A dynamically adaptive wavelet approach to stochastic computations based on polynomial chaos - capturing all scales of random modes on independent grids
- University of Shanghai for Science and Technology, Shanghai 200093 (China)
Highlights: {yields} New approach for stochastic computations based on polynomial chaos. {yields} Development of dynamically adaptive wavelet multiscale solver using space refinement. {yields} Accurate capture of steep gradients and multiscale features in stochastic problems. {yields} All scales of each random mode are captured on independent grids. {yields} Numerical examples demonstrate the need for different space resolutions per mode. - Abstract: In stochastic computations, or uncertainty quantification methods, the spectral approach based on the polynomial chaos expansion in random space leads to a coupled system of deterministic equations for the coefficients of the expansion. The size of this system increases drastically when the number of independent random variables and/or order of polynomial chaos expansions increases. This is invariably the case for large scale simulations and/or problems involving steep gradients and other multiscale features; such features are variously reflected on each solution component or random/uncertainty mode requiring the development of adaptive methods for their accurate resolution. In this paper we propose a new approach for treating such problems based on a dynamically adaptive wavelet methodology involving space-refinement on physical space that allows all scales of each solution component to be refined independently of the rest. We exemplify this using the convection-diffusion model with random input data and present three numerical examples demonstrating the salient features of the proposed method. Thus we establish a new, elegant and flexible approach for stochastic problems with steep gradients and multiscale features based on polynomial chaos expansions.
- OSTI ID:
- 21592605
- Journal Information:
- Journal of Computational Physics, Vol. 230, Issue 19; Other Information: DOI: 10.1016/j.jcp.2011.05.038; PII: S0021-9991(11)00350-0; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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