JOHANNES KEPLER UNIVERSITY LINZ Institute of Computational Mathematics Convergence Theory for IETI-DP Solvers for Discontinuous Galerkin Isogeometric Analysis That Is Explicit in h and p
JOHANNES KEPLER UNIVERSITY LINZ Institute of Computational Mathematics Convergence Theory for IETI-DP Solvers for Discontinuous Galerkin Isogeometric Analysis That Is Explicit in h and p
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林茨约翰开普勒大学计算数学研究所 IETI-DP 求解器的收敛理论，用于在 h 和 p 中显式的不连续伽辽金等几何分析
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Stefan Takacs
中科院分区：
文献类型：
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作者：
Rainer Schneckenleitner;Stefan Takacs
本文发展了Poisson问题等距多面片离散的对偶原始等距撕裂和互连(Ieti-DP)解算器的收敛理论，其中面片使用间断Galerkin耦合。所提出的理论提供了在网格尺寸h和样条度p中显式的条件数界限。我们给出了对原始自由度的各种选择的分析：顶点值、边平均值以及两者的组合。如果仅取顶点值或同时取顶点值和边平均值作为原始自由度，则边界条件数与协调情况相同。在仅取边平均的情况下，无论是收敛理论还是实验都表明，预条件系统的条件数随相邻面片上网格尺寸之比的增大而增大。
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.