The analysis of a sparse grid stochastic collocation method for partial differential equations with high-dimensional random input data.
- Florida State University, Tallahassee, FL
- Politecnico di Milano, Italy
This work describes the convergence analysis of a Smolyak-type sparse grid stochastic collocation method for the approximation of statistical quantities related to the solution of partial differential equations with random coefficients and forcing terms (input data of the model). To compute solution statistics, the sparse grid stochastic collocation method uses approximate solutions, produced here by finite elements, corresponding to a deterministic set of points in the random input space. This naturally requires solving uncoupled deterministic problems and, as such, the derived strong error estimates for the fully discrete solution are used to compare the computational efficiency of the proposed method with the Monte Carlo method. Numerical examples illustrate the theoretical results and are used to compare this approach with several others, including the standard Monte Carlo.
- Research Organization:
- Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 934852
- Report Number(s):
- SAND2007-8093; TRN: US200815%%178
- Country of Publication:
- United States
- Language:
- English
Similar Records
Sparse grid collocation schemes for stochastic natural convection problems
A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties
Related Subjects
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
APPROXIMATIONS
CONVERGENCE
MONTE CARLO METHOD
PARTIAL DIFFERENTIAL EQUATIONS
COMPARATIVE EVALUATIONS
Stochastic partial differential equations.
Numerical grid generation (Numerical analysis)
Stochastic analysis.