Publications Details

On Practical Modifications to the Barnes-Hut Multipole Method for Electromagnetic Scattering

Driessen, B.J.; Kotulski, J.D.

This paper presents a simple methodology for quickly predicting and optimizing computer run time for the Barnes-Hut multipole method for boundary element electromagnetic scattering problems. The methodology is easily extended to other multipole methods (e.g., Greengard-Rokhlin) and to other physics. The idea is to simply COZM t 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 :un-time to perform a single matrix-vector multiply. By counting operations instead of actually performing them, the time to predict the computer run time is orders of magnitude smaller than the time to actually perform the associated calculations. This allows for very quick optimization of parameters, such as the maximum number of elements in a final generation cell of the tree. Numerical examples are presented herein in which the rate of return (time saved over time spent finding optimal parameter values) is significantly more than two orders of magnitude.