An Efficient Preconditioner Based on Higher Order Hierarchical Basis Functions

BAN Yong-ling; NIE Zai-ping; YU Zhe-feng

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An Efficient Preconditioner Based on Higher Order Hierarchical Basis Functions

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- An Efficient Preconditioner Based on Higher Order Hierarchical Basis Functions
- Acta Electronica Sinica Vol. 35, Issue 9, Pages: 1739-1744(2007)
- 作者机构：
  
  1. 电子科技大学电子工程学院,四川,成都,610054
  2. 中国空气动力研究与发展中心,四川,绵阳,621000
  3. 电子科技大学电子工程学院四川成都,610054
  4. 中国空气动力研究与发展中心四川绵阳,621000
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN82
- Published：2007
- 稿件说明：
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BAN Yong-ling, NIE Zai-ping, YU Zhe-feng. An Efficient Preconditioner Based on Higher Order Hierarchical Basis Functions[J]. Acta Electronica Sinica, 2007, 35(9): 1739-1744.
DOI：

BAN Yong-ling, NIE Zai-ping, YU Zhe-feng. An Efficient Preconditioner Based on Higher Order Hierarchical Basis Functions[J]. Acta Electronica Sinica, 2007, 35(9): 1739-1744. DOI：

摘要

基于六面体的高阶叠层基函数

提出了一种新颖的构造预条件矩阵的方法.该方法基于叠层基函数特有的嵌套性质

利用特殊的编号策略

将由有限元方法导致的系数矩阵分成块矩阵的形式

最后由不完全LU分解(ILU)导出近似的预条件矩阵.结合该预条件技术

发展了一种叠层预条件-GMRES算法

并将该预条件算法用于加速三维腔体散射的矢量有限元/边界积分(FE-BI)矩阵方程的迭代求解

讨论了该预条件算法中块矩阵ILU分解截断门限

对算法的影响.

Abstract

A preconditioner is proposed for accelerating solutions of finite element matrix equations.The preconditioner is constructed from a sequence of hierarchical vector spaces spanned by higher order hexahedral basis functions.The preconditioned GMRES algorithm with the precondtioner presented is developed and applied to solve the vector finite element-boundary integral (FE-BI) matrix equations for simulation of scattering from three-dimensional cavities.Numerical results show that the preconditioner for solving the FE-BI systems exhibits superior efficiency and reduced the CPU time significantly.

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