Finite-element analysis of dielectric scatterers using the absorbing boundary condition

When open-region scattering problems are solved by the finite-element method (FEM), the infinite region exterior to the scatterer must be truncated by an artificial outer boundary in order to permit practical implementation on a digital computer. It is shown how an absorbing boundary condition (ABC) can be enforced at this boundary to truncate the mesh at distances close to the surface of the scatterer, so that the ABC not only simulates the outward propagating nature of the scattered field but also ensures the well-posedness of the problem. It is found that if the finite-element problem is formulated using the scattered field as the primary unknown, the solution agrees well with the method-of-moments solution. However, the FEM solution is found to have significant errors if the problem is formulated using the total field