Using the Nonuniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE Simulations
Partial Differential Equation simulations can produce large amounts of data. These datasets are very slow to transfer, for example, from an off-site supercomputer to a local research facility. There have been many model reduction techniques that have been proposed and utilized over the past three de...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | International Journal of Aerospace Engineering |
| Online Access: | http://dx.doi.org/10.1155/2019/8291616 |
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| author | Brenton T. Hall Ching-Shan Chou Jen-Ping Chen |
| author_facet | Brenton T. Hall Ching-Shan Chou Jen-Ping Chen |
| author_sort | Brenton T. Hall |
| collection | DOAJ |
| description | Partial Differential Equation simulations can produce large amounts of data. These datasets are very slow to transfer, for example, from an off-site supercomputer to a local research facility. There have been many model reduction techniques that have been proposed and utilized over the past three decades. Two of the most popular techniques are the Proper Orthogonal Decomposition and Dynamic Mode Decomposition. Nonuniform Dynamic Mode Decomposition (NU-DMD) is one of the newest techniques as it was introduced in 2015 by Guéniat et al. In this paper, the NU-DMD’s mathematics are explained in detail, and three versions of the NU-DMD’s algorithm are outlined. Furthermore, different numerical experiments were performed on the NU-DMD to ascertain its behavior with respect to errors, memory usage, and computational efficiency. It was shown that the NU-DMD could reduce an advection-diffusion simulation to 6.0075% of its original memory storage size. The NU-DMD was also applied to a computational fluid dynamics simulation of a NASA single-stage compressor rotor, which resulted in a reduced model of the simulation (using only three of the five simulation variables) that used only about 4.67% of the full simulation’s storage with an overall average percent error of 8.90%. It was concluded that the NU-DMD, if used appropriately, could be used to possibly reduce a model that uses 400 GB of memory to a model that uses as little as 18.67 GB with less than 9% error. Further conclusions were made about how to best implement the NU-DMD. |
| format | Article |
| id | doaj-art-9cb852c266a44628ba05e044d56afcd1 |
| institution | Kabale University |
| issn | 1687-5966 1687-5974 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
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| series | International Journal of Aerospace Engineering |
| spelling | doaj-art-9cb852c266a44628ba05e044d56afcd12025-02-03T06:05:04ZengWileyInternational Journal of Aerospace Engineering1687-59661687-59742019-01-01201910.1155/2019/82916168291616Using the Nonuniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE SimulationsBrenton T. Hall0Ching-Shan Chou1Jen-Ping Chen2Ohio State University, Columbus, OH 43210, USAOhio State University, Columbus, OH 43210, USAOhio State University, Columbus, OH 43210, USAPartial Differential Equation simulations can produce large amounts of data. These datasets are very slow to transfer, for example, from an off-site supercomputer to a local research facility. There have been many model reduction techniques that have been proposed and utilized over the past three decades. Two of the most popular techniques are the Proper Orthogonal Decomposition and Dynamic Mode Decomposition. Nonuniform Dynamic Mode Decomposition (NU-DMD) is one of the newest techniques as it was introduced in 2015 by Guéniat et al. In this paper, the NU-DMD’s mathematics are explained in detail, and three versions of the NU-DMD’s algorithm are outlined. Furthermore, different numerical experiments were performed on the NU-DMD to ascertain its behavior with respect to errors, memory usage, and computational efficiency. It was shown that the NU-DMD could reduce an advection-diffusion simulation to 6.0075% of its original memory storage size. The NU-DMD was also applied to a computational fluid dynamics simulation of a NASA single-stage compressor rotor, which resulted in a reduced model of the simulation (using only three of the five simulation variables) that used only about 4.67% of the full simulation’s storage with an overall average percent error of 8.90%. It was concluded that the NU-DMD, if used appropriately, could be used to possibly reduce a model that uses 400 GB of memory to a model that uses as little as 18.67 GB with less than 9% error. Further conclusions were made about how to best implement the NU-DMD.http://dx.doi.org/10.1155/2019/8291616 |
| spellingShingle | Brenton T. Hall Ching-Shan Chou Jen-Ping Chen Using the Nonuniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE Simulations International Journal of Aerospace Engineering |
| title | Using the Nonuniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE Simulations |
| title_full | Using the Nonuniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE Simulations |
| title_fullStr | Using the Nonuniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE Simulations |
| title_full_unstemmed | Using the Nonuniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE Simulations |
| title_short | Using the Nonuniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE Simulations |
| title_sort | using the nonuniform dynamic mode decomposition to reduce the storage required for pde simulations |
| url | http://dx.doi.org/10.1155/2019/8291616 |
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