Multivariate quadrature rules on crosslet sparse grids
Multivariate quadrature rules on crosslet sparse grids
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DOI：
10.1007/s11075-021-01217-3
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发表时间：
2021-11
影响因子：
2.1
通讯作者：
Qinjiao Gao;Xingping Sun;Shenggang Zhang
中科院分区：
文献类型：
--
作者：
Qinjiao Gao;Xingping Sun;Shenggang Zhang
本文引入了一种新的节点集结构：用于高维数值积分的十字网格，并基于这种节点集在d维欧氏空间的单位立方体上建立了对称求积规则。我们的算法给出了相同的顺序的准确性，建立在完整的网格，但需要更少的节点，因此在执行中遇到的计算复杂性要小得多。理论分析和数值模拟表明，基于交叉网格的求积规则适用于具有局部非光滑性的被积函数。本文的研究工作揭示了求积法则与拟插值之间的密切联系。
We introduce a new configuration of node sets: crosslet grids for high-dimensional numerical integration, and develop symmetric quadrature rules on the unit cube of thed-dimensional Euclidean space based on these node sets. Our algorithms give the same order of accuracy as those established on full grids, but require much fewer nodes, and therefore encounter far less computational complexity in execution. Theoretical analysis and numerical simulations show that quadrature rules based on crosslet grids are effective when applied to integrands that have localized nonsmoothness. The research work here reveals a close connection between quadrature rules and quasi-interpolation.