Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Rigorous quantitative analysis of multigrid, I: constant coefficients two-level cycle with L2-norm
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
SIAM Journal on Numerical Analysis
On red-black SOR smoothing in multigrid
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Advances in Engineering Software - Special issue on large-scale analysis, design and intelligent synthesis environments
Multigrid
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
Iterative Solvers for the Stochastic Finite Element Method
SIAM Journal on Scientific Computing
A robust multigrid approach for variational image registration models
Journal of Computational and Applied Mathematics
A local Fourier convergence analysis of a multigrid method using symbolic computation
Journal of Symbolic Computation
Hi-index | 31.45 |
Partial differential equations with random coefficients appear for example in reliability problems and uncertainty propagation models. Various approaches exist for computing the stochastic characteristics of the solution of such a differential equation. In this paper, we consider the spectral expansion approach. This method transforms the continuous model into a large discrete algebraic system. We study the convergence properties of iterative methods for solving this discretized system. We consider one-level and multi-level methods. The classical Fourier mode analysis technique is extended towards the stochastic case. This is done by taking the eigenstructure into account of a certain matrix that depends on the random structure of the problem. We show how the convergence properties depend on the particulars of the algorithm, on the discretization parameters and on the stochastic characteristics of the model. Numerical results are added to illustrate some of our theoretical findings.