Computational efficiencies of approximated exponential functions for transport calculations of the characteristics method

In this paper, various approximations of the exponential function are tested from the viewpoint of computational efficiency, i.e. accuracy and computation time. Since considerable part of computation time is devoted to the evaluation of the exponential function in transport calculations using the characteristics method, reduction of its computation time is important. Evaluations of the approximations are carried out on a Linux operating system using two different processors, i.e. Xeon 2.8GHz with 2MB L3 cache and Pentium-III 800 MHz with 512 KB L2 cache. In order to grasp the impact of approximation error of the exponential function on transport calculation results, some sensitivity calculations are executed using the characteristics method. The evaluation results indicate that the table lookup method with linear interpolation or second-order interpolation is computationally efficient for practical calculations.