Analysis of the Stochastic Quarter-Five Spot Problem Using Polynomial Chaos
Abstract
:1. Introduction
2. Mathematical Statement of the Quarter-Five Spot Problem
2.1. The Deterministic Problem
2.2. The Stochastic Problem
3. Solution Implementation
3.1. The Deterministic Problem
Numerical Example
3.2. The Stochastic Quarter-Five Spot Problem
- First: Using PCE
- Second: Using KL expansion
4. Results
4.1. Case of PCE Only
4.2. Case of KL with PCE
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Mean difference percentage | 0.0035 | 0.0039 | 0.0031 |
Variance difference percentage | 2.56 | 2.61 | 2.52 |
Number of terms for convergence | 12 | 8 | 5 |
Method | |||
---|---|---|---|
PCE | 0.4 | 1 | |
KL-PCE | 0.01 | 0.5 | 0.1 |
KL-PCE | 0.02 | 0.3 | 0.9 |
KL-PCE | 0.1 | 0.8 | 4 |
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AbdelFattah, H.; Al-Johani, A.; El-Beltagy, M. Analysis of the Stochastic Quarter-Five Spot Problem Using Polynomial Chaos. Molecules 2020, 25, 3370. https://doi.org/10.3390/molecules25153370
AbdelFattah H, Al-Johani A, El-Beltagy M. Analysis of the Stochastic Quarter-Five Spot Problem Using Polynomial Chaos. Molecules. 2020; 25(15):3370. https://doi.org/10.3390/molecules25153370
Chicago/Turabian StyleAbdelFattah, Hesham, Amnah Al-Johani, and Mohamed El-Beltagy. 2020. "Analysis of the Stochastic Quarter-Five Spot Problem Using Polynomial Chaos" Molecules 25, no. 15: 3370. https://doi.org/10.3390/molecules25153370