Discussion of 'Efficient Algorithm for Computing Einstein Integrals' by Junke Guo and Pierre Y. Julien

摘要

The discussers have found an explicit approximation for the Einstein Integrals which result in a discrepancy less than 1% to the approximation of the writers, though the approximation has greater errors when the dimensionless reference height becomes bigger than 0.01 for the first integral and 0.007 for the second integral. However, a huge fraction of natural conditions is covered by this approximation. The calculation speed is more than two orders faster than the approximation of the writers and nearly twice as fast as the recurrence formula suggested by Guo et al. (1996), which is the foundation for the suggested formula. The combination of the explicit approximation and the recurrence formula is suggested as an optimal algorithm for the estimation of both integrals. In the following, the recurrence formula of Guo et al. (Approximation Ⅱ) and the explicit approximation (Approximation Ⅲ) by the discusser will be compared with respect to performance and accuracy with the actual formulation of the writers (Approximation Ⅰ).