A composite preconditioner for the electromagnetic scattering from a large cavity

In this paper, we propose a composite preconditioner for the electromagnetic scattering from a large cavity. The electromagnetic cavity problem is described by the Helmholtz equation with a nonlocal boundary condition on the aperture of the cavity and Dirichlet (or Neumann) boundary conditions on the walls of the cavity. The preconditioner proposed here combines the optimal sine transform based approximation with a layered medium model. Using fast Fourier transforms, the computational cost of every iteration is O ( N 2 log N ) on an N × N uniform partition of the unit square. Numerical results for a model problem show that the new preconditioner is more efficient than those recently considered in the literature. For the cavity with a small portion of non-layered media, we propose a sparse preconditioned conjugate orthogonal conjugate gradient solver combined with the new preconditioner. Numerical results for a model problem are reported to demonstrate the efficiency of the sparse solver.