Lopsided scaled HSS preconditioner for steady-state space-fractional diffusion equations
For the discrete linear system resulting from certain steady-state space-fractional diffusion equations, we construct a lopsided scaled HSS (LSHSS) iteration method and establish its convergence theory. From the LSHSS, we obtain the corresponding matrix splitting preconditioner. By further replacing...
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| Veröffentlicht in: | Calcolo 2021-06, Vol.58 (2), Article 26 |
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| creator | Chen, Fang Li, Tian-Yi Muratova, Galina V. |
| description | For the discrete linear system resulting from certain steady-state space-fractional diffusion equations, we construct a lopsided scaled HSS (LSHSS) iteration method and establish its convergence theory. From the LSHSS, we obtain the corresponding matrix splitting preconditioner. By further replacing the involved Toeplitz matrix with certain circulant matrix, we construct a fast LSHSS (FLSHSS) preconditioner in order to accelerate the convergence rates of the Krylov subspace iteration methods. Theoretical analyses and numerical experiments show good performance of the FLSHSS preconditioning. |
| doi_str_mv | 10.1007/s10092-021-00419-4 |
| format | Article |
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From the LSHSS, we obtain the corresponding matrix splitting preconditioner. By further replacing the involved Toeplitz matrix with certain circulant matrix, we construct a fast LSHSS (FLSHSS) preconditioner in order to accelerate the convergence rates of the Krylov subspace iteration methods. Theoretical analyses and numerical experiments show good performance of the FLSHSS preconditioning.</description><identifier>ISSN: 0008-0624</identifier><identifier>EISSN: 1126-5434</identifier><identifier>DOI: 10.1007/s10092-021-00419-4</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Convergence ; Iterative methods ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Numerical Analysis ; Numerical methods ; Preconditioning ; Steady state ; Theory of Computation</subject><ispartof>Calcolo, 2021-06, Vol.58 (2), Article 26</ispartof><rights>Istituto di Informatica e Telematica (IIT) 2021</rights><rights>Istituto di Informatica e Telematica (IIT) 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-1eecb264ed5e9eff9a8643656be6b3a040b8b5ff8c9be1edd4bf6767895ab24e3</citedby><cites>FETCH-LOGICAL-c319t-1eecb264ed5e9eff9a8643656be6b3a040b8b5ff8c9be1edd4bf6767895ab24e3</cites><orcidid>0000-0002-6894-5428</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10092-021-00419-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10092-021-00419-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51298</link.rule.ids></links><search><creatorcontrib>Chen, Fang</creatorcontrib><creatorcontrib>Li, Tian-Yi</creatorcontrib><creatorcontrib>Muratova, Galina V.</creatorcontrib><title>Lopsided scaled HSS preconditioner for steady-state space-fractional diffusion equations</title><title>Calcolo</title><addtitle>Calcolo</addtitle><description>For the discrete linear system resulting from certain steady-state space-fractional diffusion equations, we construct a lopsided scaled HSS (LSHSS) iteration method and establish its convergence theory. 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Theoretical analyses and numerical experiments show good performance of the FLSHSS preconditioning.</description><subject>Convergence</subject><subject>Iterative methods</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical Analysis</subject><subject>Numerical methods</subject><subject>Preconditioning</subject><subject>Steady state</subject><subject>Theory of Computation</subject><issn>0008-0624</issn><issn>1126-5434</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9UMtKA0EQHETBGP0BTwueR-ed3aMENULAQxS8DfPokQ0xu5nePfj3TlzBmzR0dTdVRVOEXHN2yxlb3GHpjaBMcMqY4g1VJ2TGuTBUK6lOyYwxVlNmhDonF4jbsmpVqxl5X3c9thFihcHtCqw2m6rPELp9bIe220OuUpcrHMDFL4qDG6DC3gWgKbtwZLhdFduURixzBYfRHY94Sc6S2yFc_eKcvD0-vC5XdP3y9Ly8X9MgeTNQDhC8MAqihgZSalxtlDTaeDBeOqaYr71OqQ6NBw4xKp_MwizqRjsvFMg5uZl8-9wdRsDBbrsxl6fQCi21ZLxUYYmJFXKHmCHZPrefLn9ZzuwxQTslaEuC9idBq4pITiIs5P0H5D_rf1TfoKJ1dw</recordid><startdate>20210601</startdate><enddate>20210601</enddate><creator>Chen, Fang</creator><creator>Li, Tian-Yi</creator><creator>Muratova, Galina V.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-6894-5428</orcidid></search><sort><creationdate>20210601</creationdate><title>Lopsided scaled HSS preconditioner for steady-state space-fractional diffusion equations</title><author>Chen, Fang ; Li, Tian-Yi ; Muratova, Galina V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-1eecb264ed5e9eff9a8643656be6b3a040b8b5ff8c9be1edd4bf6767895ab24e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Convergence</topic><topic>Iterative methods</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical Analysis</topic><topic>Numerical methods</topic><topic>Preconditioning</topic><topic>Steady state</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Fang</creatorcontrib><creatorcontrib>Li, Tian-Yi</creatorcontrib><creatorcontrib>Muratova, Galina V.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Calcolo</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Fang</au><au>Li, Tian-Yi</au><au>Muratova, Galina V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Lopsided scaled HSS preconditioner for steady-state space-fractional diffusion equations</atitle><jtitle>Calcolo</jtitle><stitle>Calcolo</stitle><date>2021-06-01</date><risdate>2021</risdate><volume>58</volume><issue>2</issue><artnum>26</artnum><issn>0008-0624</issn><eissn>1126-5434</eissn><abstract>For the discrete linear system resulting from certain steady-state space-fractional diffusion equations, we construct a lopsided scaled HSS (LSHSS) iteration method and establish its convergence theory. 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| subjects | Convergence Iterative methods Mathematical analysis Mathematics Mathematics and Statistics Numerical Analysis Numerical methods Preconditioning Steady state Theory of Computation |
| title | Lopsided scaled HSS preconditioner for steady-state space-fractional diffusion equations |
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