局部共振频率在波导中平滑形状缺陷的重建
Reconstruction of smooth shape defects in waveguides using locally resonant frequencies
论文作者
论文摘要
本文旨在提出一种使用局部共振频率在2D波导中缓慢改变宽度缺陷的新方法。在这些频率下，根据称为局部共振点的参数，局部共振模式在通风函数的形式下以通风函数的形式传播。在这个特定点，已知波导的局部宽度，并且可以从波场的边界测量值中恢复其位置。在不同频率的情况下，使用相同的过程，我们在所有波导中产生宽度的良好近似值。给定在波导表面进行的多频测量，我们提供了一种L \ Infty稳定的显式方法来重建波导的宽度。我们最终在数值数据上验证了我们的方法，并讨论了其应用程序和限制。
This article aims to present a new method to reconstruct slowly varying width defects in 2D waveguides using locally resonant frequencies. At these frequencies, locally resonant modes propagate in the waveguide under the form of Airy functions depending on a parameter called the locally resonant point. In this particular point, the local width of the waveguide is known and its location can be recovered from boundary measurements of the wavefield. Using the same process for different frequencies, we produce a good approximation of the width in all the waveguide. Given multi-frequency measurements taken at the surface of the waveguide, we provide a L \infty-stable explicit method to reconstruct the width of the waveguide. We finally validate our method on numerical data, and we discuss its applications and limits.
