Paper Info
Title
Arbitrary high-order C0 tensor product Galerkin finite element methods for the electromagnetic scattering from a large cavity
Abstract
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.
Year
DOI
Venue
2013
10.1016/j.jcp.2013.02.015
J. Comput. Physics
Keywords
Field
DocType
c0 tensor product,nonlocal operator,arbitrary high-order,boundary condition,electromagnetic scattering,large cavity,cavity problem,nonlocal boundary condition,numerical result,fast algorithm,electromagnetic cavity problem,galerkin finite element method,helmholtz equation
Tensor product,Boundary value problem,Mathematical optimization,Mathematical analysis,Galerkin method,Integral equation,Finite element method,Helmholtz equation,Fast Fourier transform,Electromagnetic cavity,Mathematics
Journal
Volume
ISSN
Citations 
242,
0021-9991
3
PageRank 
References 
Authors
0.44
14
3
Name
Order
Citations
PageRank
Kui Du1346.50
Weiwei Sun215415.12
Xiaoping Zhang3375.73