Exponential degenerate kernel function for electromagnetic scattering problems

An efficient exponential degenerate kernel function is proposed for electromagnetic scattering problem in this Letter, which provides another diagonal form of the translation matrix. The exponential degenerate kernel function is numerically determined for kernel independency. The error analysis verifies that less expansion terms are needed for the given accuracy for simulations. Numerical results validate the accuracy of the proposed degenerate kernel. It can be concluded that the proposed kernel approximation outperforms the expansion in the fast multipole method in both computational time and storage.