Abstract:

An ultra weak variational method was proposed for the time harmonic scattering problem in view of total internal reflection microscopy as a model. Based on the partition of the computational domain, the problem was transformed into the one on the skeleton of the mesh. By Green identity, the equivalent ultra weak variational formulation was deduced. Then plane wave functions and evanescent wave functions were used to approximate the local property of the solution. The method is suitable for the problems with big wave number, and has a fast rate of convergence, by which  the scattering problem in near field can be effectively solved.

Key words: ultra weak variational formulation, plane wave function, evanescent wave function