• Continuum limit of discrete Sommerfeld problems on square lattice

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    • Keywords


      Sommerfeld half-plane; crack; rigid ribbon; continuum limit; Wiener–Hopf; Toeplitz operator.

    • Abstract


      A low-frequency approximation of the discrete Sommerfeld diffraction problems, involving the scattering of a time harmonic lattice wave incident on square lattice by a discrete Dirichlet or a discrete Neumann half-plane, is investigated. It is established that the exact solution of the discrete model converges to the solution of the continuum model, i.e., the continuous Sommerfeld problem, in the discrete Sobolev space defined by Hackbusch. A proof of convergence has been provided for both types of boundary conditions when the imaginary part of incident wavenumber is positive.

    • Author Affiliations



      1. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
    • Dates

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