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Separated response surfaces for flows in parametrised domains: Comparison of a priori and a posteriori PGD algorithms

Matteo Giacomini, LUCA BORCHINI, Rubén Sevilla Orcid Logo, Antonio Huerta

Finite Elements in Analysis and Design, Volume: 196, Start page: 103530

Swansea University Authors: LUCA BORCHINI, Rubén Sevilla Orcid Logo

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DOI (Published version): 10.1016/j.finel.2021.103530

Abstract

Reduced order models (ROM) are commonly employed to solve parametric problems and to devise inexpensive response surfaces to evaluate quantities of interest in real-time. There are many families of ROMs in the literature and choosing among them is not always a trivial task. This work presents a comp...

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Published in: Finite Elements in Analysis and Design
ISSN: 0168-874X
Published: Elsevier BV 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa55795
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There are many families of ROMs in the literature and choosing among them is not always a trivial task. This work presents a comparison of the performance of a priori and a posteriori proper generalised decomposition (PGD) algorithms for an incompressible Stokes flow problem in a geometrically parametrised domain. This problem is particularly challenging as the geometric parameters affect both the solution manifold and the computational spatial domain. The difficulty is further increased because multiple geometric parameters are considered and extended ranges of values are analysed for the parameters and this leads to significant variations in the flow features. Using a set of numerical experiments involving geometrically parametrised microswimmers, the two PGD algorithms are extensively compared in terms of their accuracy and their computational cost, expressed as a function of the number of full-order solves required.</abstract><type>Journal Article</type><journal>Finite Elements in Analysis and Design</journal><volume>196</volume><journalNumber/><paginationStart>103530</paginationStart><paginationEnd/><publisher>Elsevier BV</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0168-874X</issnPrint><issnElectronic/><keywords>Reduced order models, A priori, A posteriori, Proper generalised decomposition, Response surfaces, Geometry parametrisation</keywords><publishedDay>15</publishedDay><publishedMonth>11</publishedMonth><publishedYear>2021</publishedYear><publishedDate>2021-11-15</publishedDate><doi>10.1016/j.finel.2021.103530</doi><url/><notes/><college>COLLEGE NANME</college><CollegeCode>COLLEGE CODE</CollegeCode><institution>Swansea University</institution><apcterm/><funders>This work was partially supported by the European Union's Horizon 2020 research and innovation programme under the Marie Sk&#x142;odowska-Curie Actions (Grant number: 675919) that financed the Ph.D. fellowship of L.B. and by the Spanish Ministry of Economy and Competitiveness (Grant number: DPI2017-85139-C2-2-R). M.G. and A.H. are also grateful for the support provided by the Spanish Ministry of Economy and Competitiveness through the Severo Ochoa programme for centres of excellence in RTD (Grant number: CEX2018-000797-S) and the Generalitat de Catalunya (Grant number: 2017-SGR-1278). 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spelling 2022-08-17T12:32:30.2479430 v2 55795 2020-12-01 Separated response surfaces for flows in parametrised domains: Comparison of a priori and a posteriori PGD algorithms 3a70ff1fdfec53f49ebb134370f5502c LUCA BORCHINI LUCA BORCHINI true false b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 2020-12-01 Reduced order models (ROM) are commonly employed to solve parametric problems and to devise inexpensive response surfaces to evaluate quantities of interest in real-time. There are many families of ROMs in the literature and choosing among them is not always a trivial task. This work presents a comparison of the performance of a priori and a posteriori proper generalised decomposition (PGD) algorithms for an incompressible Stokes flow problem in a geometrically parametrised domain. This problem is particularly challenging as the geometric parameters affect both the solution manifold and the computational spatial domain. The difficulty is further increased because multiple geometric parameters are considered and extended ranges of values are analysed for the parameters and this leads to significant variations in the flow features. Using a set of numerical experiments involving geometrically parametrised microswimmers, the two PGD algorithms are extensively compared in terms of their accuracy and their computational cost, expressed as a function of the number of full-order solves required. Journal Article Finite Elements in Analysis and Design 196 103530 Elsevier BV 0168-874X Reduced order models, A priori, A posteriori, Proper generalised decomposition, Response surfaces, Geometry parametrisation 15 11 2021 2021-11-15 10.1016/j.finel.2021.103530 COLLEGE NANME COLLEGE CODE Swansea University This work was partially supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Actions (Grant number: 675919) that financed the Ph.D. fellowship of L.B. and by the Spanish Ministry of Economy and Competitiveness (Grant number: DPI2017-85139-C2-2-R). M.G. and A.H. are also grateful for the support provided by the Spanish Ministry of Economy and Competitiveness through the Severo Ochoa programme for centres of excellence in RTD (Grant number: CEX2018-000797-S) and the Generalitat de Catalunya (Grant number: 2017-SGR-1278). R.S. also acknowledges the support of the Engineering and Physical Sciences Research Council (Grant number: EP/P033997/1). 2022-08-17T12:32:30.2479430 2020-12-01T11:15:27.9479466 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Matteo Giacomini 1 LUCA BORCHINI 2 Rubén Sevilla 0000-0002-0061-6214 3 Antonio Huerta 4 55795__18782__a8839bda23584d1fa11544ebd4ec64f5.pdf 55795.pdf 2020-12-01T11:17:35.1388879 Output 16610413 application/pdf Accepted Manuscript true 2022-06-24T00:00:00.0000000 Released under the terms of a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) License true eng https://creativecommons.org/licenses/by-nc-nd/4.0/ 47 Rebecca Kelleher 0000-0002-6791-2886 R.Kelleher@Swansea.ac.uk true true
title Separated response surfaces for flows in parametrised domains: Comparison of a priori and a posteriori PGD algorithms
spellingShingle Separated response surfaces for flows in parametrised domains: Comparison of a priori and a posteriori PGD algorithms
LUCA BORCHINI
Rubén Sevilla
title_short Separated response surfaces for flows in parametrised domains: Comparison of a priori and a posteriori PGD algorithms
title_full Separated response surfaces for flows in parametrised domains: Comparison of a priori and a posteriori PGD algorithms
title_fullStr Separated response surfaces for flows in parametrised domains: Comparison of a priori and a posteriori PGD algorithms
title_full_unstemmed Separated response surfaces for flows in parametrised domains: Comparison of a priori and a posteriori PGD algorithms
title_sort Separated response surfaces for flows in parametrised domains: Comparison of a priori and a posteriori PGD algorithms
author_id_str_mv 3a70ff1fdfec53f49ebb134370f5502c
b542c87f1b891262844e95a682f045b6
author_id_fullname_str_mv 3a70ff1fdfec53f49ebb134370f5502c_***_LUCA BORCHINI
b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
author LUCA BORCHINI
Rubén Sevilla
author2 Matteo Giacomini
LUCA BORCHINI
Rubén Sevilla
Antonio Huerta
format Journal article
container_title Finite Elements in Analysis and Design
container_volume 196
container_start_page 103530
publishDate 2021
institution Swansea University
issn 0168-874X
doi_str_mv 10.1016/j.finel.2021.103530
publisher Elsevier BV
college_str Faculty of Science and Engineering
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department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
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description Reduced order models (ROM) are commonly employed to solve parametric problems and to devise inexpensive response surfaces to evaluate quantities of interest in real-time. There are many families of ROMs in the literature and choosing among them is not always a trivial task. This work presents a comparison of the performance of a priori and a posteriori proper generalised decomposition (PGD) algorithms for an incompressible Stokes flow problem in a geometrically parametrised domain. This problem is particularly challenging as the geometric parameters affect both the solution manifold and the computational spatial domain. The difficulty is further increased because multiple geometric parameters are considered and extended ranges of values are analysed for the parameters and this leads to significant variations in the flow features. Using a set of numerical experiments involving geometrically parametrised microswimmers, the two PGD algorithms are extensively compared in terms of their accuracy and their computational cost, expressed as a function of the number of full-order solves required.
published_date 2021-11-15T04:10:16Z
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