评估ATAM计算效率提高程度的新算法  

A new algorithm for evaluating computing efficiency of ATAM

作　　者：李琦 李彬 孟晓军[1] 唐小微 LI Qi;LI Bin;MENG Xiaojun;TANG Xiaowei(College of Mechanical and Architectural Engineering,Taishan University,Taian 271000,China;State Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]泰山学院机械与建筑工程学院,山东泰安271000 [2]大连理工大学海岸和近海工程国家重点实验室,辽宁大连116024

出　　处：《振动与冲击》2021年第7期62-67,118,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金重点项目(51639002);国家重点研究开发计划(2018YFC1505305);山东省自然科学基金联合专项(ZR2018-LE017)。

摘　　要：在《与荷载同步变化的时间步自动调整方法》中提出的时间步自动调整方法(apriori time adaptive method,ATAM)是先验式误差评估研究领域的一次有益尝试。在ATAM使用过程中,由于一般情况下难以获得解析解,所以对数值计算程序应用ATAM自动调整时间步长后,相比时间步调整前,无法评估计算效率具体提高了多少。为了解决这个问题,提出了解决方法并对其进行了验证。在此基础上,进一步提出了一种简易评估算法,并推导出评估计算效率提高程度的计算公式。根据此计算公式,不需要采用最小时间步长代入到原数值程序中进行计算,可直接获得计算效率的提高程度,节省了大量计算成本。同时,对简易评估算法进行了验证,结果证实所提算法实用有效。The method of time step automatic adjustment proposed in“The time step automatic adjustment method with synchronous change of load”is a beneficial attempt in the field of prior error evaluation,it is called the apriori time adaptive method(ATAM).In process of using ATAM,it is generally difficult to obtain analytical solutions.Therefore,it is impossible to evaluate the improvement degree of calculation efficiency after applying ATAM in numerical computing programs.Here,a method to solve this problem was proposed and verified.Then,a simplified evaluation algorithm was further proposed,and a calculation formula to estimate the improvement degree of computing efficiency was deduced.It was shown that according to this calculation formula,the minimum time step is not needed to be substituted into the original numerical program for improving the computing efficiency;using the new evaluation algorithm can directly improve the computing efficiency and save a lot of computing costs;the practicability and effectiveness of the new evaluation algorithm are verified.

关 键 词：时间自适应 先验法 计算效率 计算精度 

分 类 号：TU311.3[建筑科学—结构工程]