Spectral element FETI-DP and BDDC preconditioners with multi-element subdomains
Spectral element FETI-DP and BDDC preconditioners with multi-element subdomains
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具有多元素子域的谱元素 FETI-DP 和 BDDC 预处理器
DOI：
10.1016/j.cma.2008.08.017
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发表时间：
2008
影响因子：
7.2
通讯作者：
O. Rheinbach
中科院分区：
文献类型：
--
作者：
A. Klawonn;L. Pavarino;O. Rheinbach
由谱有限元或hp型有限元生成的离散系统比由标准低阶有限元或有限差分生成的离散系统更病态。本文主要研究基于Gauss-Lobatto-Legendre（GLL）求积的谱元，以及约束平衡区域分解（BDDC）和双原始有限元撕裂与互连（FETI-DP）算法族中原始和对偶非重叠区域分解方法的构造。新的结果提出的光谱多元素的情况下，也为不精确的FETI-DP方法的光谱元素在平面上。理论上的收敛性估计表明，这些方法的收敛速度与椭圆算子的子域数和系数跳跃无关，而仅与谱度p、子域数与单元数之比H/h有多对数关系.在Linux机群上进行的并行数值实验证实了这些结果，其谱度可达p=32，子域数可达数千，系数跳跃可达8个数量级。
The discrete systems generated by spectral or hp-version finite elements are much more ill-conditioned than the ones generated by standard low-order finite elements or finite differences. This paper focuses on spectral elements based on Gauss–Lobatto–Legendre (GLL) quadrature and the construction of primal and dual non-overlapping domain decomposition methods belonging to the family of Balancing Domain Decomposition methods by Constraints (BDDC) and Dual-Primal Finite Element Tearing and Interconnecting (FETI-DP) algorithms. New results are presented for the spectral multi-element case and also for inexact FETI-DP methods for spectral elements in the plane. Theoretical convergence estimates show that these methods have a convergence rate independent of the number of subdomains and coefficient jumps of the elliptic operator, while there is only a polylogarithmic dependence on the spectral degree p and the ratio H/h of subdomain and element sizes. Parallel numerical experiments on a Linux cluster confirm these results for tests with spectral degree up to p=32, thousands of subdomains and coefficient jumps up to 8 orders of magnitude.