| The efect of ghost forces for a quasicontinuum method in three dimension |
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| 作者姓名： | CUI Long MING PingBing |
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| 作者单位： | LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences |
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| 基金项目： | supported by National Natural Science Foundation of China(Grant Nos.10932011,91230203 and 11021101) |
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| 摘 要： | We study the efect of"ghost forces"for a quasicontinuum method in three dimension with a planar interface."Ghost forces"are the inconsistency of the quasicontinuum method across the interface between the atomistic region and the continuum region.Numerical results suggest that"ghost forces"may lead to a negilible error on the solution,while lead to a fnite size error on the gradient of the solution.The error has a layer-like profle,and the interfacial layer width is of O(ε).The error in certain component of the displacement gradient decays algebraically from O(1)to O(ε)away from the interface.A surrogate model is proposed and analyzed,which suggests the same scenario for the efect of"ghost forces".Our analysis is based on the explicit solution of the surrogate model.
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| 关 键 词： | quasicontinuum method atomistic-to-continuum ghost force |
The effect of ghost forces for a quasicontinuum method in three dimension |
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| CUI Long,MING PingBing.The efect of ghost forces for a quasicontinuum method in three dimension[J].中国科学 数学(英文版),2013,56(12):2571-2589. |
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| Authors: | Long Cui PingBing Ming |
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| Institution: | 1. LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
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| Abstract: | We study the effect of “ghost forces” for a quasicontinuum method in three dimension with a planar interface. “Ghost forces” are the inconsistency of the quasicontinuum method across the interface between the atomistic region and the continuum region. Numerical results suggest that “ghost forces” may lead to a negilible error on the solution, while lead to a finite size error on the gradient of the solution. The error has a layer-like profile, and the interfacial layer width is of O(?). The error in certain component of the displacement gradient decays algebraically from O(1) to O(?) away from the interface. A surrogate model is proposed and analyzed, which suggests the same scenario for the effect of “ghost forces”. Our analysis is based on the explicit solution of the surrogate model. |
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