Boundary conditions for the solution of open-region electromagnetic scattering problems

Abstract

When solving open-region radiation problems using finite mathematics techniques, an absorbing boundary condition must be used to truncate the mesh region. A review of analytical absorbing boundary conditions that have been derived previously is presented, and an alternate, analytical-type, absorbing boundary operator is derived. It is found that when the outer boundary is brought very close to the scatterer to minimize the mesh region in the finite element solution of electrically large body problems, nonphysical reflections introduce significant errors in the solution. An analysis of the source of these errors is discussed, which highlights the underlying fundamental limitations encountered in the derivation of highly accurate and local absorbing boundary conditions in analytical forms. Next, a methodology for deriving boundary conditions that are local but still represent an approximation of the exact boundary condition is proposed. The numerically derived boundary operators are found to enhance the accuracy and efficiency of the finite element solution, without significant degradation of the sparsity of the system matrix. Finally, a systematic finite element method is developed for the purpose of solving a class of unbounded geometries, including inhomogeneously filled cavities or troughs. Numerical results are presented to show the validity and flexibility of the new technique.