Adaptive absorbing boundary conditions for high accuracy scattering

Two kinds of absorbing boundary conditions (ABCs) are described in the literature: global ABCs that provide exact results but generate dense matrices on the boundary, and local ABCs that provide approximate results but generate sparse matrices. Both kinds of ABCs may be used to truncate solution regions to finite size with finite element or finite difference methods. However, heretofore, developers had to choose between the high accuracy but slow speed of global ABCs, or the low accuracy but high speed of local ABCs. The paper proposes a new, adaptive approach for generating local ABCs. In this adaptive procedure, the scattered field is computed iteratively and the parameters defining the local ABC at each point on the boundary adapt to the local characteristics of the scattered field. The result is a ABC with high efficiency because it maintains the sparsity of the finite element or finite difference matrix, yet it provides high accuracy because the local parameters ate adjusted to converge to exact results.<>