Highly accurate surface and volume integration on implicit domains by means of moment‐fitting
Highly accurate surface and volume integration on implicit domains by means of moment‐fitting
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DOI：
10.1002/nme.4569
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发表时间：
2013-11
影响因子：
2.9
通讯作者：
B. Müller;F. Kummer;M. Oberlack
中科院分区：
文献类型：
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作者：
B. Müller;F. Kummer;M. Oberlack
本文介绍了一种新的数值积分方法，该方法适用于由水平集函数定义的曲面和体上的数值积分。该方法是基于一个小的线性系统的解决方案的基础上的一个简化的变体的矩拟合方程。数值实验表明，由此产生的求积规则的精度超过传统方法的精度的数量级。使用矩的顺序为p，测量的实验顺序的收敛超过HP。因此，他们的建设是非常有效的，因为只需要粗略的计算网格。概念上的简单性允许非常一般的网格类型，这是由四边形，三角形和六面体网格上的数值实验证明的应用程序。版权所有© 2013约翰威利父子有限公司.
We introduce a new method for the numerical integration over curved surfaces and volumes defined by a level set function. The method is based on the solution of a small linear system based on a simplified variant of the moment‐fitting equations. Numerical experiments suggest that the accuracy of the resulting quadrature rules exceeds the accuracy of traditional methods by orders of magnitude. Using moments up to an order of p, the measured experimental orders of convergence exceed hp. Consequently, their construction is very efficient because only coarse computational grids are required. The conceptual simplicity allows for the application on very general grid types, which is demonstrated by numerical experiments on quadrilateral, triangular and hexahedral grids. Copyright © 2013 John Wiley & Sons, Ltd.