Interval Arithmetic and Computational Science: Rounding and Truncation Errors in N-Body Methods

Interval arithmetic is an alternative computational paradigm that enables arithmetic operations to be performed with guarantee error bounds. In this paper interval arithmetic is used to compare the accuracy of various methods for computing the electrostatic energy for a system of point charges. A number of summation approaches that scale as O(N²) are considered, as is an O(N) scaling Fast Multipole Method (FMM). Results are presented for various sizes of water cluster in which each water molecule is described using the popular TIP3P water model. For FMM a subtle balance between the dominance of either rounding or truncation errors is demonstrated.