Modular parametric PGD enabling online solution of partial differential equations
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916159707676672 |
|---|---|
| author | Pasquale, Angelo Kazemzadeh-Parsi, Mohammad-Javad Di Lorenzo, Daniele Champaney, Victor Ammar, Amine Chinesta, Francisco |
| author_facet | Pasquale, Angelo Kazemzadeh-Parsi, Mohammad-Javad Di Lorenzo, Daniele Champaney, Victor Ammar, Amine Chinesta, Francisco |
| contents | In the present work, a new methodology is proposed for building surrogate parametric models of engineering systems based on modular assembly of pre-solved modules. Each module is a generic parametric solution considering parametric geometry, material and boundary conditions. By assembling these modules and satisfying continuity constraints at the interfaces, a parametric surrogate model of the full problem can be obtained. In the present paper, the PGD technique in connection with NURBS geometry representation is used to create a parametric model for each module. In this technique, the NURBS objects allow to map the governing boundary value problem from a parametric non-regular domain into a regular reference domain and the PGD is used to create a reduced model in the reference domain. In the assembly stage, an optimization problem is solved to satisfy the continuity constraints at the interfaces. The proposed procedure is based on the offline--online paradigm: the offline stage consists of creating multiple pre-solved modules which can be afterwards assembled in almost real-time during the online stage, enabling quick evaluations of the full system response. To show the potential of the proposed approach some numerical examples in heat conduction and structural plates under bending are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09312 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modular parametric PGD enabling online solution of partial differential equations Pasquale, Angelo Kazemzadeh-Parsi, Mohammad-Javad Di Lorenzo, Daniele Champaney, Victor Ammar, Amine Chinesta, Francisco Computational Engineering, Finance, and Science In the present work, a new methodology is proposed for building surrogate parametric models of engineering systems based on modular assembly of pre-solved modules. Each module is a generic parametric solution considering parametric geometry, material and boundary conditions. By assembling these modules and satisfying continuity constraints at the interfaces, a parametric surrogate model of the full problem can be obtained. In the present paper, the PGD technique in connection with NURBS geometry representation is used to create a parametric model for each module. In this technique, the NURBS objects allow to map the governing boundary value problem from a parametric non-regular domain into a regular reference domain and the PGD is used to create a reduced model in the reference domain. In the assembly stage, an optimization problem is solved to satisfy the continuity constraints at the interfaces. The proposed procedure is based on the offline--online paradigm: the offline stage consists of creating multiple pre-solved modules which can be afterwards assembled in almost real-time during the online stage, enabling quick evaluations of the full system response. To show the potential of the proposed approach some numerical examples in heat conduction and structural plates under bending are presented. |
| title | Modular parametric PGD enabling online solution of partial differential equations |
| topic | Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2403.09312 |