Name
Title | ||
|---|---|---|
Algebraic multigrid for stationary and time-dependent partial differential equations with stochastic coefficients |
Abstract | ||
|---|---|---|
We consider the numerical solution of time-dependent partial differential equations (PDEs) with random coefficients. A spectral approach, called stochastic finite element method, is used to compute the statistical characteristics of the solution. This method transforms a stochastic PDE into a coupled system of deterministic equations by means of a Galerkin projection onto a generalized polynomial chaos. An algebraic multigrid (AMG) method is presented to solve the algebraic systems that result after discretization of this coupled system. High-order time integration schemes of an implicit Runge-Kutta type and spatial discretization on unstructured finite element meshes are considered. The convergence properties of the AMG method are demonstrated by a convergence analysis and by numerical tests. Copyright (c) 2008 John Wiley & Sons, Ltd. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1002/nla.568 | NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS |
Keywords | Field | DocType |
partial differential equations with random coefficients,Karhunen-Loeve expansion,polynomial chaos,algebraic multigrid,implicit Runge-Kutta time discretization | Runge–Kutta method,Runge–Kutta methods,Mathematical optimization,Mathematical analysis,Differential algebraic geometry,Numerical partial differential equations,Differential algebraic equation,Stochastic partial differential equation,Mathematics,Multigrid method,hp-FEM | Journal |
Volume | Issue | ISSN |
15 | 2-3 | 1070-5325 |
Citations | PageRank | References |
7 | 0.67 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Eveline Rosseel | 1 | 47 | 3.31 |
| Tim Boonen | 2 | 19 | 1.91 |
| S. Vandewalle | 3 | 74 | 10.06 |