Large scale nonconforming domain decomposition methods
Large scale nonconforming domain decomposition methods
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大规模非一致性域分解方法
DOI：
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发表时间：
2014
期刊：
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通讯作者：
A. Samaké
中科院分区：
文献类型：
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作者：
A. Samaké
本文研究区域分解方法，通常分为重叠施瓦茨方法和依赖于非重叠子域的迭代子结构方法。我们主要研究了Mortar有限元方法，它是一种在近似空间上具有弱连续约束的子结构方法。我们引入了一个有限元框架的子结构预条件的设计和分析的线性系统所产生的这样一个离散化方法的有效解决方案。特别考虑到粗网格预处理器的建设，特别是在这项工作中提出的主要变体，使用不连续Galerkin内部惩罚方法作为粗问题。其他区域分解方法，如施瓦茨方法和所谓的三场方法进行了调查，目的是建立一个通用的教学和研究编程环境，这些方法的范围广泛。我们开发了一个先进的计算框架，致力于并行实现的数值方法和预处理在这篇论文中介绍。在大规模并行结构上进行的数值实验表明了预处理器的有效性和可扩展性，以及并行算法的性能。
This thesis investigates domain decomposition methods, commonly classified as either overlapping Schwarz methods or iterative substructuring methods relying on nonoverlapping subdomains. We mainly focus on the mortar finite element method, a nonconforming approach of substructuring method involving weak continuity constraints on the approximation space. We introduce a finite element framework for the design and the analysis of the substructuring preconditioners for an efficient solution of the linear system arising from such a discretization method. Particular consideration is given to the construction of the coarse grid preconditioner, specifically the main variant proposed in this work, using a Discontinuous Galerkin interior penalty method as coarse problem. Other domain decomposition methods, such as Schwarz methods and the so-called three-field method are surveyed with the purpose of establishing a generic teaching and research programming environment for a wide range of these methods. We develop an advanced computational framework dedicated to the parallel implementation of numerical methods and preconditioners introduced in this thesis. The efficiency and the scalability of the preconditioners, and the performance of parallel algorithms are illustrated by numerical experiments performed on large scale parallel architectures.