A separated representation involving multiple time scales within the Proper Generalized Decomposition framework
Abstract Solutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes aris...
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2021
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oai:doaj.org-article:1681b41ff3b14d99b5b187b05057e5272021-11-28T12:09:36ZA separated representation involving multiple time scales within the Proper Generalized Decomposition framework10.1186/s40323-021-00211-72213-7467https://doaj.org/article/1681b41ff3b14d99b5b187b05057e5272021-11-01T00:00:00Zhttps://doi.org/10.1186/s40323-021-00211-7https://doaj.org/toc/2213-7467Abstract Solutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors. The proposed methodology is based on a time-separated representation within the standard Proper Generalized Decomposition, where the time coordinate is transformed into a multi-dimensional time through new separated coordinates, each representing one scale, while continuity is ensured in the scale coupling. For instance, when considering two different time scales, the governing Partial Differential Equation is commuted into a nonlinear system that iterates between the so-called microtime and macrotime, so that the time coordinate can be viewed as a 2D time. The macroscale effects are taken into account by means of a finite element-based macro-discretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the time domain. The resulting separated representation allows us a very fine time discretization without impacting the computational efficiency. The proposed formulation is explored and numerically verified on thermal and elastodynamic problems.Angelo PasqualeAmine AmmarAntonio FalcóSimona PerottoElías CuetoJean-Louis DuvalFrancisco ChinestaSpringerOpenarticleModel Order ReductionTime multiscaleProper Generalized DecompositionThermal problemsElastodynamicsMechanics of engineering. Applied mechanicsTA349-359Systems engineeringTA168ENAdvanced Modeling and Simulation in Engineering Sciences, Vol 8, Iss 1, Pp 1-22 (2021) |
| institution |
DOAJ |
| collection |
DOAJ |
| language |
EN |
| topic |
Model Order Reduction Time multiscale Proper Generalized Decomposition Thermal problems Elastodynamics Mechanics of engineering. Applied mechanics TA349-359 Systems engineering TA168 |
| spellingShingle |
Model Order Reduction Time multiscale Proper Generalized Decomposition Thermal problems Elastodynamics Mechanics of engineering. Applied mechanics TA349-359 Systems engineering TA168 Angelo Pasquale Amine Ammar Antonio Falcó Simona Perotto Elías Cueto Jean-Louis Duval Francisco Chinesta A separated representation involving multiple time scales within the Proper Generalized Decomposition framework |
| description |
Abstract Solutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors. The proposed methodology is based on a time-separated representation within the standard Proper Generalized Decomposition, where the time coordinate is transformed into a multi-dimensional time through new separated coordinates, each representing one scale, while continuity is ensured in the scale coupling. For instance, when considering two different time scales, the governing Partial Differential Equation is commuted into a nonlinear system that iterates between the so-called microtime and macrotime, so that the time coordinate can be viewed as a 2D time. The macroscale effects are taken into account by means of a finite element-based macro-discretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the time domain. The resulting separated representation allows us a very fine time discretization without impacting the computational efficiency. The proposed formulation is explored and numerically verified on thermal and elastodynamic problems. |
| format |
article |
| author |
Angelo Pasquale Amine Ammar Antonio Falcó Simona Perotto Elías Cueto Jean-Louis Duval Francisco Chinesta |
| author_facet |
Angelo Pasquale Amine Ammar Antonio Falcó Simona Perotto Elías Cueto Jean-Louis Duval Francisco Chinesta |
| author_sort |
Angelo Pasquale |
| title |
A separated representation involving multiple time scales within the Proper Generalized Decomposition framework |
| title_short |
A separated representation involving multiple time scales within the Proper Generalized Decomposition framework |
| title_full |
A separated representation involving multiple time scales within the Proper Generalized Decomposition framework |
| title_fullStr |
A separated representation involving multiple time scales within the Proper Generalized Decomposition framework |
| title_full_unstemmed |
A separated representation involving multiple time scales within the Proper Generalized Decomposition framework |
| title_sort |
separated representation involving multiple time scales within the proper generalized decomposition framework |
| publisher |
SpringerOpen |
| publishDate |
2021 |
| url |
https://doaj.org/article/1681b41ff3b14d99b5b187b05057e527 |
| work_keys_str_mv |
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