Numerical study of high frequency asymptotics of the symbol of the   Dirichlet-to-Neumann operator in 2D diffraction problems
  A high-frequency asymptotics of the symbol of the Dirichlet-to-Neumann map, treated as a periodic pseudodifferential operator, in 2D diffraction problems is discussed. Numerical results support a conjecture on a universal limit shape of the symbol. 
Margo Kondratieva and Sergey Sadov