Novel adaptive meshfree integration techniques in meshless methods
Novel adaptive meshfree integration techniques in meshless methods
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DOI：
10.1002/nme.4268
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发表时间：
2012-06
影响因子：
2.9
通讯作者：
Donat Racz;T. Bui
中科院分区：
文献类型：
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作者：
Donat Racz;T. Bui
针对无网格方法中区域积分的复杂问题，提出了两种基于映射技术的自适应数值积分方法。详细介绍了几种将复杂积分域映射为简单得多的积分域（如正方形、三角形或圆形）的映射方法。文中所述的方法既适用于整体弱形式，也适用于局部弱形式，并可对高度非线性的无网格被积函数进行精确计算。避免了现有无网格方法中用于积分目的的背景网格或单元结构的笨拙过程的必要性，并且许多需要域积分的无网格方法现在可以成为“真正的无网格”。通过二维数值算例验证了所提方法的有效性和实用性，计算精度得到了显著提高。将所得结果与解析解和其它方法进行了比较，发现它们具有很好的一致性。此外，还对本文方法应用于三维情况进行了检验。版权所有© 2012约翰威利父子有限公司.
We propose two strategies of novel adaptive numerical integration based on mapping techniques for solving the complicated problems of domain integration encountered in meshfree methods. Several mapping methods are presented in detail that map a complex integration domain to much simpler ones, for example, squares, triangles or circles. The techniques described in the paper can be applied to both global and local weak forms, and the highly nonlinear meshfree integrands are evaluated with controlled accuracy. The necessity of the clumsy procedure of background mesh or cell structures used for integration purpose in existing meshfree methods is avoided, and many meshfree methods that require the domain integration can now become ‘truly meshfree’. Various numerical examples in two dimensions are considered to demonstrate the applicability and the effectiveness of the proposed methods and it shows that the accuracy is improved significantly. Their obtained results are compared with analytical solutions and other approaches and very good agreements are found. Additionally, some three‐dimensional cases applied by the present methods are also examined. Copyright © 2012 John Wiley & Sons, Ltd.