Probabilistic interpretation of conjugate gradient iterations in spectral stochastic finite element method

被引：0
|
作者：
机构：
[1] [1,Ghosh, Debraj
来源：
Ghosh, D. (dghosh@civil.iisc.ernet.in) | 1600年 / AIAA International卷 / 52期
关键词：
The spectral stochastic finite element method (SSFEM) is one of the popular choices for analyzing uncertain systems; mainly due to its computational speed. It is shown that; although the successive iterates are conjugate to each other in the product space; the orthogonality of the successive residuals holds only in an inner product defined deterministically; that is; without involving an expectation operator. These observations imply that the existing result on orthogonality of the residuals in the deterministic CG method does not directly extend to a stochastic case. Some of the properties of the CG in a deterministic setting are found to have their stochastic counterparts. For instance; conjugacy of the search directions and monotonic nonincreasing property of the error also hold in the product space; with the usual inner product and norm; whereas the orthogonality of the residual does not hold in the usual inner product in the product space. However; here the orthogonality holds with a different norm that does not involve the expectation operator;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Journal article (JA)
引用
收藏
相关论文
共 50 条
  • [31] Multigrid preconditioned conjugate-gradient solver for mixed finite-element method
    John David Wilson
    Richard L. Naff
    Computational Geosciences, 2010, 14 : 289 - 299
  • [32] A spectral conjugate gradient method for unconstrained optimization
    Birgin, EG
    Martínez, JM
    APPLIED MATHEMATICS AND OPTIMIZATION, 2001, 43 (02): : 117 - 128
  • [33] Nonlinear conjugate gradient method for spectral tomosynthesis
    Landi, G.
    Piccolomini, E. Loli
    Nagy, J.
    INVERSE PROBLEMS, 2019, 35 (09)
  • [34] A Spectral Conjugate Gradient Method with Descent Property
    Jian, Jinbao
    Yang, Lin
    Jiang, Xianzhen
    Liu, Pengjie
    Liu, Meixing
    MATHEMATICS, 2020, 8 (02)
  • [35] A conjugate gradient method for the spectral partitioning of graphs
    Kruyt, NP
    PARALLEL COMPUTING, 1997, 22 (11) : 1493 - 1502
  • [36] A Spectral Conjugate Gradient Method for Unconstrained Optimization
    E. G. Birgin
    J. M. Martínez
    Applied Mathematics & Optimization, 2001, 43 : 117 - 128
  • [37] Stochastic optimization using the stochastic preconditioned conjugate gradient method
    Oakley, DR
    Sues, RH
    AIAA JOURNAL, 1996, 34 (09) : 1969 - 1971
  • [38] Performance evaluation of norm scaling algorithm for conjugate gradient method with application to parallel finite element method
    Yamada, T
    Yagawa, G
    COMPUTATIONAL MECHANICS, VOLS 1 AND 2, PROCEEDINGS: NEW FRONTIERS FOR THE NEW MILLENNIUM, 2001, : 149 - 154
  • [39] Numerical convergence of a spectral stochastic finite element method (SSFEM) in lognormal context
    Baroth, J
    Bodé, L
    Bressolette, P
    Fogli, M
    APPLICATIONS OF STATISTICS AND PROBABILITY IN CIVIL ENGINEERING, VOLS 1 AND 2, 2003, : 217 - 224
  • [40] Application of the spectral stochastic finite element method for performance prediction of composite structures
    Ngah, M. F.
    Young, A.
    COMPOSITE STRUCTURES, 2007, 78 (03) : 447 - 456
12345