TY - JOUR
T1 - Arbitrary high-order C0 tensor product Galerkin finite element methods for the electromagnetic scattering from a large cavity
AU - Du, Kui
AU - Sun, Weiwei
AU - Zhang, Xiaoping
PY - 2013/6/1
Y1 - 2013/6/1
N2 - 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 C0 piecewise polynomials of degree κ ≥ 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(N2logN) operations on an N × N 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. © 2013 Elsevier Inc.
AB - 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 C0 piecewise polynomials of degree κ ≥ 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(N2logN) operations on an N × N 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. © 2013 Elsevier Inc.
KW - Electromagnetic scattering
KW - Fast algorithm
KW - Helmholtz equation
KW - Tensor product FEM
UR - http://www.scopus.com/inward/record.url?scp=84875058545&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84875058545&origin=recordpage
U2 - 10.1016/j.jcp.2013.02.015
DO - 10.1016/j.jcp.2013.02.015
M3 - RGC 21 - Publication in refereed journal
VL - 242
SP - 181
EP - 195
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
ER -