On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems
The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three...
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| Veröffentlicht in: | Probabilistic engineering mechanics 2015-07, Vol.41 (C), p.60-72 |
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| container_title | Probabilistic engineering mechanics |
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| creator | Field, R.V. Grigoriu, M. Emery, J.M. |
| description | The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method. Rather, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems. |
| doi_str_mv | 10.1016/j.probengmech.2015.05.002 |
| format | Article |
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| ispartof | Probabilistic engineering mechanics, 2015-07, Vol.41 (C), p.60-72 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Approximation theory Collection Collocation Effectiveness ENGINEERING Galerkin methods MATHEMATICS AND COMPUTING Monte Carlo simulation Probabilistic methods Probability theory Random variables and fields Reduced order models Stochastic differential equations Stochasticity Uncertainty propagation |
| title | On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems |
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