Explicit moment integration algorithm and its application

The calculation of moment is often used in finite element method, volume calculation, moment of inertia calculation, etc. A discrete method of the computational domain in three-dimensional space was proposed firstly based on the superposition of moment. An explicit formula was derived in three-dimensional space and then extended to n-dimensional space, which can be easily implemented on the computer. Secondly, a parallel algorithm of moment calculation was designed and implemented with mixed Fortran and Python. Thirdly, a zero-order and second-order moment was calculated in a multi-fidelity example. The efficiency of the algorithm was compared with a serial algorithm and a successive dimensionality reduction algorithm. Meanwhile, efficiency analysis and error analysis were presented. The result shows that the explicit moment integration algorithm can be easily implemented with programs and runs faster than the serial algorithm. It is highly parallel and can also be easily extended to a higher dimensional space. The algorithm is highly parallel, whose error mainly comes from the discrete process of the computational domain.