SIAM Journal on Numerical Analysis
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
A Fast Algorithm for the Electromagnetic Scattering from a Large Cavity
SIAM Journal on Scientific Computing
Analysis of electromagnetic scattering from an overfilled cavity in the ground plane
Journal of Computational Physics
Applied Numerical Mathematics
A Compact Fourth Order Scheme for the Helmholtz Equation in Polar Coordinates
Journal of Scientific Computing
Compact optimal quadratic spline collocation methods for the Helmholtz equation
Journal of Computational Physics
Journal of Computational Physics
A composite preconditioner for the electromagnetic scattering from a large cavity
Journal of Computational Physics
A new preconditioner for the interface system arising in a fast Helmholtz solver
Computers & Mathematics with Applications
The Method of Difference Potentials for the Helmholtz Equation Using Compact High Order Schemes
Journal of Scientific Computing
Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number
Journal of Computational Physics
A Fast Preconditioned Iterative Algorithm for the Electromagnetic Scattering from a Large Cavity
Journal of Scientific Computing
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The paper is concerned with the electromagnetic scattering from a large cavity embedded in an infinite ground plane. 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. A tensor product Galerkin finite element method (FEM) is proposed, in which spaces of C^0 piecewise polynomials of degree @k=1 are employed. By the fast Fourier transform and the Toeplitz-type structure of the approximation to the nonlocal operator in the nonlocal boundary condition, a fast algorithm is designed for solving the linear system arising from the cavity problem with (vertically) layered media, which requires O(N^2logN) operations on an NxN uniform partition. Numerical results for model problems illustrate the efficiency of the fast algorithm and exhibit the expected optimal global convergence rates of the finite element methods. Moreover, our numerical results also show that the high-order approximations are especially effective for problems with large wave numbers.