An efficient sixth-order solution for anisotropic Poisson equation with completed Richardson extrapolation and multiscale multigrid method
We present an efficient numerical method for anisotropic Poisson equations. The sixth-order accuracy is achieved through applying completed Richardson extrapolation on two fourth-order solutions computed from different scale grids with unequal mesh size discretization. Theoretical analysis is conduc...
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| Veröffentlicht in: | Computers & mathematics with applications (1987) 2017-04, Vol.73 (8), p.1865-1877 |
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| container_title | Computers & mathematics with applications (1987) |
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| creator | Dai, Ruxin Lin, Pengpeng Zhang, Jun |
| description | We present an efficient numerical method for anisotropic Poisson equations. The sixth-order accuracy is achieved through applying completed Richardson extrapolation on two fourth-order solutions computed from different scale grids with unequal mesh size discretization. Theoretical analysis is conducted to demonstrate that the Richardson extrapolation is able to obtain a sixth-order solution by removing the leading truncation error terms of the fourth-order solution from grid with unequal mesh sizes. The gain in efficiency is obtained through adopting partial semi-coarsening multigrid method to solve the resulting linear systems and multiscale multigrid computation to speed up the whole solution. Numerical experiments are conducted to verify the accuracy and efficiency of the proposed method and the results are compared with the existing fourth-order methods for solving 2D and 3D anisotropic Poisson equations. |
| doi_str_mv | 10.1016/j.camwa.2017.02.020 |
| format | Article |
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The sixth-order accuracy is achieved through applying completed Richardson extrapolation on two fourth-order solutions computed from different scale grids with unequal mesh size discretization. Theoretical analysis is conducted to demonstrate that the Richardson extrapolation is able to obtain a sixth-order solution by removing the leading truncation error terms of the fourth-order solution from grid with unequal mesh sizes. The gain in efficiency is obtained through adopting partial semi-coarsening multigrid method to solve the resulting linear systems and multiscale multigrid computation to speed up the whole solution. Numerical experiments are conducted to verify the accuracy and efficiency of the proposed method and the results are compared with the existing fourth-order methods for solving 2D and 3D anisotropic Poisson equations.</description><identifier>ISSN: 0898-1221</identifier><identifier>EISSN: 1873-7668</identifier><identifier>DOI: 10.1016/j.camwa.2017.02.020</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Accuracy ; Anisotropic Poisson equation ; Anisotropy ; Coarsening ; Completed Richardson extrapolation ; Extrapolation ; Linear systems ; Multiscale analysis ; Multiscale multigrid computation ; Numerical analysis ; Poisson distribution ; Poisson equation ; Sixth-order compact scheme ; Studies ; Unequal mesh sizes</subject><ispartof>Computers & mathematics with applications (1987), 2017-04, Vol.73 (8), p.1865-1877</ispartof><rights>2017 Elsevier Ltd</rights><rights>Copyright Elsevier BV Apr 15, 2017</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c376t-c748649e5afa0bdf93496f7996105c3951a4560fadb229816c34c84ed68f7ec33</citedby><cites>FETCH-LOGICAL-c376t-c748649e5afa0bdf93496f7996105c3951a4560fadb229816c34c84ed68f7ec33</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.camwa.2017.02.020$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Dai, Ruxin</creatorcontrib><creatorcontrib>Lin, Pengpeng</creatorcontrib><creatorcontrib>Zhang, Jun</creatorcontrib><title>An efficient sixth-order solution for anisotropic Poisson equation with completed Richardson extrapolation and multiscale multigrid method</title><title>Computers & mathematics with applications (1987)</title><description>We present an efficient numerical method for anisotropic Poisson equations. The sixth-order accuracy is achieved through applying completed Richardson extrapolation on two fourth-order solutions computed from different scale grids with unequal mesh size discretization. Theoretical analysis is conducted to demonstrate that the Richardson extrapolation is able to obtain a sixth-order solution by removing the leading truncation error terms of the fourth-order solution from grid with unequal mesh sizes. The gain in efficiency is obtained through adopting partial semi-coarsening multigrid method to solve the resulting linear systems and multiscale multigrid computation to speed up the whole solution. Numerical experiments are conducted to verify the accuracy and efficiency of the proposed method and the results are compared with the existing fourth-order methods for solving 2D and 3D anisotropic Poisson equations.</description><subject>Accuracy</subject><subject>Anisotropic Poisson equation</subject><subject>Anisotropy</subject><subject>Coarsening</subject><subject>Completed Richardson extrapolation</subject><subject>Extrapolation</subject><subject>Linear systems</subject><subject>Multiscale analysis</subject><subject>Multiscale multigrid computation</subject><subject>Numerical analysis</subject><subject>Poisson distribution</subject><subject>Poisson equation</subject><subject>Sixth-order compact scheme</subject><subject>Studies</subject><subject>Unequal mesh sizes</subject><issn>0898-1221</issn><issn>1873-7668</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9kN1qGzEQhUVJoY7bJ-iNoNfr6GetlS56EUx_AoaEkFwLRRrVMuvVRtLWySv0qSt7cx0YmGH4zhzmIPSVkhUlVFztV9YcjmbFCO1WhNUiH9CCyo43nRDyAi2IVLKhjNFP6DLnPSGk5Yws0L_rAYP3wQYYCs7hpeyamBwknGM_lRAH7GPCZgg5lhTHYPFdDDnXPTxP5gwcQ9lhGw9jDwUcvg92Z5I7Iy8lmTH2M2cGhw9TX0K2pod5_JNCXULZRfcZffSmz_DlrS_R488fD5vfzfb2183mettY3onS2K6VolWwNt6QJ-cVb5XwnVKCkrXlak1NuxbEG_fEmJJUWN5a2YIT0ndgOV-ib_PdMcXnCXLR-ziloVpqqlhHuawOleIzZVPMOYHXYwoHk141JfoUut7rc-j6FLomrBapqu-zCuoDfwMknU_JWnAhgS3axfCu_j_KP498</recordid><startdate>20170415</startdate><enddate>20170415</enddate><creator>Dai, Ruxin</creator><creator>Lin, Pengpeng</creator><creator>Zhang, Jun</creator><general>Elsevier Ltd</general><general>Elsevier BV</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></search><sort><creationdate>20170415</creationdate><title>An efficient sixth-order solution for anisotropic Poisson equation with completed Richardson extrapolation and multiscale multigrid method</title><author>Dai, Ruxin ; Lin, Pengpeng ; Zhang, Jun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c376t-c748649e5afa0bdf93496f7996105c3951a4560fadb229816c34c84ed68f7ec33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Accuracy</topic><topic>Anisotropic Poisson equation</topic><topic>Anisotropy</topic><topic>Coarsening</topic><topic>Completed Richardson extrapolation</topic><topic>Extrapolation</topic><topic>Linear systems</topic><topic>Multiscale analysis</topic><topic>Multiscale multigrid computation</topic><topic>Numerical analysis</topic><topic>Poisson distribution</topic><topic>Poisson equation</topic><topic>Sixth-order compact scheme</topic><topic>Studies</topic><topic>Unequal mesh sizes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dai, Ruxin</creatorcontrib><creatorcontrib>Lin, Pengpeng</creatorcontrib><creatorcontrib>Zhang, Jun</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>Computers & mathematics with applications (1987)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dai, Ruxin</au><au>Lin, Pengpeng</au><au>Zhang, Jun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An efficient sixth-order solution for anisotropic Poisson equation with completed Richardson extrapolation and multiscale multigrid method</atitle><jtitle>Computers & mathematics with applications (1987)</jtitle><date>2017-04-15</date><risdate>2017</risdate><volume>73</volume><issue>8</issue><spage>1865</spage><epage>1877</epage><pages>1865-1877</pages><issn>0898-1221</issn><eissn>1873-7668</eissn><abstract>We present an efficient numerical method for anisotropic Poisson equations. The sixth-order accuracy is achieved through applying completed Richardson extrapolation on two fourth-order solutions computed from different scale grids with unequal mesh size discretization. Theoretical analysis is conducted to demonstrate that the Richardson extrapolation is able to obtain a sixth-order solution by removing the leading truncation error terms of the fourth-order solution from grid with unequal mesh sizes. The gain in efficiency is obtained through adopting partial semi-coarsening multigrid method to solve the resulting linear systems and multiscale multigrid computation to speed up the whole solution. Numerical experiments are conducted to verify the accuracy and efficiency of the proposed method and the results are compared with the existing fourth-order methods for solving 2D and 3D anisotropic Poisson equations.</abstract><cop>Oxford</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.camwa.2017.02.020</doi><tpages>13</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Computers & mathematics with applications (1987), 2017-04, Vol.73 (8), p.1865-1877 |
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| source | Elsevier ScienceDirect Journals Complete; EZB-FREE-00999 freely available EZB journals |
| subjects | Accuracy Anisotropic Poisson equation Anisotropy Coarsening Completed Richardson extrapolation Extrapolation Linear systems Multiscale analysis Multiscale multigrid computation Numerical analysis Poisson distribution Poisson equation Sixth-order compact scheme Studies Unequal mesh sizes |
| title | An efficient sixth-order solution for anisotropic Poisson equation with completed Richardson extrapolation and multiscale multigrid method |
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