The algorithm of simplex integration in three-dimension and its characteristic analysis

An algorithm of integration written by C++ language are proposed based on the analysis of simplex integration over a polynomial expression in three-dimension, and the calculational procedure for simplex integration is described with concrete examples in this paper. Firstly, we analyze the accuracy of the simplex integration through comparing the theoretical results with calculated results, in which parameters include the volume and gravity centers and the integral field is regular but with hollow. Then, the influence of graphic conditions on the results of simplex integration are discussed through comparing the theoretical results with calculated results in different edge length ratio(10^-5-10⁵). Secondly, the adaptive characteristics of simplex integration algorithm are discussed through analyzing integral results in irregular integral space with hollow. Finally, the precision of simplex integration are discussed which the integral term is high-order polynomial, and the integral spaces are also irregular with hollow. The results show that the relative error between calculated results and theoretical results is about 10^-15-10^-14, and the graphics conditions have minimal impact on integral results and the impact has not systematic characteristics. In conclusion, the difference between the calculated results and theoretical results is caused by computing error, and the results of simplex integration have high stability and accuracy.