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Keywords:

  • Diffraction;
  • three-quarter-plane;
  • Babinet principle;
  • matricial coupling;
  • equivalence after extension.

Abstract

The modelling of diffraction of time-harmonic electromagnetic or acoustic waves from obstacles and screens leads to boundary value problems for the three-dimensional Helmholtz equation with Dirichlet, Neumann, or other conditions on the boundary. A prominent example is the problem of diffraction from a quarter-plane in ℝ3, which admits an explicit solution. In this paper the Dirichlet and Neumann problems for the three-quarter-plane are solved by an algebraic trick: the matricial coupling of operators associated to “dual” boundary value problems, a kind of abstract Babinet principle.