Multivariate quadrature rules on crosslet sparse grids
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 the d-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.
Crosslet grids, Multivariate quadrature, Quasi-interpolation
Gao, Qinjiao, Xingping Sun, and Shenggang Zhang. "Multivariate quadrature rules on crosslet sparse grids." Numerical Algorithms (2021): 1-12.