A sub-domain RPIM with condensation of degree of freedom

Hu, Dean; Li, Yangyang; Han, Xu; Yang, Gang; Jiang, Chao

doi:10.1016/j.enganabound.2013.04.014

Cited by 2 publications

(2 citation statements)

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“…The S‒FEM is more efficient than mesh‒free Galerkin methods that are based on nodal integration, because the predefined elements with node connectivity are used for interpolation, integration, and assembling the global system equations in S‒FEM. The local discrete equations based on element are one of the reasons to improve the computational efficiency in mesh‒based method .…”

Section: Introductionmentioning

confidence: 99%

“…The S-FEM is more efficient than mesh-free Galerkin methods that are based on nodal integration, because the predefined elements with node connectivity are used for interpolation, integration, and assembling the global system equations in S-FEM. The local discrete equations based on element are one of the reasons to improve the computational efficiency in mesh-based method [38].However, as discussed earlier, the S-FEM is developed on the basis of the standard FEM framework; the elements with node connectivity is not convenient and flexible for the adaptive mesh refinement compared with mesh-free method, because no element connectivity is required besides nodal information in discrete process of the mesh-free method. We note that the sub-domains divided from problem domain by domain decomposition methods are usually used for isogeometric analysis [39] and parallel computing [40,41].…”

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confidence: 99%

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A sub‒domain smoothed Galerkin method for solid mechanics problems

Wang

Liu

et al. 2014

Numerical Meth Engineering

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SUMMARYA sub‒domain smoothed Galerkin method is proposed to integrate the advantages of mesh‒free Galerkin method and FEM. Arbitrarily shaped sub‒domains are predefined in problems domain with mesh‒free nodes. In each sub‒domain, based on mesh‒free Galerkin weak formulation, the local discrete equation can be obtained by using the moving Kriging interpolation, which is similar to the discretization of the high‒order finite elements. Strain smoothing technique is subsequently applied to the nodal integration of sub‒domain by dividing the sub‒domain into several smoothing cells. Moreover, condensation of DOF can also be introduced into the local discrete equations to improve the computational efficiency. The global governing equations of present method are obtained on the basis of the scheme of FEM by assembling all local discrete equations of the sub‒domains. The mesh‒free properties of Galerkin method are retained in each sub‒domain. Several 2D elastic problems have been solved on the basis of this newly proposed method to validate its computational performance. These numerical examples proved that the newly proposed sub‒domain smoothed Galerkin method is a robust technique to solve solid mechanics problems based on its characteristics of high computational efficiency, good accuracy, and convergence. Copyright © 2014 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%