在应用独立覆盖流形法进行自适应分析的前期研究中,发现独立覆盖内部误差不易控制的问题,基于此,提出独立覆盖误差分析的子模型法。在单独的独立覆盖内进行覆盖函数的升阶操作,通过高、低阶之间的相对误差获得独立覆盖内部的逐点误差指标。详细介绍了子模型法的实施步骤,用重力坝算例验证了该方法能有效控制独立覆盖内部误差,不仅解决了目前存在的问题,还为将来实现逐点的误差控制打下基础。最后对独立覆盖流形法的收敛原理及误差控制方法进行了初步的理论分析和讨论。
Abstract
In previous research of adaptive analysis using Numerical Manifold Method based on independent covers, the internal error in an independent cover cannot be effectively controlled. In view of this, a submodel method for error analysis of independent covers is presented, in which, by means of increasing the cover function order in an individual independent cover, a new error estimator for point-by-point error is obtained by calculating the differences of the results between high-order and low-order cover functions. The procedures of the submodel method are introduced in detail, and a case study of a gravity dam shows that the method could effectively control the internal error of independent covers, laying foundation for point-by-point error control in the future. Finally some preliminary theoretical analysis and discussions are given for the convergence principle and the error-control method of Numerical Manifold Method based on independent covers.
关键词
数值流形方法 /
独立覆盖 /
误差分析 /
子模型法 /
自适应分析
Key words
Numerical Manifold Method(NMM) /
independent covers /
error analysis /
submodel method /
adaptive analysis
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参考文献
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基金
国家自然科学基金项目(51409012);中央级公益性科研院所基本科研业务费项目(CKSF2016266/CL)
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