Some practical remarks in solving partial differential equations using reduced order schemes obtained through the POD method
In this paper we address the subject of mathematical modelling, more precisely the optimization of algorithms for numerically solving partial differential equations. The problem proposed to be tackled in this paper is the implementation of an algorithm for solving partial differential equations in a...
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| Format: | Article |
| Language: | English |
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National Institute for Aerospace Research “Elie Carafoli” - INCAS
2022-03-01
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| Series: | INCAS Bulletin |
| Subjects: | |
| Online Access: | https://bulletin.incas.ro/files/solomon__oltei__bogoi__vol_14_iss_1.pdf |
| _version_ | 1819122227680903168 |
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| author | Alexandru SOLOMON Valentin Claudiu OLTEI Alina BOGOI |
| author_facet | Alexandru SOLOMON Valentin Claudiu OLTEI Alina BOGOI |
| author_sort | Alexandru SOLOMON |
| collection | DOAJ |
| description | In this paper we address the subject of mathematical modelling, more precisely the optimization of algorithms for numerically solving partial differential equations. The problem proposed to be tackled in this paper is the implementation of an algorithm for solving partial differential equations in a significantly faster way than that obtained through applying finite difference schemes. The proper orthogonal decomposition (POD) method is a modern and efficient method of reducing the number of variables that occur as a result of applying centred difference schemes to partial differential equations, thus reducing the running time of the algorithm and the accumulation of truncation errors. Therefore, the POD method has been implemented to obtain a reduced order scheme applied to different partial differential equations, with some practical applications and comparisons with the analytical solutions. |
| first_indexed | 2024-12-22T06:49:06Z |
| format | Article |
| id | doaj.art-02c219e5317f474196e245e2f50f5575 |
| institution | Directory Open Access Journal |
| issn | 2066-8201 2247-4528 |
| language | English |
| last_indexed | 2024-12-22T06:49:06Z |
| publishDate | 2022-03-01 |
| publisher | National Institute for Aerospace Research “Elie Carafoli” - INCAS |
| record_format | Article |
| series | INCAS Bulletin |
| spelling | doaj.art-02c219e5317f474196e245e2f50f55752022-12-21T18:35:12ZengNational Institute for Aerospace Research “Elie Carafoli” - INCASINCAS Bulletin2066-82012247-45282022-03-0114118719610.13111/2066-8201.2022.14.1.15Some practical remarks in solving partial differential equations using reduced order schemes obtained through the POD methodAlexandru SOLOMON0Valentin Claudiu OLTEI1Alina BOGOI2Department of Aerospace Sciences, POLITEHNICA University Bucharest, Splaiul Independentei 313, 060042, Bucharest, Romania, alexandru.solomon@stud.aero.upb.roDepartment of Aerospace Sciences, POLITEHNICA University Bucharest, Splaiul Independentei 313, 060042, Bucharest, Romania, valentin.oltei@stud.aero.upb.roDepartment of Aerospace Sciences, POLITEHNICA University Bucharest, Splaiul Independentei 313, 060042, Bucharest, Romania, alina.bogoi@upb.roIn this paper we address the subject of mathematical modelling, more precisely the optimization of algorithms for numerically solving partial differential equations. The problem proposed to be tackled in this paper is the implementation of an algorithm for solving partial differential equations in a significantly faster way than that obtained through applying finite difference schemes. The proper orthogonal decomposition (POD) method is a modern and efficient method of reducing the number of variables that occur as a result of applying centred difference schemes to partial differential equations, thus reducing the running time of the algorithm and the accumulation of truncation errors. Therefore, the POD method has been implemented to obtain a reduced order scheme applied to different partial differential equations, with some practical applications and comparisons with the analytical solutions.https://bulletin.incas.ro/files/solomon__oltei__bogoi__vol_14_iss_1.pdfreduced order method (rom)proper orthogonal decomposition (pod)singular value decomposition (svd) |
| spellingShingle | Alexandru SOLOMON Valentin Claudiu OLTEI Alina BOGOI Some practical remarks in solving partial differential equations using reduced order schemes obtained through the POD method INCAS Bulletin reduced order method (rom) proper orthogonal decomposition (pod) singular value decomposition (svd) |
| title | Some practical remarks in solving partial differential equations using reduced order schemes obtained through the POD method |
| title_full | Some practical remarks in solving partial differential equations using reduced order schemes obtained through the POD method |
| title_fullStr | Some practical remarks in solving partial differential equations using reduced order schemes obtained through the POD method |
| title_full_unstemmed | Some practical remarks in solving partial differential equations using reduced order schemes obtained through the POD method |
| title_short | Some practical remarks in solving partial differential equations using reduced order schemes obtained through the POD method |
| title_sort | some practical remarks in solving partial differential equations using reduced order schemes obtained through the pod method |
| topic | reduced order method (rom) proper orthogonal decomposition (pod) singular value decomposition (svd) |
| url | https://bulletin.incas.ro/files/solomon__oltei__bogoi__vol_14_iss_1.pdf |
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