STOCHASTIC GALERKIN MATRICES

被引：51

作者：

Ernst, Oliver G. ^{[1
]}

Ullmann, Elisabeth ^{[1
]}

机构：

[1] Tech Univ Bergakad Freiberg, Inst Numer Math & Optimierung, D-09596 Freiberg, Germany

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2010年 / 31卷 / 04期

关键词：

stochastic Galerkin method; stochastic finite elements; orthogonal polynomials; UNCERTAINTY; EQUATIONS; SYSTEMS;

D O I：

10.1137/080742282

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the structural, spectral, and sparsity properties of Stochastic Galerkin matrices as they arise in the discretization of linear differential equations with random coefficient functions. These matrices are characterized as the Galerkin representation of polynomial multiplication operators. In particular, it is shown that the global Galerkin matrix associated with complete polynomials cannot be diagonalized in the stochastically linear case.

引用

页码：1848 / 1872

页数：25

共 24 条

[11]

Ghanem R, 1991, STOCHASTIC FINITE EL

[12] Numerical solution of spectral stochastic finite element systems [J].

Ghanem, RG ;

Kruger, RM .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1996, 129 (03) :289-303

[13]

Horn R. A., 2006, Topics in Matrix Analysis, V7th

[14]

Horn R. A., 1999, MATRIX ANAL

[15] Multi-resolution-analysis scheme for uncertainty quantification in chemical systems [J].

Le Maitre, O. P. ;

Najm, H. N. ;

Pebay, P. P. ;

Ghanem, R. G. ;

Knio, O. M. .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2007, 29 (02) :864-889

[16] Uncertainty propagation using Wiener-Haar expansions [J].

Le Maître, OP ;

Knio, OM ;

Najm, HN ;

Ghanem, RG .

JOURNAL OF COMPUTATIONAL PHYSICS, 2004, 197 (01) :28-57

[17] LINEARIZATION OF THE PRODUCT OF SYMMETRICAL ORTHOGONAL POLYNOMIALS [J].

MARKETT, C .

CONSTRUCTIVE APPROXIMATION, 1994, 10 (03) :317-338

[18] Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations [J].

Matthies, HG ;

Keese, A .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2005, 194 (12-16) :1295-1331

[19] Iterative solution of systems of linear equations arising in the context of stochastic finite elements [J].

Pellissetti, MF ;

Ghanem, RG .

ADVANCES IN ENGINEERING SOFTWARE, 2000, 31 (8-9) :607-616

[20] Block-diagonal preconditioning for spectral stochastic finite-element systems [J].

Powell, Catherine E. ;

Elman, Howard C. .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2009, 29 (02) :350-375

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