High-order integral equation methods for problems of scattering by bumps and cavities on half-planes

This paper presents high-order integral equation methods for evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced in this paper apply to eight classical scattering problems, namely: scattering by a dielectric bump on a perfectly conducting or a dielectric half-plane, and scattering by a filled, overfilled or void dielectric cavity on a perfectly conducting or a dielectric half-plane. In all cases field representations based on single-layer potentials for appropriately chosen Green functions are used. The numerical far fields and near fields exhibit excellent convergence as discretizations are refined--even at and around points where singular fields and infinite currents exist.Comment: 25 pages, 7 figure

Time Domain Analysis of Electromagnetic Scattering From Multiple Cavities Embedded in a Ground Plane

This work examines the scattered fields produced when a transient wave is reflected from an infinite perfect electric conductor (PEC) ground plane with multiple embedded cavities. Incident and reflected waves will be decomposed into transverse magnetic to the z direction (TMz) and transverse electric to the z direction (TEz) polarizations, with primary focus given to the TMz. Cavities may be unfilled, partially filled, or fully filled with non-magnetic dielectric material and no assumptions are made regarding similarity, regularity, or periodicity. The Newmark method is used to discretize time and a variational formulation is presented for each time step. The principle outcome is to show that the variational formulation of the scalar problem is well posed. Additionally, the variational formulation is applied in a stable numerical model using the finite element-boundary integral (FE-BI) method. Interior fields are approximated using the finite element method (FEM) for each time step, then the boundary integral is applied using the appropriate Green’s function to approximate exterior scattered fields. The exterior fields for one time step provide the boundary conditions for the interior problem at the next time step. In this way, the numerical model marches through time. Various numerical experiments are run to examine the effect of coupling on aperture and external fields. Of particular interest are the differences between single-cavity and multiple-cavity solutions

A Finite Element Approach to Model Electromagnetic Fields Scattered by a Buried Cavity

This research investigates the plane-wave scattering from a two-dimensional arbitrarily shaped cavity embedded in an infinite metallic surface that has been covered with a layer or layers of dielectric material, considering both transverse electric and transverse magnetic polarizations. Due to the shape of the cavity, this problem is approached using the finite element method. This approach provides a boundary condition at the opening of the cavity which accounts for the effect of the overlayer(s) while confining the problem to the finite domain of the cavity itself. After determination of the solution for the electric and magnetic fields at the cavity aperture, the strength of the return echo can then be calculated and displayed in a radar cross section. In addition, numerical verifications and experiments illustrating the efficacy of the approach will be provided by comparison to other previously tested methods