On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers
On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers
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DOI：
10.1002/nme.4769
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发表时间：
2014-11
影响因子：
2.9
通讯作者：
N. Collier;Lisandro Dalcin;V. Calo
中科院分区：
文献类型：
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作者：
N. Collier;Lisandro Dalcin;V. Calo
我们比较了等几何Galerkin和配置方法的计算效率偏微分方程的渐近制度。我们定义了一个度量，以确定何时数值实验已经达到这个制度。然后，我们应用这些思想来分析不同的等距离散化的性能，其中包括C0有限元空间和高连续空间。我们得到的总自由度的收敛性和成本估计，然后进行渐近数值比较的效率，这些方法应用到椭圆问题。这些估计是假设基础解是光滑的，在每个非零结跨度中使用全高斯求积，并使用直接多波前求解器找到离散系统的数值解。我们的结论是，在本文详细描述的假设下，更高连续的基函数提供了边际效益。版权所有© 2014约翰威利父子有限公司.
We compare the computational efficiency of isogeometric Galerkin and collocation methods for partial differential equations in the asymptotic regime. We define a metric to identify when numerical experiments have reached this regime. We then apply these ideas to analyze the performance of different isogeometric discretizations, which encompass C0 finite element spaces and higher‐continuous spaces. We derive convergence and cost estimates in terms of the total number of degrees of freedom and then perform an asymptotic numerical comparison of the efficiency of these methods applied to an elliptic problem. These estimates are derived assuming that the underlying solution is smooth, the full Gauss quadrature is used in each non‐zero knot span and the numerical solution of the discrete system is found using a direct multi‐frontal solver. We conclude that under the assumptions detailed in this paper, higher‐continuous basis functions provide marginal benefits. Copyright © 2014 John Wiley & Sons, Ltd.