Title :
Vector one-way wave absorbing boundary conditions for FEM applications
Author :
Sun, Weimin ; Balanis, Constantine A.
Author_Institution :
Telecommun. Res. Center, Arizona State Univ., Tempe, AZ, USA
fDate :
6/1/1994 12:00:00 AM
Abstract :
In the paper a derivation is presented which leads to a new and general class of vector absorbing boundary conditions (ABCs) for use with the finite element method (FEM). The derivation is based on a vector one-way wave equation and a polynomial approximation of the vector radical. It is shown that wide-angle absorbing boundary conditions, as proposed in Halpern and Trefethen (1988) for optimal absorption of out-going waves, can be obtained in vector form. Vector plane waves are used to evaluate the accuracy and the reflection performance of these boundary conditions in a wide range of incidence angles. The implementation of the vector ABCs in a FEM formulation is also provided to show how up to the fifth-order absorbing accuracy can be achieved with derivatives only up to the second-order. A possible formulation is described which not only yields a third-order accuracy with first-order derivatives, but also retains the symmetry of the FEM matrix
Keywords :
approximation theory; boundary-value problems; electromagnetic wave reflection; electromagnetic wave scattering; finite element analysis; matrix algebra; polynomials; FEM applications; fifth-order absorbing accuracy; finite element method; first-order derivatives; incidence angles; matrix; optimal absorption; outgoing waves; polynomial approximation; reflection performance; second-order derivatives; third-order accuracy; vector one-way wave absorbing boundary conditions; vector radical; wide-angle absorbing boundary conditions; Absorption; Boundary conditions; Electromagnetic modeling; Finite difference methods; Finite element methods; Lead; Partial differential equations; Polynomials; Reflection; Sun;
Journal_Title :
Antennas and Propagation, IEEE Transactions on