在独立覆盖流形法通用计算公式的基础上,给出了计算程序的整体流程。对一维至三维各种几何形体(包括分区、条带和边界面)的积分方式进行总结,基于点、线、面、体的单纯形几何元素开发积分程序,实现网格形状的通用性。提出将积分模块与被积函数模块分开考虑的编程思路,然后再将两者任意组合,使程序具备了扩展性,有望实现偏微分方程求解的通用性。通过级数公式和相应的各种坐标以及坐标转换矩阵、级数矩阵的确定,实现了级数的通用性。所有计算参数都可以通过用户子程序输入公式,实现输入参数的通用性。最终可用较少的程序代码,实现弹性力学运动微分方程、传导方程、波动方程的一维至三维稳态和瞬态分析(含一类至三类边界条件)。

Based on the general calculation formula of the manifold method based on independent covers presented in the previous article, we provide the flowchart of the calculation program. First, we summarize the integration methods for various geometric shapes (such as partitions, stripes, and boundary faces) that may appear in one- to three-dimensional spaces. On this basis, we develop integration programs according to simplex geometric elements of points, lines, faces, and bodies. This approach ensures the universality for any mesh shape. Next, we propose a programming strategy that separates the integration module from the integrand function module. The arbitrary combination of these two modules endows the program with extensibility and the potential to achieve universality in solving partial differential equations. Moreover, the universality of series is realized through the determination of series formulas, corresponding coordinates, coordinate transformation matrices, and series matrices. In addition, all calculation parameters can be input via formulas using user subroutines, thus achieving universality of input parameters. Ultimately, with relatively less program code, we can conduct one- to three- dimensional steady-state and transient analyses of the differential equations of motion in elasticity, conduction equations, and wave equations, including one to three types of boundary conditions.