Mesh sampling and weighting for the hyperreduction of nonlinear Petrov–Galerkin reduced‐order models with local reduced‐order bases

The energy‐conserving sampling and weighting (ECSW) method is a hyper‐reduction method originally developed for accelerating the performance of Galerkin projection‐based reduced‐order models (PROMs) associated with large‐scale finite element models, when the underlying projected operators need to be...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	International journal for numerical methods in engineering Ročník 122; číslo 7; s. 1846 - 1874
Hlavní autoři:	Grimberg, Sebastian, Farhat, Charbel, Tezaur, Radek, Bou‐Mosleh, Charbel
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Hoboken, USA John Wiley & Sons, Inc 15.04.2021 Wiley Subscription Services, Inc
Témata:	Computational fluid dynamics Finite difference method Finite element method Galerkin method hyper‐reduction local basis machine learning Mathematical models nonlinear model reduction Petrov–Galerkin reduced mesh Reduction Sampling Subspaces Turbulent flow Weighting
ISSN:	0029-5981, 1097-0207
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Abstract	The energy‐conserving sampling and weighting (ECSW) method is a hyper‐reduction method originally developed for accelerating the performance of Galerkin projection‐based reduced‐order models (PROMs) associated with large‐scale finite element models, when the underlying projected operators need to be frequently recomputed as in parametric and/or nonlinear problems. In this paper, this hyper‐reduction method is extended to Petrov–Galerkin PROMs where the underlying high‐dimensional models can be associated with arbitrary finite element, finite volume, and finite difference semi‐discretization methods. Its scope is also extended to cover local PROMs based on piecewise‐affine approximation subspaces, such as those designed for mitigating the Kolmogorov n‐width barrier issue associated with convection‐dominated flow problems. The resulting ECSW method is shown in this paper to be robust and accurate. In particular, its offline phase is shown to be fast and parallelizable, and the potential of its online phase for large‐scale applications of industrial relevance is demonstrated for turbulent flow problems with O(107) and O(108) degrees of freedom. For such problems, the online part of the ECSW method proposed in this paper for Petrov–Galerkin PROMs is shown to enable wall‐clock time and CPU time speedup factors of several orders of magnitude while delivering exceptional accuracy.
AbstractList	The energy‐conserving sampling and weighting (ECSW) method is a hyper‐reduction method originally developed for accelerating the performance of Galerkin projection‐based reduced‐order models (PROMs) associated with large‐scale finite element models, when the underlying projected operators need to be frequently recomputed as in parametric and/or nonlinear problems. In this paper, this hyper‐reduction method is extended to Petrov–Galerkin PROMs where the underlying high‐dimensional models can be associated with arbitrary finite element, finite volume, and finite difference semi‐discretization methods. Its scope is also extended to cover local PROMs based on piecewise‐affine approximation subspaces, such as those designed for mitigating the Kolmogorov n‐width barrier issue associated with convection‐dominated flow problems. The resulting ECSW method is shown in this paper to be robust and accurate. In particular, its offline phase is shown to be fast and parallelizable, and the potential of its online phase for large‐scale applications of industrial relevance is demonstrated for turbulent flow problems with O(107) and O(108) degrees of freedom. For such problems, the online part of the ECSW method proposed in this paper for Petrov–Galerkin PROMs is shown to enable wall‐clock time and CPU time speedup factors of several orders of magnitude while delivering exceptional accuracy. The energy‐conserving sampling and weighting (ECSW) method is a hyper‐reduction method originally developed for accelerating the performance of Galerkin projection‐based reduced‐order models (PROMs) associated with large‐scale finite element models, when the underlying projected operators need to be frequently recomputed as in parametric and/or nonlinear problems. In this paper, this hyper‐reduction method is extended to Petrov–Galerkin PROMs where the underlying high‐dimensional models can be associated with arbitrary finite element, finite volume, and finite difference semi‐discretization methods. Its scope is also extended to cover local PROMs based on piecewise‐affine approximation subspaces, such as those designed for mitigating the Kolmogorov n ‐width barrier issue associated with convection‐dominated flow problems. The resulting ECSW method is shown in this paper to be robust and accurate. In particular, its offline phase is shown to be fast and parallelizable, and the potential of its online phase for large‐scale applications of industrial relevance is demonstrated for turbulent flow problems with O (10 7 ) and O (10 8 ) degrees of freedom. For such problems, the online part of the ECSW method proposed in this paper for Petrov–Galerkin PROMs is shown to enable wall‐clock time and CPU time speedup factors of several orders of magnitude while delivering exceptional accuracy.
Author	Grimberg, Sebastian Bou‐Mosleh, Charbel Farhat, Charbel Tezaur, Radek
Author_xml	– sequence: 1 givenname: Sebastian orcidid: 0000-0002-9188-0562 surname: Grimberg fullname: Grimberg, Sebastian email: sjg@stanford.edu organization: Stanford University – sequence: 2 givenname: Charbel orcidid: 0000-0003-2563-8820 surname: Farhat fullname: Farhat, Charbel organization: Stanford University – sequence: 3 givenname: Radek surname: Tezaur fullname: Tezaur, Radek organization: Stanford University – sequence: 4 givenname: Charbel surname: Bou‐Mosleh fullname: Bou‐Mosleh, Charbel organization: Notre Dame University‐Louaize
BookMark	eNp10L1OwzAQB3ALFYm2IPEIllhYUmwnzseIqlKQWmCAOXLtS-OSxMVOqbp1ZUPiDfskJC0TH5N18u_udP8e6lSmAoTOKRlQQthVVcIgDIl_hLqUJJFHGIk6qNt8JR5PYnqCes4tCKGUE7-L3qfgcuxEuSx0NceiUngNep7XbZUZi-sccL5ZgrWgVrLWpsImw83SxoOw-BFqa95228-xKMC-6ArvIajd9sNYBRaXRkHh8FrXOS6MFMUvMRMO3Ck6zkTh4Oz77aPnm9HT8NabPIzvhtcTT7LE972ME05DQgPJYlAqCHzBAj9mUoQ0ns1EyHnGqBRKJSqKJY1EFCnuR1xwHlIW-X10cZi7tOZ1Ba5OF2Zlq2ZlyjhJWNAExho1OChpjXMWslTqWrTn11boIqUkbeNOm7jTNu6m4fJHw9LqUtjNX9Q70LUuYPOvS--no73_Anh3lWE
CitedBy_id	crossref_primary_10_1016_j_cma_2023_116298 crossref_primary_10_1016_j_jcp_2023_112420 crossref_primary_10_1016_j_cma_2025_117920 crossref_primary_10_1016_j_energy_2025_136019 crossref_primary_10_1007_s00466_025_02670_w crossref_primary_10_1137_24M1695099 crossref_primary_10_1016_j_cma_2025_117863 crossref_primary_10_1016_j_compfluid_2025_106568 crossref_primary_10_1016_j_cpc_2025_109501 crossref_primary_10_1515_cmam_2021_0131 crossref_primary_10_3390_math10091495 crossref_primary_10_1002_nme_7240 crossref_primary_10_1016_j_ijnonlinmec_2025_105092 crossref_primary_10_2514_1_J063840 crossref_primary_10_5802_crmeca_191 crossref_primary_10_1007_s42967_023_00308_3 crossref_primary_10_1016_j_jcp_2023_112356 crossref_primary_10_1016_j_jcp_2022_111348 crossref_primary_10_1051_meca_2022001 crossref_primary_10_1063_5_0220705 crossref_primary_10_1016_j_compstruc_2025_107867 crossref_primary_10_1016_j_jcp_2021_110336 crossref_primary_10_1016_j_cma_2024_117638 crossref_primary_10_1016_j_ymssp_2024_112261 crossref_primary_10_1137_21M1435343 crossref_primary_10_1016_j_cma_2025_118325 crossref_primary_10_1016_j_finel_2025_104439 crossref_primary_10_1098_rsta_2021_0206 crossref_primary_10_1016_j_finel_2024_104237 crossref_primary_10_1016_j_cma_2022_115392 crossref_primary_10_1007_s00366_025_02172_6 crossref_primary_10_1002_nme_7590 crossref_primary_10_1038_s41598_024_56118_x crossref_primary_10_1016_j_compfluid_2025_106783 crossref_primary_10_1016_j_ymssp_2025_112638 crossref_primary_10_2514_1_J063116 crossref_primary_10_1016_j_jcp_2025_113817 crossref_primary_10_1016_j_cma_2023_115988 crossref_primary_10_1002_nme_7179 crossref_primary_10_1016_j_jcp_2025_114067 crossref_primary_10_1016_j_cma_2022_115747 crossref_primary_10_2514_1_J062869 crossref_primary_10_1007_s11831_025_10299_4 crossref_primary_10_3390_axioms14050385
Cites_doi	10.1016/j.jcp.2020.109681 10.1016/0098-3004(84)90020-7 10.1016/j.jcp.2013.02.028 10.1145/1409060.1409118 10.1137/090766498 10.2514/6.2016-1814 10.1002/nme.4274 10.1002/nme.4668 10.2514/1.J057791 10.1002/nme.5332 10.1002/nme.6505 10.4271/840300 10.2514/6.2012-2686 10.2514/6.2001-879 10.1080/13873954.2011.547674 10.1137/130932715 10.1016/j.cma.2016.10.022 10.1137/1.9780898718713 10.1109/TAC.2008.2006102 10.1007/978-1-4614-6570-6_18 10.1002/nme.2086 10.1016/j.jcp.2004.07.015 10.1090/conm/218/03046 10.1002/nme.4820 10.1137/1.9781611971217 10.1137/130924408 10.1016/j.physd.2003.03.001 10.2514/3.9465 10.2514/1.J057797 10.1016/j.crma.2004.08.006 10.1016/0045-7825(93)90141-J 10.1007/978-3-642-20671-9_39 10.1002/nme.2406 10.1002/nme.3050 10.1016/j.cma.2018.02.028 10.1145/1073204.1073300 10.1002/nme.4371 10.1051/m2an:2007031 10.1007/978-0-387-84858-7 10.1063/1.868459 10.1364/JOSAA.12.001657 10.1137/070694855
ContentType	Journal Article
Copyright	2020 John Wiley & Sons, Ltd. 2021 John Wiley & Sons, Ltd.
Copyright_xml	– notice: 2020 John Wiley & Sons, Ltd. – notice: 2021 John Wiley & Sons, Ltd.
DBID	AAYXX CITATION 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D
DOI	10.1002/nme.6603
DatabaseName	CrossRef Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional
DatabaseTitle	CrossRef Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional
DatabaseTitleList	Civil Engineering Abstracts CrossRef
DeliveryMethod	fulltext_linktorsrc
Discipline	Applied Sciences Engineering Mathematics
EISSN	1097-0207
EndPage	1874
ExternalDocumentID	10_1002_nme_6603 NME6603
Genre	article
GrantInformation_xml	– fundername: Boeing funderid: 45047 – fundername: Office of Naval Research funderid: N00014‐17‐1‐2749 – fundername: King Abdulaziz City for Science and Technology (KACST) – fundername: Air Force Office of Scientific Research funderid: FA9550‐17‐1‐0182
GroupedDBID	-~X .3N .4S .DC .GA 05W 0R~ 10A 1L6 1OB 1OC 1ZS 33P 3SF 3WU 4.4 4ZD 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5GY 5VS 66C 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHHS AAHQN AAMNL AANLZ AAONW AAXRX AAYCA AAZKR ABCQN ABCUV ABIJN ABJNI ACAHQ ACCFJ ACCZN ACGFS ACIWK ACPOU ACXBN ACXQS ADBBV ADEOM ADIZJ ADKYN ADMGS ADOZA ADXAS ADZMN ADZOD AEEZP AEIGN AEIMD AENEX AEQDE AEUQT AEUYR AFBPY AFFPM AFGKR AFPWT AFWVQ AFZJQ AHBTC AITYG AIURR AIWBW AJBDE AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALUQN ALVPJ AMBMR AMYDB ARCSS ATUGU AUFTA AZBYB AZVAB BAFTC BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BY8 CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM DU5 EBS F00 F01 F04 F5P G-S G.N GNP GODZA H.T H.X HBH HGLYW HHY HZ~ IX1 J0M JPC KQQ LATKE LAW LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MXFUL MXSTM N04 N05 NF~ O66 O9- OIG P2P P2W P2X P4D Q.N Q11 QB0 QRW R.K ROL RWI RWS RX1 RYL SUPJJ TN5 TUS UB1 V2E W8V W99 WBKPD WIB WIH WIK WLBEL WOHZO WQJ WRC WXSBR WYISQ XG1 XPP XV2 ZZTAW ~02 ~IA ~WT AAMMB AAYXX AEFGJ AEYWJ AGHNM AGXDD AGYGG AIDQK AIDYY CITATION O8X 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D
ID	FETCH-LOGICAL-c2933-f50516014c28edd443a24382ca618bba655f21cadd9d78c17a77d5375a5561273
IEDL.DBID	DRFUL
ISICitedReferencesCount	60
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000606664200001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0029-5981
IngestDate	Fri Jul 25 12:18:30 EDT 2025 Sat Nov 29 06:43:59 EST 2025 Tue Nov 18 22:14:58 EST 2025 Wed Jan 22 16:29:34 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	7
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c2933-f50516014c28edd443a24382ca618bba655f21cadd9d78c17a77d5375a5561273
Notes	Funding information Air Force Office of Scientific Research, FA9550‐17‐1‐0182; Boeing, 45047; King Abdulaziz City for Science and Technology (KACST), Office of Naval Research, N00014‐17‐1‐2749 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0002-9188-0562 0000-0003-2563-8820
PQID	2509242072
PQPubID	996376
PageCount	29
ParticipantIDs	proquest_journals_2509242072 crossref_citationtrail_10_1002_nme_6603 crossref_primary_10_1002_nme_6603 wiley_primary_10_1002_nme_6603_NME6603
PublicationCentury	2000
PublicationDate	15 April 2021
PublicationDateYYYYMMDD	2021-04-15
PublicationDate_xml	– month: 04 year: 2021 text: 15 April 2021 day: 15
PublicationDecade	2020
PublicationPlace	Hoboken, USA
PublicationPlace_xml	– name: Hoboken, USA – name: Bognor Regis
PublicationTitle	International journal for numerical methods in engineering
PublicationYear	2021
Publisher	John Wiley & Sons, Inc Wiley Subscription Services, Inc
Publisher_xml	– name: John Wiley & Sons, Inc – name: Wiley Subscription Services, Inc
References	2015; 57 2004; 189 2010; 32 2012 2015; 102 1995; 15 2019; 57 1995; 12 1985; 7 2009 1998; 218 2019; 344 2006 2005 2016; 2016 2013; 242 2008; 30 2008; 53 2011; 4 2011; 17 2008; 73 1993; 102 2017; 313 2005; 24 1995; 7 2009; 77 2017; 109 2012; 92 2012; 91 2020; 2 2001 2020 2005; 202 1984; 10 1986; 24 2008; 27 2011; 86 2014; 36 2005; 6 1984 2016 2007; 41 2013 2004; 339 2014; 98 2020; 419 1922 e_1_2_9_31_1 e_1_2_9_50_1 e_1_2_9_10_1 e_1_2_9_35_1 e_1_2_9_12_1 e_1_2_9_33_1 Ohlberger M (e_1_2_9_44_1) 2016 Farhat C (e_1_2_9_8_1) 2020 e_1_2_9_14_1 e_1_2_9_39_1 e_1_2_9_16_1 e_1_2_9_37_1 e_1_2_9_18_1 e_1_2_9_41_1 e_1_2_9_20_1 e_1_2_9_22_1 e_1_2_9_45_1 e_1_2_9_24_1 e_1_2_9_43_1 e_1_2_9_4_1 e_1_2_9_2_1 e_1_2_9_26_1 e_1_2_9_49_1 e_1_2_9_28_1 e_1_2_9_47_1 e_1_2_9_11_1 e_1_2_9_34_1 e_1_2_9_13_1 e_1_2_9_32_1 e_1_2_9_15_1 e_1_2_9_38_1 e_1_2_9_17_1 e_1_2_9_36_1 Nguyen NC (e_1_2_9_6_1) 2005 e_1_2_9_19_1 e_1_2_9_42_1 e_1_2_9_40_1 e_1_2_9_21_1 e_1_2_9_46_1 e_1_2_9_23_1 e_1_2_9_7_1 e_1_2_9_5_1 e_1_2_9_3_1 e_1_2_9_9_1 e_1_2_9_25_1 e_1_2_9_27_1 e_1_2_9_48_1 e_1_2_9_29_1 Pinkus A (e_1_2_9_30_1) 1985
References_xml	– volume: 30 start-page: 3270 issue: 6 year: 2008 end-page: 3288 article-title: Model reduction for large‐scale systems with high‐dimensional parametric input space publication-title: SIAM J Sci Comput – year: 2009 – volume: 53 start-page: 2237 issue: 10 year: 2008 end-page: 2251 article-title: Missing point estimation in models described by proper orthogonal decomposition publication-title: IEEE Trans Autom Control – volume: 92 start-page: 891 issue: 10 year: 2012 end-page: 916 article-title: Nonlinear model order reduction based on local reduced‐order bases publication-title: Int J Numer Methods Eng – volume: 218 start-page: 479 year: 1998 end-page: 485 article-title: A minimum overlap restricted additive Schwarz preconditioner and applications in 3D flow simulations publication-title: Contemp Math – volume: 2 year: 2020 – start-page: 203 year: 2013 end-page: 212 – volume: 57 start-page: 2297 issue: 6 year: 2019 end-page: 2307 article-title: Nonlinear model order reduction via lifting transformations and proper orthogonal decomposition publication-title: AIAA J – volume: 57 start-page: 4978 issue: 11 year: 2019 end-page: 4991 article-title: Feasible probabilistic learning method for model‐form uncertainty quantification in vibration analysis publication-title: AIAA J – volume: 4 start-page: 369 year: 2011 end-page: 377 – year: 2001 – volume: 7 start-page: 2102 issue: 9 year: 1995 end-page: 2104 article-title: Details of the drag curve near the onset of vortex shedding publication-title: Phys Fluids – volume: 344 start-page: 1104 year: 2019 end-page: 1123 article-title: An LP empirical cubature procedure for reduced basis treatment of parametrized nonlinear PDEs publication-title: Comput Methods Appl Mech Eng – volume: 15 year: 1995 – volume: 41 start-page: 575 issue: 3 year: 2007 end-page: 605 article-title: Efficient reduced‐basis treatment of nonaffine and nonlinear partial differential equations publication-title: ESIAM Math Model Numer Anal – volume: 339 start-page: 667 issue: 9 year: 2004 end-page: 672 article-title: An 'empirical interpolation' method: application to efficient reduced‐basis discretization of partial differential equations publication-title: Comptes Rendus Mathematique – year: 2016 – volume: 24 start-page: 1453 issue: 9 year: 1986 end-page: 1460 article-title: Comparison of finite volume flux vector splittings for the Euler equations publication-title: AIAA J – volume: 77 start-page: 75 issue: 1 year: 2009 end-page: 89 article-title: Hyper‐reduction of mechanical models involving internal variables publication-title: Int J Numer Methods Eng – year: 2012 – volume: 202 start-page: 346 issue: 1 year: 2005 end-page: 366 article-title: A priori hyperreduction method: an adaptive approach publication-title: J Comput Phys – volume: 73 start-page: 521 issue: 4 year: 2008 end-page: 543 article-title: A ‘best points’ interpolation method for efficient approximation of parametrized functions publication-title: Int J Numer Methods Eng – volume: 24 start-page: 982 issue: 3 year: 2005 end-page: 990 article-title: Real‐time subspace integration for St. Venant‐Kirchoff deformable models publication-title: ACM Trans Graph – volume: 12 start-page: 1657 issue: 8 year: 1995 end-page: 1664 article-title: Karhunen‐Loève procedure for gappy data publication-title: J Opt Soc Am A – year: 1984 – volume: 6 year: 2005 – start-page: 1529 year: 2005 end-page: 1564 – volume: 17 start-page: 423 issue: 4 year: 2011 end-page: 442 article-title: A training set and multiple bases generation approach for parameterized model reduction based on adaptive grids in parameter space publication-title: Math Comput Model Dyn Syst – volume: 32 start-page: 2737 issue: 5 year: 2010 end-page: 2764 article-title: Nonlinear model reduction via discrete empirical interpolation publication-title: SIAM J Sci Comput – volume: 189 start-page: 115 year: 2004 end-page: 129 article-title: Model reduction for compressible flows using POD and Galerkin projection publication-title: Phys D Nonlinear Phenomena – volume: 2016 start-page: 1 year: 2016 end-page: 12 – year: 2006 – volume: 7 year: 1985 – volume: 10 start-page: 191 issue: 2–3 year: 1984 end-page: 203 article-title: FCM: the fuzzy ‐means clustering algorithm publication-title: Comput Geosci – year: 2020 – volume: 98 start-page: 625 issue: 9 year: 2014 end-page: 662 article-title: Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy‐based mesh sampling and weighting for computational efficiency publication-title: Int J Numer Methods Eng – volume: 86 start-page: 155 issue: 2 year: 2011 end-page: 181 article-title: Efficient non‐linear model reduction via a least‐squares Petrov‐Galerkin projection and compressive tensor approximations publication-title: Int J Numer Methods Eng – volume: 419 year: 2020 article-title: On the stability of projection‐based model order reduction for convection‐dominated laminar and turbulent flows publication-title: J Comput Phys – year: 1922 – volume: 102 start-page: 1077 issue: 5 year: 2015 end-page: 1110 article-title: Structure‐preserving, stability, and accuracy properties of the energy‐conserving sampling and weighting method for the hyper reduction of nonlinear finite element dynamic models publication-title: Int J Numer Methods Eng – volume: 313 start-page: 687 year: 2017 end-page: 722 article-title: Dimensional hyper‐reduction of nonlinear finite element models via empirical cubature publication-title: Comput Methods Appl Mech Eng – volume: 102 start-page: 61 issue: 1 year: 1993 end-page: 88 article-title: Two‐dimensional viscous flow computations on the connection machine: unstructured meshes, upwind schemes and massively parallel computations publication-title: Comput Methods Appl Mech Eng – volume: 27 start-page: 165.1 issue: 5 year: 2008 end-page: 165.10 article-title: Optimizing cubature for the efficient integration of subspace deformations publication-title: ACM Trans Graph – volume: 36 start-page: A168 issue: 1 year: 2014 end-page: A192 article-title: Localized discrete empirical interpolation method publication-title: SIAM J Sci Comput – volume: 109 start-page: 1623 issue: 12 year: 2017 end-page: 1654 article-title: Accelerated mesh sampling for the hyper reduction of nonlinear computational models publication-title: Int J Numer Methods Eng – volume: 91 start-page: 358 issue: 4 year: 2012 end-page: 377 article-title: Stabilization of projection‐based reduced‐order models publication-title: Int J Numer Methods Eng – volume: 57 start-page: 483 issue: 4 year: 2015 end-page: 531 article-title: A survey of projection‐based model reduction methods for parametric dynamical systems publication-title: SIAM Rev – volume: 242 start-page: 623 year: 2013 end-page: 647 article-title: The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows publication-title: J Comput Phys – ident: e_1_2_9_29_1 doi: 10.1016/j.jcp.2020.109681 – ident: e_1_2_9_40_1 doi: 10.1016/0098-3004(84)90020-7 – ident: e_1_2_9_25_1 doi: 10.1016/j.jcp.2013.02.028 – ident: e_1_2_9_19_1 doi: 10.1145/1409060.1409118 – ident: e_1_2_9_16_1 doi: 10.1137/090766498 – ident: e_1_2_9_27_1 doi: 10.2514/6.2016-1814 – ident: e_1_2_9_31_1 doi: 10.1002/nme.4274 – ident: e_1_2_9_20_1 doi: 10.1002/nme.4668 – ident: e_1_2_9_7_1 doi: 10.2514/1.J057791 – ident: e_1_2_9_42_1 doi: 10.1002/nme.5332 – start-page: 1 volume-title: Proceedings of ALGORITMY year: 2016 ident: e_1_2_9_44_1 – ident: e_1_2_9_37_1 doi: 10.1002/nme.6505 – ident: e_1_2_9_32_1 doi: 10.4271/840300 – ident: e_1_2_9_38_1 doi: 10.2514/6.2012-2686 – volume-title: Model Order Reduction: Snapshot‐Based Methods and Algorithms year: 2020 ident: e_1_2_9_8_1 – ident: e_1_2_9_47_1 doi: 10.2514/6.2001-879 – ident: e_1_2_9_49_1 – ident: e_1_2_9_36_1 doi: 10.1080/13873954.2011.547674 – ident: e_1_2_9_3_1 doi: 10.1137/130932715 – ident: e_1_2_9_21_1 doi: 10.1016/j.cma.2016.10.022 – ident: e_1_2_9_2_1 doi: 10.1137/1.9780898718713 – ident: e_1_2_9_13_1 doi: 10.1109/TAC.2008.2006102 – ident: e_1_2_9_17_1 doi: 10.1007/978-1-4614-6570-6_18 – ident: e_1_2_9_12_1 doi: 10.1002/nme.2086 – ident: e_1_2_9_14_1 doi: 10.1016/j.jcp.2004.07.015 – ident: e_1_2_9_48_1 doi: 10.1090/conm/218/03046 – ident: e_1_2_9_23_1 doi: 10.1002/nme.4820 – ident: e_1_2_9_28_1 – ident: e_1_2_9_43_1 doi: 10.1137/1.9781611971217 – ident: e_1_2_9_18_1 doi: 10.1137/130924408 – ident: e_1_2_9_4_1 doi: 10.1016/j.physd.2003.03.001 – ident: e_1_2_9_45_1 doi: 10.2514/3.9465 – ident: e_1_2_9_41_1 doi: 10.2514/1.J057797 – ident: e_1_2_9_10_1 doi: 10.1016/j.crma.2004.08.006 – volume-title: A Series of Modern Surveys in Mathematics year: 1985 ident: e_1_2_9_30_1 – ident: e_1_2_9_46_1 doi: 10.1016/0045-7825(93)90141-J – ident: e_1_2_9_35_1 doi: 10.1007/978-3-642-20671-9_39 – ident: e_1_2_9_15_1 doi: 10.1002/nme.2406 – ident: e_1_2_9_24_1 doi: 10.1002/nme.3050 – ident: e_1_2_9_22_1 doi: 10.1016/j.cma.2018.02.028 – ident: e_1_2_9_5_1 doi: 10.1145/1073204.1073300 – start-page: 1529 volume-title: Handbook of Materials Modeling year: 2005 ident: e_1_2_9_6_1 – ident: e_1_2_9_33_1 doi: 10.1002/nme.4371 – ident: e_1_2_9_11_1 doi: 10.1051/m2an:2007031 – ident: e_1_2_9_26_1 – ident: e_1_2_9_39_1 doi: 10.1007/978-0-387-84858-7 – ident: e_1_2_9_50_1 doi: 10.1063/1.868459 – ident: e_1_2_9_9_1 doi: 10.1364/JOSAA.12.001657 – ident: e_1_2_9_34_1 doi: 10.1137/070694855
SSID	ssj0011503
Score	2.5980406
Snippet	The energy‐conserving sampling and weighting (ECSW) method is a hyper‐reduction method originally developed for accelerating the performance of Galerkin...
SourceID	proquest crossref wiley
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	1846
SubjectTerms	Computational fluid dynamics Finite difference method Finite element method Galerkin method hyper‐reduction local basis machine learning Mathematical models nonlinear model reduction Petrov–Galerkin reduced mesh Reduction Sampling Subspaces Turbulent flow Weighting
Title	Mesh sampling and weighting for the hyperreduction of nonlinear Petrov–Galerkin reduced‐order models with local reduced‐order bases
URI	https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fnme.6603 https://www.proquest.com/docview/2509242072
Volume	122
WOSCitedRecordID	wos000606664200001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVWIB databaseName: Wiley Online Library - Journals customDbUrl: eissn: 1097-0207 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0011503 issn: 0029-5981 databaseCode: DRFUL dateStart: 19960101 isFulltext: true titleUrlDefault: https://onlinelibrary.wiley.com providerName: Wiley-Blackwell
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Nb9QwEB2hLQc4UChUXbogIyE4hW7sJHaOVduFA7tCiEq9RU7ssJXatIrLct1rb5X6D_eXdMb5YBEgVeKSKNKMZNkznufx5A3AW60wjJVcBFEu0wDx7RhdKuX40GOlZay1yH2zCTmbqZOT9EtbVUn_wjT8EH3CjTzD79fk4Dp3e2ukoef2Q5IQ0ecGR7ONB7Bx-HVy_Lm_Q0CoI7oCjzhVYUc9O-Z7ne7vwegXwlzHqT7QTDb_Z4hP4UkLL9l-Yw_P4IGttmCzhZqsdWS3BY_XeAjxa9qTt7rncD21bs6cplrz6jvTlWE_fQKVvhDjMpRlczy_1jXxvtLKsouSVc2Idc2oS9fFYrW8_YjRh3LxzAtas1reeKpP5vvvOEZJYOaj6R8SFF3dCzieHH07-BS0HRuCAmGDCErEUyEe8aKCK2tMFAnN6aax0Emo8lwncVzysMA9NTVSFaHUUppYoEn4Lp1SbMMAR2t3gOXCiEigjrQq4mWoDaqqyNg8iVJukyG875YuK1o6c-qqcZY1RMw8w9nPaPaH8KaXvGwoPP4iM-pWP2ud2GWIDvF0yseSD-GdX-d_6mez6RG9X95XcBcecaqOIdbIeASDq_qHfQUPi8XVqatft6Z8B5O6_BY
linkProvider	Wiley-Blackwell
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3fS9xAEB5EhbYP_mqlV61dQexT6mV3k93gU2k9Fe-OUhR8C5vsRgV7lsTqq6--Ffof-pc4s0nOk1oo-JIQmIFlZ2bn29nNNwAbRmMaK7gIZKaSAPFtF0Mq4fgwXW1UZIzIfLMJNRzq4-Pk2xRst__C1PwQ44IbRYZfrynAqSC9NcEa-sN9imNi-pyR6EXo3jNfv_eO-uNDBMQ6or3hESU6bLlnu3yr1X2cjR4g5iRQ9ZmmN_-sMS7AXAMw2efaIxZhyo2WYL4Bm6wJ5WoJXk0wEeLXYEzfWr2G24GrTlll6Lb56ISZkWXXvoRKX4hyGcqyU9zBliUxv5Jt2UXBRvWQTcmoT9fF1d3Nn13MP1SNZ17Q2bub357sk_kOPBWjMjDz-fQvCcqv1Rs46u0cftkLmp4NQY7AQQQFIqoQN3ky59pZK6UwnM4acxOHOstMHEUFD3NcVROrdB4qo5SNBDqF79OpxDJM42jdW2CZsEIK1FFOS16ExqKqltZlsUy4izvwsbVdmjeE5tRX4zytqZh5irOf0ux3YH0s-bMm8XhCZrU1f9qEcZUiPsT9Ke8q3oFNb-h_6qfDwQ693_2v4Ad4sXc46Kf9_eHBCrzkdFeGOCSjVZi-LH-59zCbX12eVeVa49f3mMcAFQ
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3fSxwxEB7kLKIP2vqDXrVtBNGnrbdJdpPFp1K9WvQOkQq-LdlNthbqKbtWX331rdD_0L_Emezu9UoVCr7sEpiBkMlkvkySbwA2jMYwVnARyEwlAeLbHrpUwvFjetqoyBiR-WITajjUp6fJ0RTstG9han6IccKNPMOv1-Tg7tIW2xOsoefuQxwT0-e0pBoyHZjePe6fHI4PERDriPaGR5TosOWe7fHtVvfvaPQHYk4CVR9p-gvP6uNLmG8AJvtYz4hXMOVGi7DQgE3WuHK1CHMTTITYGozpW6sluBu46oxVhm6bj74xM7LsxqdQqYUol6EsO8MdbFkS8yvZll0UbFR32ZSM6nRdXN_f_v6M8Yey8cwLOnt_-8uTfTJfgadilAZmPp7-I0HxtVqGk_7e10_7QVOzIcgROIigQEQV4iZP5lw7a6UUhtNZY27iUGeZiaOo4GGOq2pilc5DZZSykcBJ4et0KrECHeytew0sE1ZIgTrKacmL0FhU1dK6LJYJd3EXtlrbpXlDaE51NX6kNRUzT3H0Uxr9LqyPJS9rEo9HZNZa86eNG1cp4kPcn_Ke4l3Y9IZ-Uj8dDvbo_-Z_Bd_DzNFuPz38MjxYhVlOV2WIQjJag85V-dO9hRf59dX3qnzXTOsHJfX_gQ
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Mesh+sampling+and+weighting+for+the+hyperreduction+of+nonlinear+Petrov%E2%80%93Galerkin+reduced%E2%80%90order+models+with+local+reduced%E2%80%90order+bases&rft.jtitle=International+journal+for+numerical+methods+in+engineering&rft.au=Grimberg%2C+Sebastian&rft.au=Farhat%2C+Charbel&rft.au=Tezaur%2C+Radek&rft.au=Bou%E2%80%90Mosleh%2C+Charbel&rft.date=2021-04-15&rft.pub=John+Wiley+%26+Sons%2C+Inc&rft.issn=0029-5981&rft.eissn=1097-0207&rft.volume=122&rft.issue=7&rft.spage=1846&rft.epage=1874&rft_id=info:doi/10.1002%2Fnme.6603&rft.externalDBID=10.1002%252Fnme.6603&rft.externalDocID=NME6603
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0029-5981&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0029-5981&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0029-5981&client=summon