最小二乘等几何分析的多重网格方法

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最小二乘等几何分析的多重网格方法

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- 最小二乘等几何分析的多重网格方法
- Issue 7, Pages: 124-130(2014)
- 作者机构：
  
  1. 西安交通大学机械结构强度与振动国家重点实验室
  2. 长动集团武汉汽轮发电机有限公司
- 作者简介：
- 基金信息：
- DOI：
  CLC： O241.5
- Published：2014
- 稿件说明：
移动端阅览
[J]. 2014, (7): 124-130.
DOI：

[J]. 2014, (7): 124-130. DOI：

摘要

针对最小二乘等几何分析得到的代数方程系数矩阵的条件数大、迭代求解成本高的问题

提出了求解该方程的多重网格法。该方法在密网格上进行误差光顺

使高频误差快速衰减

在疏网格上进行误差修正

使低频误差快速衰减。通过节点插入算法自动生成不同尺寸的网格

根据离散B样条建立网格转换矩阵。采用该方法求解了泊松方程

对比了多重网格迭代与Gauss-Seidel迭代、PCG迭代的收敛性

结果表明Gauss-Seidel迭代收敛速度最慢

PCG迭代收敛速度随着代数方程自由度的增加而变慢

多重网格的收敛速度最快

能够有效求解最小二乘等几何分析得到的代数方程

解决了矩阵条件数过大的问题

并且收敛速度与网格尺寸无关。

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references

陶文铨著.计算传热学的近代进展[M].科学出版社,2000.

K.P.S. Gahalaut,J.K. Kraus,S.K. Tomar.Multigrid methods for isogeometric discretization[J].Computer Methods in Applied Mechanics and Engineering,2013.

D. Santhosh Kumar,K. Suresh Kumar,Manab Kumar Das.A Fine Grid Solution for a Lid-Driven Cavity Flow Using Multigrid Method[J].Engineering Applications of Computational Fluid M,2009(3).

V. Prabhakar,J. N. Reddy.A stress‐based least‐squares finite‐element model for incompressible Navier–Stokes equations[J].International Journal for Numerical Methods in Fluids,2007.

J.P. Pontaza,J.N. Reddy.Least-squares finite element formulations for viscous incompressible and compressible fluid flows[J].Computer Methods in Applied Mechanics and Engineering,2005(19).

T.J.R. Hughes,J.A. Cottrell,Y. Bazilevs.Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement[J].Computer Methods in Applied Mechanics and Engineering,2005(39).

A. K. Aziz,R. B. Kellogg,A. B. Stephens.Least squares methods for elliptic systems[J].Mathematics of Computation,1985(169).

陈德祥,徐自力,刘石,冯永新.求解Stokes方程的最小二乘等几何分析方法[J].西安交通大学学报,2013(05).

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