TY - JOUR

T1 - A generalized and efficient method for finite cover generation in the numerical manifold method

AU - Cai, Yongchang

AU - Zhuang, Xiaoying

AU - Zhu, Hehua

N1 - Funding information: The authors gratefully acknowledge the support of National Basic Research Program of China (973 Program: 2011CB013800), Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT, IRT1029), the Fundamental

PY - 2013/4/17

Y1 - 2013/4/17

N2 - The numerical manifold method (NMM) based on the concept of finite covers and the partition of unity (PU) provides a unified framework to analyze continuum and discontinuum without changing predefined mesh in a discretized way. The NMM has been applied in the modeling of fluid structure interaction as well as in rock mechanics including the analysis of block system, jointed rock and fractured body, showing particular advantages over other PU based methods. Unlike other PU methods, the degrees of freedoms in the NMM are associated with the physical covers, rather than the nodes, which allow it to be naturally adapted to the changing geometries in analyzing complex discontinuum such as multiple intersecting cracks and branched cracks. Despite these recent advances, there is no publication available to date describing the physical cover generation of the NMM in a systematic way or giving a general principle of cover numbering, which has practically limited a wider application of the NMM. To address this issue, a generalized cover generation method is developed in the paper based on the concept of "detached physical cover" where manifold elements belonging to the same mathematical cover and having common mathematical edges are collected to form a new detached physical cover. The present method has a concise formulation for implementation, and is effective and generally applicable for dealing with interfaces, inclusions or discontinuities of complex geometry. A test example is performed showing the correctness, robustness and efficiency of the proposed method.

AB - The numerical manifold method (NMM) based on the concept of finite covers and the partition of unity (PU) provides a unified framework to analyze continuum and discontinuum without changing predefined mesh in a discretized way. The NMM has been applied in the modeling of fluid structure interaction as well as in rock mechanics including the analysis of block system, jointed rock and fractured body, showing particular advantages over other PU based methods. Unlike other PU methods, the degrees of freedoms in the NMM are associated with the physical covers, rather than the nodes, which allow it to be naturally adapted to the changing geometries in analyzing complex discontinuum such as multiple intersecting cracks and branched cracks. Despite these recent advances, there is no publication available to date describing the physical cover generation of the NMM in a systematic way or giving a general principle of cover numbering, which has practically limited a wider application of the NMM. To address this issue, a generalized cover generation method is developed in the paper based on the concept of "detached physical cover" where manifold elements belonging to the same mathematical cover and having common mathematical edges are collected to form a new detached physical cover. The present method has a concise formulation for implementation, and is effective and generally applicable for dealing with interfaces, inclusions or discontinuities of complex geometry. A test example is performed showing the correctness, robustness and efficiency of the proposed method.

KW - finite cover

KW - manifold element

KW - mathematical cover

KW - Numerical manifold method

KW - physical cover

UR - http://www.scopus.com/inward/record.url?scp=84877250266&partnerID=8YFLogxK

U2 - 10.1142/S021987621350028X

DO - 10.1142/S021987621350028X

M3 - Article

AN - SCOPUS:84877250266

VL - 10

JO - International Journal of Computational Methods

JF - International Journal of Computational Methods

SN - 0219-8762

IS - 5

M1 - 1350028

ER -