Abstract:

A least squares method was used to solve the time harmonic scattering problem corresponding to total internal reflection microscopy. The trial space was constructed via plane wave functions and evanescent wave functions and the functional was defined by means of the interface jumps of the solution and its normal derivative and the discrepancy with respect to the boundary condition. Our method easily used needs fewer elements with high accuracy. Numerical
 examples presented illustrate the effectiveness of the approach.

Key words: Helmholtz equation, least squares method, plane wave function