Numerical algorithms for inverse and direct diffraction problems of rectangular grating

This paper is concerned with the rectangular diffraction grating problem, firstly we design a fast algorithm for direct problem, which called least-squares finite element method, and use it to calculate the total field u. Secondly, use Sequential Monte Carlo sampling method to calculate the width and the height of the rectangular grating. The results show that the combination of the least squares finite element method and SMC method can better estimate the width and the height of the rectangular grating and improve the computation speed.