English

Diffraction by a set of collinear cracks on a square lattice: an iterative Wiener-Hopf method

Mathematical Physics 2024-04-30 v1 Analysis of PDEs Complex Variables math.MP

Abstract

The diffraction of a time-harmonic plane wave on collinear finite defects in a square lattice is studied. This problem is reduced to a matrix Wiener-Hopf equation. This work adapts the recently developed iterative Wiener-Hopf method to this situation. The method was motivated by wave scattering in continuous media but it is shown here that it can also be employed in a discrete lattice setting. The numerical results are validated against a different method using discrete Green's functions. Unlike the latter approach, the complexity of the present algorithm is shown to be virtually independent of the length of the cracks.

Keywords

Cite

@article{arxiv.2402.15799,
  title  = {Diffraction by a set of collinear cracks on a square lattice: an iterative Wiener-Hopf method},
  author = {Elena Medvedeva and Raphael Assier and Anastasia Kisil},
  journal= {arXiv preprint arXiv:2402.15799},
  year   = {2024}
}