论文标题
IETI-DP求解器的收敛理论，用于不连续的Galerkin同几何分析，在H和P中是显式的
Convergence theory for IETI-DP solvers for discontinuous Galerkin Isogeometric Analysis that is explicit in h and p
论文作者
论文摘要
在本文中，我们开发了一种用于双重质量几何撕裂和互连（IETI-DP）求解器的收敛理论，用于用于泊松问题的iSOGEOMETRIC多块离散，其中斑块是使用不连续的Galerkin耦合的。提出的理论提供了在网格大小h和样条度p中显式的条件数量界限。我们提供了针对原始自由度的各种选择的分析：顶点值，边缘平均值和两者的组合。如果仅将顶点值或顶点值和边缘平均值视为原始自由度，则条件数与符合情况相同。如果只采用边缘平均值，则收敛理论和实验都表明，预处理系统的条件数将随着邻近斑块上的网格大小的比率而生长。
In this paper, we develop a convergence theory for Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) solvers for isogeometric multi-patch discretizations of the Poisson problem, where the patches are coupled using discontinuous Galerkin. The presented theory provides condition number bounds that are explicit in the grid sizes h and in the spline degrees p. We give an analysis that holds for various choices for the primal degrees of freedom: vertex values, edge averages, and a combination of both. If only the vertex values or both vertex values and edge averages are taken as primal degrees of freedom, the condition number bound is the same as for the conforming case. If only the edge averages are taken, both the convergence theory and the experiments show that the condition number of the preconditioned system grows with the ratio of the grid sizes on neighboring patches.
