Finite Element Solution for Electromagnetic Scattering from Two-Dimensional Bodies.

Abstract

The problem of two-dimensional electromagnetic scattering from bodies in free space has been formulated using a differential equation finite element method. An incident plane wave polarized so as to excite only E-wave fields has been assumed. A weak integral statement was obtained using an approach equivalent to the weighted residuals method, the weighting functions being selected by Galerkin's method. The finite element mesh of general first-order quadrilaterals extended outward into the far field region of the scattering body, where the boundary condition at the outer boundary was obtained from the asymptotic expression for the scattered field. In order to compare the finite element method with an integral equation moment method, a special case was solved numerically, namely that of a thin, infinitely long resistive strip. Accurate numerical results from a moment method solution were available to serve as a check on the accuracy of the finite element method results. For a perfectly conducting strip (the limiting case of a resistive strip) the finite element mesh contained special triangular elements at the edges of the strip to model the singularities in the magnetic field which occur there. Two important disadvantages of the finite element solution became apparent. First, the boundary condition used at the outer boundary leads to the presence of st and ing waves in the computed scattered field, a non-physical result. Second, the computer memory required increases much more rapidly with strip width than in the moment method solution. The finite element method used was thus unable to compete with the moment method solution for the thin strip problem. However, to demonstrate a problem for which a moment method solution may be less attractive because of its increased memory requirements, numerical results were obtained using the finite element method for scattering from a body consisting of a thin resistive strip embedded in a dielectric cylinder.