The Helmholtz Dirichlet and Neumann problems on piecewise smooth open
curves
The Helmholtz Dirichlet and Neumann problems on piecewise smooth open
curves
A numerical scheme is presented for solving the Helmholtz equation with Dirichlet or Neumann boundary conditions on piecewise smooth open curves, where the curves may have corners and multiple junctions. Existing integral equation methods for smooth open curves rely on analyzing the exact singularities of the density at endpoints for …