On the Investigation of Triangular Interpolation-based Multilevel Fast Multipole Algorithm

The efficiency of the multilevel fast multipole algorithm (MFLMA) is improved by using the triangular interpolation instead of the commonly used Lagrange interpolation. For pth-degree interpolation, the data points used for the triangular interpolation are only $(p+2)/(2p + 2)$ of the Lagrange interpolation, while the interpolation accuracy is in the same order. Numerical results of electromagnetic scattering from conducting sphere are shown to illustrate the accuracy and efficiency of the proposed method.