How I Got Lost in a Random Domain
Documents
Abstract
This report solves an elliptic problem on a rough domain. It represents the rough geometry with a stochastic parameterization of the boundary and employs a random mapping to transform the deterministic problem on a random domain into a stochastic problem on a deterministic domain. The moments of the solution are computed with a Monte Carlo method and a stochastic Galerkin technique.
Figures
| One realization of the random domain and its mapped domain |
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| One realization of the random solution and its mapped solution | |
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| Comparison of moments of solution computed with SG and MC | |
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