A Combination of BIM and BEM for efficiently analyzing optical elements

We propose the revised boundary integral method (RBIM) that combines the boundary integral method (BIM) and the boundary element method (BEM) together. It is well known that the boundary integral equations are cast into matrix form for ease of computer implementation, and the points on the diagonal line of the matrix present the superposition of the observation and the source points. The points are called singularity points which can cause the big error bar. Thus, we consider replacing the BIM by the BEM at the diagonal line, comparing the numerical results by using the RBIM, the BIM, the BEM, and the analytical method, and find the error bar caused by the RBIM is smaller than that of the BIM. It indicates that the RBIM is not only faster than the BEM, but also it is preciser than BIM