A Novel Meshless Element Method for Elliptic Equation

Xiaosong Zhu, Xuanhong Liang, Yunhao Qiu, Youyuan Wang
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Abstract

Meshless method based on strong form has the advantages of high computational speed and convenient application, but it suffers low accuracy and instability. In this paper, we propose a meshless virtual element method (VEM) based on strong-form to promote accuracy and instability. Virtual element is built around each node for establishing local function, which used to calculate the derivative of shape function. The optimal selection of point-cloud with adaptive algorithm is proposed to balance the stability and accuracy of interpolation. Numerical simulation demonstrates that VEM has improvement in stability compared with other conventional strong-form method, just needing additional small calculation. and surpass finite element method (FEM) in accuracy and the ability for catching high gradient change.
一种新的椭圆方程无网格元法
基于强形式的无网格法具有计算速度快、应用方便等优点,但精度低、不稳定。本文提出了一种基于强形式的无网格虚元法(VEM),以提高精度和不稳定性。在每个节点周围建立虚元,建立局部函数,用局部函数计算形状函数的导数。为了平衡插值的稳定性和精度,提出了用自适应算法优化点云的方法。数值模拟结果表明,与其他传统的强形式方法相比,该方法的稳定性得到了提高,只需要额外的少量计算。在精度和捕捉高梯度变化的能力上均优于有限元法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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