An Efficient Solver for Cumulative Density Function-based Solutions of Uncertain Kinematic Wave Models
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866910753356775424 |
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| author | Cheng, Ming Qin, Yi Narayan, Akil Zhong, Xinghui Zhu, Xueyu Wang, Peng |
| author_facet | Cheng, Ming Qin, Yi Narayan, Akil Zhong, Xinghui Zhu, Xueyu Wang, Peng |
| contents | We develop a numerical framework to implement the cumulative density function (CDF) method for obtaining the probability distribution of the system state described by a kinematic wave model. The approach relies on Monte Carlo Simulations (MCS) of the fine-grained CDF equation of system state, as derived by the CDF method. This fine-grained CDF equation is solved via the method of characteristics. Each method of characteristics solution is far more computationally efficient than the direct solution of the kinematic wave model, and the MCS estimator of the CDF converges relatively quickly. We verify the accuracy and robustness of our procedure via comparison with direct MCS of a particular kinematic wave system, the Saint-Venant equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_08520 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | An Efficient Solver for Cumulative Density Function-based Solutions of Uncertain Kinematic Wave Models Cheng, Ming Qin, Yi Narayan, Akil Zhong, Xinghui Zhu, Xueyu Wang, Peng Numerical Analysis Computational Physics 65M22, 65M25 We develop a numerical framework to implement the cumulative density function (CDF) method for obtaining the probability distribution of the system state described by a kinematic wave model. The approach relies on Monte Carlo Simulations (MCS) of the fine-grained CDF equation of system state, as derived by the CDF method. This fine-grained CDF equation is solved via the method of characteristics. Each method of characteristics solution is far more computationally efficient than the direct solution of the kinematic wave model, and the MCS estimator of the CDF converges relatively quickly. We verify the accuracy and robustness of our procedure via comparison with direct MCS of a particular kinematic wave system, the Saint-Venant equation. |
| title | An Efficient Solver for Cumulative Density Function-based Solutions of Uncertain Kinematic Wave Models |
| topic | Numerical Analysis Computational Physics 65M22, 65M25 |
| url | https://arxiv.org/abs/1901.08520 |