Extending the fast multipole method to charges inside or outside a dielectric sphere

In this paper, we propose a novel method to extend the fast multipole method (FMM) to calculate the electrostatic potential due to charges inside or outside a dielectric sphere. The key result which allows such an extension is the construction of a small number (two for a 10−2 relative error in reaction potentials inside the sphere) of image point charges for source point charges inside or outside the dielectric sphere. Numerical results validate the accuracy and high efficiency of the resulting algorithm.