Predicting computer run-time for the Barnes-Hut multipole method for electromagnetic scattering

摘要

this paper presents a novel simple methodology for quickly predicting and optimizing computer run-time for the Barnes-Hut multipole metod for boundary element electromagnetic scattering problems. the methodology is easi9ly extended to other multipole methods (e.g. Greengard-Rokhlin) and to other physics. The novel idea is to simply count the number of element-cell interactions, number of direct Element-element interactions, and the number of cell multipole expansion creations (each expansion weighted by the number of elements in The cell), and then finally combine these three results with the associated unit costs to obtain the total computer run-time to perform a single Matrix-vector multiply.