Basis adaptation and domain decomposition for steady-state partial differential equations with random coefficients
We present a novel approach for solving steady-state stochastic partial differential equations in high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis adaptation is used to address the curse of dimensionality by constructing an accurate low-dimensional representation of the stochastic PDE solution (probability density function and/or its leading statistical moments) in each subdomain. Restricting the basis adaptation to a specific subdomain affords finding a locally accurate solution. Then, the solutions from all of the subdomains are stitched together to provide a global solution. We support our construction with numerical experiments for a steady-state diffusion equation with a random spatially dependent coefficient. Our results show that accurate global solutions can be obtained with significantly reduced computational costs.
- OSTI ID:
- 22701644
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 351; ISSN JCTPAH; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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