Numerical Analysis of a Fast Finite Element Method for a Hidden-Memory Variable-Order Time-Fractional Diffusion Equation
We investigate a fast finite element scheme to a hidden-memory variable-order time-fractional diffusion equation. Different from the traditional L1 methods, a fast approximation to the hidden-memory variable-order fractional derivative is derived to reduce the computational cost of generating coeffi...
Gespeichert in:
| Veröffentlicht in: | Journal of scientific computing 2022-05, Vol.91 (2), p.54, Article 54 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | 2 |
| container_start_page | 54 |
| container_title | Journal of scientific computing |
| container_volume | 91 |
| creator | Jia, Jinhong Wang, Hong Zheng, Xiangcheng |
| description | We investigate a fast finite element scheme to a hidden-memory variable-order time-fractional diffusion equation. Different from the traditional L1 methods, a fast approximation to the hidden-memory variable-order fractional derivative is derived to reduce the computational cost of generating coefficients from
O
(
N
2
)
to
O
(
N
log
N
)
, where
N
refers to the number of time steps. We then develop different techniques from the analysis of L1 methods to prove error estimates for the corresponding fast fully-discrete finite element scheme. Furthermore, a fast divide and conquer algorithm is proposed to reduce the complexity of solving the linear systems from
O
(
M
N
2
)
to
O
(
M
N
log
2
N
)
where
M
stands for the spatial degree of freedom. Numerical experiments are presented to substantiate the theoretical results. |
| doi_str_mv | 10.1007/s10915-022-01820-z |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2918315586</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2918315586</sourcerecordid><originalsourceid>FETCH-LOGICAL-c249t-e76051eba221ae7ead7799e65cbfc44140d69740a4cc03c65a2f42f503d8c6383</originalsourceid><addsrcrecordid>eNp9kMtKBDEQRYMoOD5-wFXAdbSSTjqdpeiMCj42o9uQSVc00g9NusHx6-1xBHeuqijOvRSHkBMOZxxAn2cOhisGQjDglQD2tUNmXOmC6dLwXTKDqlJMSy33yUHObwBgKiNm5PNhbDFF7xp60blmnWOmfaCOLlwe6CJ2cUA6b7DFbqD3OLz2NQ19moCbWNfYsXts-7Smzy5Ft2qQPaYaE13GFtkiOT_EfqqlVzGEMU87nX-MbnM8InvBNRmPf-cheVrMl5c37O7x-vby4o55Ic3AUJegOK6cENyhRldrbQyWyq-Cl5JLqEujJTjpPRS-VE4EKYKCoq58WVTFITnd9r6n_mPEPNi3fkzTT9kKw6uCK1WVEyW2lE99zgmDfU-xdWltOdiNYbs1bCfD9sew_ZpCxTaUJ7h7wfRX_U_qG21Ef28</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2918315586</pqid></control><display><type>article</type><title>Numerical Analysis of a Fast Finite Element Method for a Hidden-Memory Variable-Order Time-Fractional Diffusion Equation</title><source>SpringerNature Journals</source><source>ProQuest Central UK/Ireland</source><source>ProQuest Central</source><creator>Jia, Jinhong ; Wang, Hong ; Zheng, Xiangcheng</creator><creatorcontrib>Jia, Jinhong ; Wang, Hong ; Zheng, Xiangcheng</creatorcontrib><description>We investigate a fast finite element scheme to a hidden-memory variable-order time-fractional diffusion equation. Different from the traditional L1 methods, a fast approximation to the hidden-memory variable-order fractional derivative is derived to reduce the computational cost of generating coefficients from
O
(
N
2
)
to
O
(
N
log
N
)
, where
N
refers to the number of time steps. We then develop different techniques from the analysis of L1 methods to prove error estimates for the corresponding fast fully-discrete finite element scheme. Furthermore, a fast divide and conquer algorithm is proposed to reduce the complexity of solving the linear systems from
O
(
M
N
2
)
to
O
(
M
N
log
2
N
)
where
M
stands for the spatial degree of freedom. Numerical experiments are presented to substantiate the theoretical results.</description><identifier>ISSN: 0885-7474</identifier><identifier>EISSN: 1573-7691</identifier><identifier>DOI: 10.1007/s10915-022-01820-z</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Accuracy ; Algorithms ; Approximation ; Computational Mathematics and Numerical Analysis ; Diffusion rate ; Estimates ; Finite element analysis ; Finite element method ; Fourier transforms ; Linear systems ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Methods ; Numerical analysis ; Theoretical</subject><ispartof>Journal of scientific computing, 2022-05, Vol.91 (2), p.54, Article 54</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022</rights><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c249t-e76051eba221ae7ead7799e65cbfc44140d69740a4cc03c65a2f42f503d8c6383</citedby><cites>FETCH-LOGICAL-c249t-e76051eba221ae7ead7799e65cbfc44140d69740a4cc03c65a2f42f503d8c6383</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10915-022-01820-z$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2918315586?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>315,781,785,21392,27928,27929,33748,41492,42561,43809,51323,64389,64393,72473</link.rule.ids></links><search><creatorcontrib>Jia, Jinhong</creatorcontrib><creatorcontrib>Wang, Hong</creatorcontrib><creatorcontrib>Zheng, Xiangcheng</creatorcontrib><title>Numerical Analysis of a Fast Finite Element Method for a Hidden-Memory Variable-Order Time-Fractional Diffusion Equation</title><title>Journal of scientific computing</title><addtitle>J Sci Comput</addtitle><description>We investigate a fast finite element scheme to a hidden-memory variable-order time-fractional diffusion equation. Different from the traditional L1 methods, a fast approximation to the hidden-memory variable-order fractional derivative is derived to reduce the computational cost of generating coefficients from
O
(
N
2
)
to
O
(
N
log
N
)
, where
N
refers to the number of time steps. We then develop different techniques from the analysis of L1 methods to prove error estimates for the corresponding fast fully-discrete finite element scheme. Furthermore, a fast divide and conquer algorithm is proposed to reduce the complexity of solving the linear systems from
O
(
M
N
2
)
to
O
(
M
N
log
2
N
)
where
M
stands for the spatial degree of freedom. Numerical experiments are presented to substantiate the theoretical results.</description><subject>Accuracy</subject><subject>Algorithms</subject><subject>Approximation</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Diffusion rate</subject><subject>Estimates</subject><subject>Finite element analysis</subject><subject>Finite element method</subject><subject>Fourier transforms</subject><subject>Linear systems</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Methods</subject><subject>Numerical analysis</subject><subject>Theoretical</subject><issn>0885-7474</issn><issn>1573-7691</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp9kMtKBDEQRYMoOD5-wFXAdbSSTjqdpeiMCj42o9uQSVc00g9NusHx6-1xBHeuqijOvRSHkBMOZxxAn2cOhisGQjDglQD2tUNmXOmC6dLwXTKDqlJMSy33yUHObwBgKiNm5PNhbDFF7xp60blmnWOmfaCOLlwe6CJ2cUA6b7DFbqD3OLz2NQ19moCbWNfYsXts-7Smzy5Ft2qQPaYaE13GFtkiOT_EfqqlVzGEMU87nX-MbnM8InvBNRmPf-cheVrMl5c37O7x-vby4o55Ic3AUJegOK6cENyhRldrbQyWyq-Cl5JLqEujJTjpPRS-VE4EKYKCoq58WVTFITnd9r6n_mPEPNi3fkzTT9kKw6uCK1WVEyW2lE99zgmDfU-xdWltOdiNYbs1bCfD9sew_ZpCxTaUJ7h7wfRX_U_qG21Ef28</recordid><startdate>20220501</startdate><enddate>20220501</enddate><creator>Jia, Jinhong</creator><creator>Wang, Hong</creator><creator>Zheng, Xiangcheng</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope></search><sort><creationdate>20220501</creationdate><title>Numerical Analysis of a Fast Finite Element Method for a Hidden-Memory Variable-Order Time-Fractional Diffusion Equation</title><author>Jia, Jinhong ; Wang, Hong ; Zheng, Xiangcheng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c249t-e76051eba221ae7ead7799e65cbfc44140d69740a4cc03c65a2f42f503d8c6383</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Accuracy</topic><topic>Algorithms</topic><topic>Approximation</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Diffusion rate</topic><topic>Estimates</topic><topic>Finite element analysis</topic><topic>Finite element method</topic><topic>Fourier transforms</topic><topic>Linear systems</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Methods</topic><topic>Numerical analysis</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jia, Jinhong</creatorcontrib><creatorcontrib>Wang, Hong</creatorcontrib><creatorcontrib>Zheng, Xiangcheng</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><jtitle>Journal of scientific computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Jia, Jinhong</au><au>Wang, Hong</au><au>Zheng, Xiangcheng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Numerical Analysis of a Fast Finite Element Method for a Hidden-Memory Variable-Order Time-Fractional Diffusion Equation</atitle><jtitle>Journal of scientific computing</jtitle><stitle>J Sci Comput</stitle><date>2022-05-01</date><risdate>2022</risdate><volume>91</volume><issue>2</issue><spage>54</spage><pages>54-</pages><artnum>54</artnum><issn>0885-7474</issn><eissn>1573-7691</eissn><abstract>We investigate a fast finite element scheme to a hidden-memory variable-order time-fractional diffusion equation. Different from the traditional L1 methods, a fast approximation to the hidden-memory variable-order fractional derivative is derived to reduce the computational cost of generating coefficients from
O
(
N
2
)
to
O
(
N
log
N
)
, where
N
refers to the number of time steps. We then develop different techniques from the analysis of L1 methods to prove error estimates for the corresponding fast fully-discrete finite element scheme. Furthermore, a fast divide and conquer algorithm is proposed to reduce the complexity of solving the linear systems from
O
(
M
N
2
)
to
O
(
M
N
log
2
N
)
where
M
stands for the spatial degree of freedom. Numerical experiments are presented to substantiate the theoretical results.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10915-022-01820-z</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0885-7474 |
| ispartof | Journal of scientific computing, 2022-05, Vol.91 (2), p.54, Article 54 |
| issn | 0885-7474 1573-7691 |
| language | eng |
| recordid | cdi_proquest_journals_2918315586 |
| source | SpringerNature Journals; ProQuest Central UK/Ireland; ProQuest Central |
| subjects | Accuracy Algorithms Approximation Computational Mathematics and Numerical Analysis Diffusion rate Estimates Finite element analysis Finite element method Fourier transforms Linear systems Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Methods Numerical analysis Theoretical |
| title | Numerical Analysis of a Fast Finite Element Method for a Hidden-Memory Variable-Order Time-Fractional Diffusion Equation |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-17T09%3A51%3A08IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Numerical%20Analysis%20of%20a%20Fast%20Finite%20Element%20Method%20for%20a%20Hidden-Memory%20Variable-Order%20Time-Fractional%20Diffusion%20Equation&rft.jtitle=Journal%20of%20scientific%20computing&rft.au=Jia,%20Jinhong&rft.date=2022-05-01&rft.volume=91&rft.issue=2&rft.spage=54&rft.pages=54-&rft.artnum=54&rft.issn=0885-7474&rft.eissn=1573-7691&rft_id=info:doi/10.1007/s10915-022-01820-z&rft_dat=%3Cproquest_cross%3E2918315586%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2918315586&rft_id=info:pmid/&rfr_iscdi=true |