Two-dimensional numerical manifold method with multilayer covers

作     者：LIU ZhiJun ZHENG Hong 

作者机构：State Key Laboratory of Geomechanics and Geotechnical Engineering Institute of Rock and Soil Mechanics Chinese Academy of Sciences Key Laboratory of Urban Security and Disaster Engineering Ministry of Education Beijing University of Technology 

出 版 物：《Science China(Technological Sciences)》 (中国科学（技术科学英文版）)

年 卷 期：2016年第59卷第4期

页      面：515-530页

核心收录：

学科分类：0810[工学-信息与通信工程] 081803[工学-地质工程] 08[工学] 080104[工学-工程力学] 0818[工学-地质资源与地质工程] 0815[工学-水利工程] 0805[工学-材料科学与工程（可授工学、理学学位）] 0702[理学-物理学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by the National Basic Research Program of China("973"Project)(Grant Nos.2011CB013505&2014CB047100) the National Natural Science Foundation of China(Grant Nos.11572009&51538001) 

主　　题：numerical manifold method finite element method covers hanging nodes structured local refinement short cracks 

摘      要：In order to reach the best numerical properties with the numerical manifold method(NMM),uniform finite element meshes are always favorite while constructing mathematical covers,where all the elements are *** the presence of steep gradients or strong singularities,in principle,the locally-defined special functions can be added into the NMM space by means of the partition of unity,but they are not available to those complex problems with heterogeneity or nonlinearity,necessitating local refinement on uniform *** is believed to be one of the most important open issues in *** this study multilayer covers are proposed to solve this *** addition to the first layer cover which is the global cover and covers the whole problem domain,the second and higher layer covers with smaller elements,called local covers,are used to cover those local regions with steep gradients or strong *** global cover and the local covers have their own partition of unity,and they all participate in the approximation to the *** advantageous over the existing procedures,the proposed approach is easy to deal with any arbitrary-layer hanging nodes with no need to construct super-elements with variable number of edge nodes or introduce the Lagrange multipliers to enforce the continuity between small and big *** no limitation to cover layers,meanwhile,the creation of an even error distribution over the whole problem domain is significantly *** typical examples with steep gradients or strong singularities are analyzed to demonstrate the capacity of the proposed approach.