Global boundary conditions and fast Helmholtz solvers

Electromagnetic scattering from a conducting two-dimensional cylinder is modeled by solving Helmholtz´s equation with the far-field radiation boundary condition replaced by a global boundary condition allowing. This allows the boundary condition to be applied very near the scatterer. The discrete problem is solved by a biconjugate gradient algorithm. Incomplete LU decomposition is used as a preconditioning strategy, resulting in very fast convergence. The numerical solution is compared with known solutions and found to converge fasters for ka⩽10, where k is the wave number and a is the radius of the cylinder