独立覆盖流形法的通用计算公式和通用程序设计——(二)通用程序设计  

General Formulas and Program Design for Manifold Method Based onIndependent CoversⅡ:General Program Design

作　　者：苏海东[1,2] 杨震 颉志强 祁勇峰[1,2] 龚亚琦 SU Hai-dong;YANG Zhen;XIE Zhi-qiang;QI Yong-feng;GONG Ya-qi(Material and Engineering Structure Department,Changjiang River Scientific Research Institute,Wuhan 430010,China;Research Center of Water Engineering Safety and Disaster Prevention of Ministry ofWater Resources,Wuhan 430010,China)

机构地区：[1]长江科学院材料与结构研究所,武汉430010 [2]水利部水工程安全与病害防治中心,武汉430010

出　　处：《长江科学院院报》2025年第4期202-210,共9页Journal of Changjiang River Scientific Research Institute

基　　金：国家自然科学基金项目(U2340229)。

摘　　要：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.

关 键 词：偏微分方程 级数解 网格剖分 精确几何 独立覆盖 数值流形方法 

分 类 号：O241.82[理学—计算数学]