{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,12]],"date-time":"2024-02-12T00:12:48Z","timestamp":1707696768059},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,12,2]],"date-time":"2023-12-02T00:00:00Z","timestamp":1701475200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,2]],"date-time":"2023-12-02T00:00:00Z","timestamp":1701475200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100006469","name":"Fundo para o Desenvolvimento das Ci\u00eancias e da Tecnologia","doi-asserted-by":"publisher","award":["0122\/2020\/A3"],"id":[{"id":"10.13039\/501100006469","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004733","name":"Universidade de Macau","doi-asserted-by":"publisher","award":["MYRG2020-00208-FST","MYRG-GRG2023-00181-FST-UMDF","MYRG2022-00262-FST"],"id":[{"id":"10.13039\/501100004733","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2024,2]]},"DOI":"10.1007\/s40314-023-02514-4","type":"journal-article","created":{"date-parts":[[2023,12,2]],"date-time":"2023-12-02T17:01:56Z","timestamp":1701536516000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An efficient red\u2013black skewed extrapolation cascadic multigrid method for two-dimensional Poisson equation"],"prefix":"10.1007","volume":"43","author":[{"given":"Yuan","family":"Xu","sequence":"first","affiliation":[]},{"given":"Siu-Long","family":"Lei","sequence":"additional","affiliation":[]},{"given":"Hai-Wei","family":"Sun","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,12,2]]},"reference":[{"key":"2514_CR1","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1080\/00207169108803958","volume":"38","author":"AR Abdullah","year":"1991","unstructured":"Abdullah AR (1991) The four point explicit decoupled group (EDG) method: a fast Poisson solver. Int J Comput Math 38:61\u201370. https:\/\/doi.org\/10.1080\/00207169108803958","journal-title":"Int J Comput Math"},{"key":"2514_CR2","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1016\/j.amc.2007.02.131","volume":"191","author":"NHM Ali","year":"2007","unstructured":"Ali NHM, Chong LS (2007) Group accelerated Overrelaxation methods on rotated grid. Appl Math Comput 191:533\u2013542. https:\/\/doi.org\/10.1016\/j.amc.2007.02.131","journal-title":"Appl Math Comput"},{"key":"2514_CR3","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1080\/00207169808804726","volume":"69","author":"M Bin Othman","year":"1998","unstructured":"Bin Othman M, Bin Abdullah AR (1998) The halfsweeps multigrid method as a fast multigrid Poisson solver. Int J Comput Math 69:319\u2013329. https:\/\/doi.org\/10.1080\/00207169808804726","journal-title":"Int J Comput Math"},{"key":"2514_CR4","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/s002110050234","volume":"75","author":"FA Bornemann","year":"1996","unstructured":"Bornemann FA, Deuflhard P (1996) The cascadic multigrid method for elliptic problems. Numer Math 75:135\u2013152. https:\/\/doi.org\/10.1007\/s002110050234","journal-title":"Numer Math"},{"key":"2514_CR5","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1007\/s002110050416","volume":"82","author":"D Braess","year":"1999","unstructured":"Braess D, Dahmen W (1999) A cascadic multigrid algorithm for the stokes equations. Numer Math 82:179\u2013191. https:\/\/doi.org\/10.1007\/s002110050416","journal-title":"Numer Math"},{"key":"2514_CR6","doi-asserted-by":"publisher","first-page":"1349","DOI":"10.1007\/s11425-008-0119-7","volume":"51","author":"CM Chen","year":"2008","unstructured":"Chen CM, Hu HL, Xie ZQ et al (2008) Analysis of extrapolation cascadic multigrid method (EXCMG). Sci China Ser A Math 51:1349\u20131360. https:\/\/doi.org\/10.1007\/s11425-008-0119-7","journal-title":"Sci China Ser A Math"},{"key":"2514_CR7","doi-asserted-by":"publisher","first-page":"542","DOI":"10.1016\/j.camwa.2013.06.008","volume":"66","author":"RX Dai","year":"2013","unstructured":"Dai RX, Wang Y, Zhang J (2013) Fast and high accuracy multiscale multigrid method with multiple coarse grid updating strategy for the 3D convection diffusion equation. Comput Math Appl 66:542\u2013559. https:\/\/doi.org\/10.1016\/j.camwa.2013.06.008","journal-title":"Comput Math Appl"},{"key":"2514_CR8","doi-asserted-by":"publisher","first-page":"2051","DOI":"10.1016\/j.camwa.2018.12.024","volume":"77","author":"RX Dai","year":"2019","unstructured":"Dai RX, Lin PP, Zhang J (2019) An EXCMG accelerated multiscale multigrid computation for 3D Poisson equation. Comput Math Appl 77:2051\u20132060. https:\/\/doi.org\/10.1016\/j.camwa.2018.12.024","journal-title":"Comput Math Appl"},{"key":"2514_CR9","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1016\/j.mseb.2010.07.022","volume":"176","author":"G Donnarumma","year":"2011","unstructured":"Donnarumma G, Wo\u017any J, Lisik Z (2011) Numerical solution of the anisotropic Poisson equation for SiC semiconductors device simulation. Mater Sci Eng B Adv Funct Solid State Mater 176:293\u2013296. https:\/\/doi.org\/10.1016\/j.mseb.2010.07.022","journal-title":"Mater Sci Eng B Adv Funct Solid State Mater"},{"key":"2514_CR10","volume-title":"Computational techniques for fluid dynamics","author":"CAJ Fletcher","year":"1991","unstructured":"Fletcher CAJ (1991) Computational techniques for fluid dynamics. Springer, New York"},{"key":"2514_CR11","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1016\/0021-9991(75)90118-7","volume":"19","author":"RS Hirsh","year":"1975","unstructured":"Hirsh RS (1975) Higher order accurate difference solutions of fluid mechanics problem by a compact differencing technique. J Comput Phys 19:90\u2013109. https:\/\/doi.org\/10.1016\/0021-9991(75)90118-7","journal-title":"J Comput Phys"},{"key":"2514_CR12","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1080\/00207169908804828","volume":"71","author":"M Othman","year":"1999","unstructured":"Othman M, Abdullah AR (1999) An efficient multigrid Poisson solver. Int J Comput Math 71:541\u2013553. https:\/\/doi.org\/10.1080\/00207169908804828","journal-title":"Int J Comput Math"},{"key":"2514_CR13","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1016\/j.jcp.2017.04.069","volume":"344","author":"KJ Pan","year":"2017","unstructured":"Pan KJ, He DD, Hu HL et al (2017) A new extrapolation cascadic multigrid method for three dimensional elliptic boundary value problems. J Comput Phys 344:499\u2013515. https:\/\/doi.org\/10.1016\/j.jcp.2017.04.069","journal-title":"J Comput Phys"},{"key":"2514_CR14","doi-asserted-by":"publisher","unstructured":"Pan KJ, Wu XX, Hu HL et al (2022a) A new FV scheme and fast cell-centered multigrid solver for 3D anisotropic diffusion equations with discontinuous coefficients. J Comput Phys 449(110):794. https:\/\/doi.org\/10.1016\/j.jcp.2021.110794","DOI":"10.1016\/j.jcp.2021.110794"},{"key":"2514_CR15","doi-asserted-by":"publisher","unstructured":"Pan KJ, Wu XX, Yu YL et al (2022b) Extrapolation cascadic multigrid method for cell-centered FV discretization of diffusion equations with strongly discontinuous and anisotropic coefficients. Commun Comput Phys 31:1561\u20131584. https:\/\/doi.org\/10.4208\/cicp.OA-2021-0185","DOI":"10.4208\/cicp.OA-2021-0185"},{"key":"2514_CR16","doi-asserted-by":"publisher","first-page":"701","DOI":"10.1007\/BF01395819","volume":"52","author":"SV Parter","year":"1988","unstructured":"Parter SV (1988) Estimates for multigrid methods based on red\u2013black Gauss\u2013Seidel smoothings. Numer Math 52:701\u2013723. https:\/\/doi.org\/10.1007\/BF01395819","journal-title":"Numer Math"},{"key":"2514_CR17","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1145\/882262.882269","volume":"22","author":"P P\u00e9rez","year":"2003","unstructured":"P\u00e9rez P, Gangnet M, Blake A (2003) Poisson image editing. ACM Trans Graph 22:313\u2013318. https:\/\/doi.org\/10.1145\/882262.882269","journal-title":"ACM Trans Graph"},{"key":"2514_CR18","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718003","volume-title":"Iterative methods for sparse linear systems","author":"Y Saad","year":"2003","unstructured":"Saad Y (2003) Iterative methods for sparse linear systems. SIAM, Philadelphia"},{"key":"2514_CR19","doi-asserted-by":"publisher","first-page":"2176","DOI":"10.3934\/math.2022124","volume":"7","author":"N Saad","year":"2022","unstructured":"Saad N, Dahalan AA, Saudi A (2022) Modified Poisson compositing technique on skewed grid. AIMS Math 7:2176\u20132194. https:\/\/doi.org\/10.3934\/math.2022124","journal-title":"AIMS Math"},{"key":"2514_CR20","doi-asserted-by":"publisher","DOI":"10.1201\/9781420058277","volume-title":"Numerical techniques in electromagnetics","author":"MNO Sadiku","year":"2000","unstructured":"Sadiku MNO (2000) Numerical techniques in electromagnetics. CRC Press, Boca Raton"},{"key":"2514_CR21","doi-asserted-by":"publisher","first-page":"993","DOI":"10.3390\/sym14050993","volume":"14","author":"A Saudi","year":"2022","unstructured":"Saudi A, Dahalan AA (2022) An efficient red\u2013black skewed modified accelerated arithmetic mean iterative method for solving two-dimensional Poisson equation. Symmetry-Basel 14:993. https:\/\/doi.org\/10.3390\/sym14050993","journal-title":"Symmetry-Basel"},{"key":"2514_CR22","doi-asserted-by":"publisher","first-page":"1765","DOI":"10.1007\/s11425-007-0127-z","volume":"50","author":"ZC Shi","year":"2007","unstructured":"Shi ZC, Xu XJ, Huang YQ (2007) Economical cascadic multigrid method (ECMG). Sci China Ser A-Math 50:1765\u20131780. https:\/\/doi.org\/10.1007\/s11425-007-0127-z","journal-title":"Sci China Ser A-Math"},{"key":"2514_CR23","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1002\/num.10075","volume":"20","author":"HW Sun","year":"2004","unstructured":"Sun HW, Zhang J (2004) A high-order finite difference discretization strategy based on extrapolation for convection diffusion equations. Numer Methods Partial Differ Equ 20:18\u201332. https:\/\/doi.org\/10.1002\/num.10075","journal-title":"Numer Methods Partial Differ Equ"},{"key":"2514_CR24","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1007\/978-3-642-01970-8_50","volume-title":"Computational science\u2014ICCS 2009. Lecture notes in computer science","author":"V Volkov","year":"2009","unstructured":"Volkov V, Zherdetsky A, Turovets S et al (2009) A 3D vector-additive iterative solver for the anisotropic inhomogeneous Poisson equation in the forward EEG problem. In: Allen G, Nabrzyski J, Seidel E et al (eds) Computational science\u2014ICCS 2009. Lecture notes in computer science, vol 5544. Springer, Berlin, pp 511\u2013520. https:\/\/doi.org\/10.1007\/978-3-642-01970-8_50"},{"key":"2514_CR25","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1016\/j.jcp.2008.09.002","volume":"228","author":"Y Wang","year":"2009","unstructured":"Wang Y, Zhang J (2009) Sixth order compact scheme combined with multigrid method and extrapolation technique for 2D Poisson equation. J Comput Phys 228:137\u2013146. https:\/\/doi.org\/10.1016\/j.jcp.2008.09.002","journal-title":"J Comput Phys"},{"key":"2514_CR26","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1002\/num.20529","volume":"27","author":"Y Wang","year":"2011","unstructured":"Wang Y, Zhang J (2011) Integrated fast and high-accuracy computation of convection diffusion equations using multiscale multigrid method. Numer Methods Partial Differ Equ 27:399\u2013414. https:\/\/doi.org\/10.1002\/num.20529","journal-title":"Numer Methods Partial Differ Equ"},{"key":"2514_CR27","doi-asserted-by":"publisher","first-page":"119","DOI":"10.4208\/eajam.240222.210722","volume":"13","author":"PX Wu","year":"2023","unstructured":"Wu PX, Pan KJ, Ling WW et al (2023) An efficient EXCMG-Newton method combined with fourth-order compact schemes for semilinear Poisson equations. East Asian J Appl Math 13:119\u2013139. https:\/\/doi.org\/10.4208\/eajam.240222.210722","journal-title":"East Asian J Appl Math"},{"key":"2514_CR28","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/0096-3003(95)00276-6","volume":"80","author":"J Zhang","year":"1996","unstructured":"Zhang J (1996) Acceleration of five-point red\u2013black Gauss\u2013Seidel in multigrid for Poisson equation. Appl Math Comput 80:73\u201393. https:\/\/doi.org\/10.1016\/0096-3003(95)00276-6","journal-title":"Appl Math Comput"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-023-02514-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-023-02514-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-023-02514-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,11]],"date-time":"2024-02-11T11:18:42Z","timestamp":1707650322000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-023-02514-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,2]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,2]]}},"alternative-id":["2514"],"URL":"https:\/\/doi.org\/10.1007\/s40314-023-02514-4","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,2]]},"assertion":[{"value":"15 March 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 October 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 October 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 December 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest in the manuscript.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"3"}}