| Autor: |
Yuto Nakamura, Shintaro Sato, Naofumi Ohnishi |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
Partial Differential Equations in Applied Mathematics, Vol 9, Iss , Pp 100654- (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2666-8181 |
| DOI: |
10.1016/j.padiff.2024.100654 |
| Popis: |
This paper proposes a novel proper orthogonal decomposition method for constructing a reduced-order model. This model effectively computes solutions for various initial conditions in time-dependent partial differential equations. The mode obtained from the proposed proper orthogonal decomposition captures both the fluctuating component and the mean-field of the time-dependent solution. In this mode, the eigenvalues representing the mean-field, are significantly larger than those representing the fluctuating component. Consequently, determining the number of modes required for representing a solution cannot rely solely on the cumulative contribution rate. Therefore, the proposed method gives a scalar weight to the mean-field and controls the magnitude of the mean-field energy. We propose a method that considers the magnitude of the scaler weight alongside the cumulative contribution ratio for determining the number of modes. This method was evaluated using the time-dependent Burgers equation with parametric initial values. Our proposed method selects the appropriate mode to represent the given dataset, unlike the conventional method. A reduced-order model based on the proposed method effectively computes the time evolutions of the solutions using datasets for several parameters by imposing a condition that the cumulative contribution ratio exceeds 98%. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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