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A wavelet multi-resolution enabled interpolation Galerkin method for two-dimensional solids
Engineering Analysis With Boundary Elements ( IF 3.3 ) Pub Date : 2020-05-28 , DOI: 10.1016/j.enganabound.2020.04.007
Xiaojing Liu , G.R. Liu , Jizeng Wang , Youhe Zhou

A novel wavelet multi-resolution formulation in which arbitrary specified nodal coefficients can be exactly the function values at the corresponding nodes is proposed to approximate field functions for solid mechanics problems. This wavelet approximation is explicitly constructed based only on properly scattered nodes without any matrix inversion or ad-hoc parameters. It allows easy and automatic node generation and further refinement at any targeted zones, with a loose and explicit criterion. Using this wavelet multi-resolution approximation to create trial and weighted functions, a wavelet multi-resolution enabled interpolation Galerkin method (WMEIGM) is developed. In the proposed WMEIGM, the stiffness matrix can be efficiently evaluated through semi-analytical method. The essential boundary conditions can be imposed with ease as in the finite element method (FEM). The accuracy and convergence of the proposed WMEIGM are examined theoretically and numerically. Numerical results show that the present WMEIGM has an excellent stability against irregular nodal distribution even with an extremely large ratio of the maximum grid size to the minimum, and a strong capacity for handling irregular problem domains with complicated shape. Moreover, a robust multi-resolution enrichment technique is developed for the present WMEIGM for improving local accuracy and for capturing localized steep gradients.



中文翻译:

小波多分辨率二维插值Galerkin方法

提出了一种新颖的小波多分辨率公式,其中任意指定的节点系数可以精确地成为对应节点处的函数值,从而近似求解固体力学问题的场函数。仅基于适当分散的节点显式构造此小波逼近,而无需任何矩阵求逆或临时参数。它允许轻松,自动地生成节点,并以宽松且明确的标准在任何目标区域进行进一步的优化。使用这种小波多分辨率近似来创建试验和加权函数,开发了一种支持小波多分辨率的插值Galerkin方法(WMEIGM)。在提出的WMEIGM中,可以通过半分析方法有效地评估刚度矩阵。与有限元方法(FEM)一样,可以轻松地施加基本边界条件。从理论和数值上对提出的WMEIGM的准确性和收敛性进行了研究。数值结果表明,即使最大网格尺寸与最小值的比例非常大,本WMEIGM仍具有出色的抗不规则节点分布的稳定性,并且具有处理复杂形状不规则问题域的强大能力。而且,针对当前的WMEIGM,开发了鲁棒的多分辨率富集技术,以提高局部精度并捕获局部陡峭梯度。数值结果表明,即使最大网格尺寸与最小值的比例非常大,本WMEIGM仍具有出色的抗不规则节点分布的稳定性,并且具有处理复杂形状不规则问题域的强大能力。此外,针对当前的WMEIGM,开发了鲁棒的多分辨率富集技术,以提高局部精度并捕获局部陡峭梯度。数值结果表明,即使最大网格尺寸与最小值的比例非常大,本WMEIGM仍具有出色的抗不规则节点分布的稳定性,并且具有处理复杂形状不规则问题域的强大能力。而且,针对当前的WMEIGM,开发了鲁棒的多分辨率富集技术,以提高局部精度并捕获局部陡峭梯度。

更新日期:2020-05-28
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