ICCM Conferences, The 8th International Conference on Computational Methods (ICCM2017)

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Stable node-based smoothed finite element method: application to multiple physical problems
Cui Xiangyang

Last modified: 2017-07-07


Though the node-based smoothed finite element method (NS-FEM) possesses many superior properties and those prominent inherent properties make it very attractive for researchers, it may be “temporally” unstable when it comes to time-dependent problems. Nevertheless, many physical problems are time-dependent. To apply the NS-FEM to multiple physical problems, effective numerical improvements are essential to cure its temporal instability. Based on this, a stable node-based smoothed finite element method (SNS-FEM) is introduced and the general form of the method is presented in this paper. In the formulation of the SNS-FEM, the simplest linear triangular and tetrahedral elements are employed and the node-based smoothing domain is then constructed on top of element mesh. Gradients variance items of the field variables are considered besides the gradients of the field variables to compute the system stiffness matrix over the smoothing domain. As a result, the system stiffness is strengthened appropriately and the temporal instability of the NS-FEM is able to be cured. The SNS-FEM has been applied to analyze multiple physical problems such as acoustic, heat transfer and electromagnetism problems. Numerical results demonstrate that the SNS-FEM is temporal stability and well suited to various physical problems. In addition to this, the SNS-FEM possesses super accuracy and high computational efficiency.

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