Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Stochastic partial differential equations: a modeling, white noise functional approach
Stochastic partial differential equations: a modeling, white noise functional approach
Stochastic analysis
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
Advances in Engineering Software - Special issue on large-scale analysis, design and intelligent synthesis environments
The C++ Programming Language, Third Edition
The C++ Programming Language, Third Edition
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Generalized perturbation-based stochastic finite element method in elastostatics
Computers and Structures
Generalized spectral decomposition for stochastic nonlinear problems
Journal of Computational Physics
Efficient stochastic structural analysis using Guyan reduction
Advances in Engineering Software
SIAM Journal on Scientific Computing
Generalized stochastic perturbation technique in engineering computations
Mathematical and Computer Modelling: An International Journal
Uncertainty quantification for algebraic systems of equations
Computers and Structures
| Hi-index | 0.00 |
As an example application the elliptic partial differential equation for steady groundwater flow is considered. Uncertainties in the conductivity may be quantified with a stochastic model. A discretisation by a Galerkin ansatz with tensor products of finite element functions in space and stochastic ansatz functions leads to a certain type of stochastic finite element system (SFEM). This yields a large system of equations with a particular structure. They can be efficiently solved by Krylov subspace methods, as here the main ingredient is the multiplication with the system matrix and the application of the preconditioner. We have implemented a ''hierarchical parallel solver'' on a distributed memory architecture for this. The multiplication and the preconditioning uses a-possibly parallel-deterministic solver for the spatial discretisation as a building block in a black-box fashion. This paper is concerned with a coarser grained level of parallelism resulting from the stochastic formulation. These coarser levels are implemented by running different instances of the deterministic solver in parallel. Different possibilities for the distribution of data are investigated, and the efficiencies determined. On up to 128 processors, systems with more than 5x10^7 unknowns are solved.