Error Estimation for Numerical Methods Using the Ultra Weak Variational Formulation in Model of Near Field Scattering Problem (Journal of Computational Mathematics, 2018)
In this paper, we investigate the use of ultra weak variational formulation to solve a wave scattering problem in near field optics. In order to capture the sub-scale features of waves, we utilize evanescent wave functions together with plane wave functions to approximate the local properties of the field. We analyze the global convergence and give an error estimation of the method. Numerical examples are also presented to demonstrate the effectiveness of the strategy.
Keywords: Helmholtz equation; Ultra weak variational formulation; Plane wave function; Evanescent wave function; Absorbing boundary condition.