Derivation and application of conformal absorbing boundary conditions in 3D scattering

The computation of scattering from 3D geometries has been carried out using partial differential equation (PDE) techniques and integral equation (IE) methods. As the problem size increases, PDE techniques become more attractive since the required computational resources scale linearly with the number of unknowns. However, for open domain problems like radiation or scattering, one must also consider the efficiency and accuracy of the mesh termination scheme. As is well known, the mesh truncation condition can be exact or approximate. Exact boundary conditions like the combined finite element-boundary integral formulation implemented in Yuan (1990) result in full submatrices that severely limit the problem size. Approximate boundary conditions or absorbing boundary conditions (ABCs) are local in nature and preserve the sparsity of the finite element matrix. The ideal situation would be to enclose the scatterer inside a mesh termination boundary which is of the same shape as the scattering body. In Chatterjee and Volakis (1993), a new absorbing boundary conditions was derived which can be employed on mesh truncation surfaces conforms to the surface of the target. The present authors show how the ABCs in Chatterjee and Volakis can be incorporated into the finite element equations. They also comment on the symmetry of the system for doubly curved surfaces. In the last section, they examine the performance of these ABCs, in terms of computational cost, when applied on mesh termination surfaces conformal to the scattering object.<>