Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Superconvergence and ultraconvergence of Newton-Cotes rules for supersingular integrals
Journal of Computational and Applied Mathematics
Convergence analysis of non-conforming Trigonometric Finite Wave Elements
Journal of Computational and Applied Mathematics
Matrix decomposition algorithms for elliptic boundary value problems: a survey
Numerical Algorithms
Numerical solution of electromagnetic scattering from a large partly covered cavity
Journal of Computational and Applied Mathematics
Journal of Computational Physics
GMRES with adaptively deflated restarting and its performance on an electromagnetic cavity problem
Applied Numerical Mathematics
A composite preconditioner for the electromagnetic scattering from a large cavity
Journal of Computational Physics
A numerical study of air-vapor-heat transport through textile materials with a moving interface
Journal of Computational and Applied Mathematics
A new preconditioner for the interface system arising in a fast Helmholtz solver
Computers & Mathematics with Applications
Numerical approximations to integrals with a highly oscillatory Bessel kernel
Applied Numerical Mathematics
Modified block preconditioners for the discretized time-harmonic Maxwell equations in mixed form
Journal of Computational and Applied Mathematics
A Fast Preconditioned Iterative Algorithm for the Electromagnetic Scattering from a Large Cavity
Journal of Scientific Computing
A two-dimensional Helmhotlz equation solution for the multiple cavity scattering problem
Journal of Computational Physics
Journal of Computational Physics
Exponentially-fitted Gauss-Laguerre quadrature rule for integrals over an unbounded interval
Journal of Computational and Applied Mathematics
On evaluation of Bessel transforms with oscillatory and algebraic singular integrands
Journal of Computational and Applied Mathematics
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A fast algorithm is presented for solving electromagnetic scattering from a rectangular open cavity embedded in an infinite ground plane. The medium inside the cavity is assumed to be (vertically) layered. By introducing a transparent (artificial) boundary condition, the problem in the open cavity is reduced to a bounded domain problem. A simple finite difference method is then applied to solve the model Helmholtz equation. The fast algorithm is designed for solving the resulting discrete system in terms of the discrete Fourier transform in the horizontal direction, a Gaussian elimination in the vertical direction, and a preconditioning conjugate gradient method with a complex diagonal preconditioner for the indefinite interface system. The existence and uniqueness of the finite difference solution are established for arbitrary wave numbers. Our numerical experiments for large numbers of mesh points, up to 16 million unknowns, and for large wave numbers, e.g., between 100 and 200 wavelengths, show that the algorithm is extremely efficient. The cost for calculating the radar cross section, which is of significant interest in practice, is O(M2) for an $M \times M$ mesh. The proposed algorithm may be extended easily to solve discrete systems from other discretization methods of the model problem.