Mortar型旋转Q1元的V-cycle多重网格和区域分解方法

Mortar型旋转Q1元的V-cycle多重网格和区域分解方法

论文摘要

本文主要讨论了下面的两个问题。 在第一章中我们展现了一种Mortar类型的旋转Q1有限元的多重网格方法。为了构造和分析这种方法,我们定义了一些算子,在这些算子的基础上定义并且证明了这种V循环的多重网格是一致收敛的,它的收敛率不依赖于网格的尺寸和层数。我们通过数值实验验证了理论分析的正确性。 我们在第二章中构造了求解用旋转Q1有限元离散椭圆型偏微分方程的区域分解方法。因为旋转Q1有限元空间不包含任何协调的有限元子空间,所以我们使用了特殊的粗网格空间。我们证明预优问题的条件数是最优的。

论文目录

  • Contents
  • Abstract in English
  • Abstract in Chinese
  • Preface
  • 1 Element'>1 A V-cycle Multigrid Method for Mortar-type Rotated Q1Element
  • 1.1 Introduction
  • 1.2 Preliminaries
  • 1.3 Multigrid algorithm
  • 1.4 Convergence analysis
  • 1.5 Numerical experiments
  • 1 finite element'>2 Domain decomposition method for rotated Q1 finite element
  • 2.1 Introduction
  • 2.2 Preliminaries
  • 2.3 Domain decomposition method
  • Bibliography
  • Acknowledgements
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    Mortar型旋转Q1元的V-cycle多重网格和区域分解方法
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