Error in the finite element discretization of the scalar Helmholtz equation over electrically large regions

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Abstract
Discretization error arising from a finite element solution of the scalar Helmholtz equation for open-region geometries is studied for the simple case of scattering from dielectric slabs. In electrically large homogeneous regions, the primary source of error is found to be phase error that increases progressively in a direction away from the boundary where the excitation is coupled into the computational domain. The error can be reduced by using smaller cell sizes, using higher order polynomial basis functions, or using a modified scattered field formulation that couples the excitation into the equation in a different manner. Since the scattered field formulation locates the phase reference within the scatterer, that formulation is likely to produce more accurate numerical solutions in the immediate vicinity of the scatterer than the total field formulation, especially if the scatterer is far from the boundaries of the computational domain.