{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T12:58:25Z","timestamp":1770296305175,"version":"3.49.0"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,1,19]],"date-time":"2019-01-19T00:00:00Z","timestamp":1547856000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61703250"],"award-info":[{"award-number":["61703250"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Shandong Government","award":["ZR2017BA029"],"award-info":[{"award-number":["ZR2017BA029"]}]},{"DOI":"10.13039\/501100004306","name":"Shandong Agricultural University","doi-asserted-by":"publisher","award":["xxxy201704"],"award-info":[{"award-number":["xxxy201704"]}],"id":[{"id":"10.13039\/501100004306","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2017BF002"],"award-info":[{"award-number":["ZR2017BF002"]}],"id":[{"id":"10.13039\/501100007129","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":[[2019,3]]},"DOI":"10.1007\/s40314-019-0767-y","type":"journal-article","created":{"date-parts":[[2019,1,19]],"date-time":"2019-01-19T01:02:28Z","timestamp":1547859748000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["Conservative domain decomposition schemes for solving two-dimensional heat equations"],"prefix":"10.1007","volume":"38","author":[{"given":"Zhongguo","family":"Zhou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,1,19]]},"reference":[{"key":"767_CR1","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1090\/S0025-5718-1991-1079011-4","volume":"57","author":"C Dawson","year":"1991","unstructured":"Dawson C, Du Q, Dupont T (1991) A finite difference domain decomposition algorithm for numerical solution of heat equations. Math Comput 57:63\u201371","journal-title":"Math Comput"},{"key":"767_CR2","doi-asserted-by":"publisher","first-page":"1045","DOI":"10.1137\/0731055","volume":"31","author":"C Dawson","year":"1994","unstructured":"Dawson C, Dupont T (1994) Explicit\/implicit conservative domain decomposition procedures for parabolic problems based on block centered finite differences. SIAM J Numer Anal 31:1045\u20131061","journal-title":"SIAM J Numer Anal"},{"key":"767_CR3","doi-asserted-by":"publisher","first-page":"4501","DOI":"10.1016\/j.jcp.2010.02.019","volume":"229","author":"C Du","year":"2010","unstructured":"Du C, Liang D (2010) An efficient S-DDM iterative approach for compressible contamination fluid flows in porous media. J Comput Phys 229:4501\u20134521","journal-title":"J Comput Phys"},{"key":"767_CR4","doi-asserted-by":"publisher","first-page":"1469","DOI":"10.1137\/S0036142900381710","volume":"39","author":"Q Du","year":"2001","unstructured":"Du Q, Mu M, Wu Z (2001) Efficient parallel algorithms for parbolic problems. SIAM J Numer Anal 39:1469\u20131487","journal-title":"SIAM J Numer Anal"},{"key":"767_CR5","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1016\/j.aml.2017.11.004","volume":"78","author":"D Jia","year":"2018","unstructured":"Jia D, Sheng Z, Yuan G (2018) A conservative parallel difference method for 2-dimension diffusion equation. Appl Math Lett 78:72\u201378","journal-title":"Appl Math Lett"},{"key":"767_CR6","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.jcp.2014.04.015","volume":"272","author":"D Liang","year":"2014","unstructured":"Liang D, Du C (2014) The efficient S-DDM scheme and its analysis for solving parabolic equations. J Comput Phys 272:46\u201369","journal-title":"J Comput Phys"},{"key":"767_CR7","doi-asserted-by":"publisher","first-page":"1584","DOI":"10.1137\/040609215","volume":"44","author":"H Shi","year":"2006","unstructured":"Shi H, Liao H (2006) Unconditional stability of corrected explicit\/implicit domain decomposition algorithms for parallel approximation of heat equations. SIAM J Numer Anal 44:1584\u20131611","journal-title":"SIAM J Numer Anal"},{"key":"767_CR8","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1016\/j.amc.2006.07.003","volume":"184","author":"Z Sheng","year":"2007","unstructured":"Sheng Z, Yuan G, Hang X (2007) Unconditional stability of parallel difference schemes with second order accuracy for parabolic equation. Appl Math Comput 184:1015\u20131031","journal-title":"Appl Math Comput"},{"key":"767_CR9","doi-asserted-by":"publisher","first-page":"1352","DOI":"10.1137\/10081335X","volume":"33","author":"G Yuan","year":"2011","unstructured":"Yuan G, Yao Y, Yin L (2011) A Conservative domain decomposition produce for nonlinear diffusion problems on arbitrary quadrilateral grids. SIAM J Sci Comput 33:1352\u20131368","journal-title":"SIAM J Sci Comput"},{"key":"767_CR10","doi-asserted-by":"publisher","first-page":"1405","DOI":"10.4208\/cicp.230815.030616a","volume":"20","author":"Y Yu","year":"2016","unstructured":"Yu Y, Yao Y, Yuan G, Chen X (2016) A conservative parallel iteration scheme for nonlinear diffusion equations on unstructured meshes. Commun Comput Phys 20:1405\u20131423","journal-title":"Commun Comput Phys"},{"key":"767_CR11","doi-asserted-by":"publisher","first-page":"411","DOI":"10.4208\/cicp.070814.190615a","volume":"19","author":"Z Zhou","year":"2016","unstructured":"Zhou Z, Liang D (2016) The mass-preserving S-DDM scheme for two-dimensional parabolic equations. Commun Comput Phys 19:411\u2013441","journal-title":"Commun Comput Phys"},{"key":"767_CR12","doi-asserted-by":"crossref","first-page":"882","DOI":"10.1016\/j.amc.2018.06.021","volume":"338","author":"Z Zhou","year":"2018","unstructured":"Zhou Z, Liang D, Wong Y (2018) The new mass-conserving S-DDM scheme for two-dimensional parabolic equations with variable coefficients. Appl Math Comput 338:882\u2013902","journal-title":"Appl Math Comput"},{"key":"767_CR13","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/j.cam.2016.10.031","volume":"317","author":"Z Zhou","year":"2017","unstructured":"Zhou Z, Liang D (2017) The mass-preserving and modified-upwind splitting DDM scheme for time-dependent convection-diffusion equations. J Comput Appl Math 317:247\u2013273","journal-title":"J Comput Appl Math"},{"key":"767_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.4208\/aamm.OA-2016-0029","volume":"9","author":"Z Zhou","year":"2017","unstructured":"Zhou Z, Liang D (2017) A time second-order mass-conserved implicit-explicit domain decomposition scheme for solving the diffusion equations. Adv Appl Math Mech 9:1\u201323","journal-title":"Adv Appl Math Mech"},{"key":"767_CR15","doi-asserted-by":"publisher","first-page":"4423","DOI":"10.1007\/s40314-018-0583-9","volume":"37","author":"Z Zhou","year":"2018","unstructured":"Zhou Z, Liang D (2018) Mass-preserving time second-order explicit-implicit domain decomposition schemes for solving parabolic equations with variable coefficients. Comput Appl Math 37:4423\u20134442","journal-title":"Comput Appl Math"},{"key":"767_CR16","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1137\/S1064827501384755","volume":"24","author":"Y Zhuang","year":"2002","unstructured":"Zhuang Y, Sun X (2002) Stabilitized explicit-implicit domain decomposition methods for the numerical solution of parabolic equations. SIAM J Sci Comput 24:335\u2013358","journal-title":"SIAM J Sci Comput"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-019-0767-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s40314-019-0767-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-019-0767-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,10]],"date-time":"2022-09-10T17:32:25Z","timestamp":1662831145000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s40314-019-0767-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,19]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["767"],"URL":"https:\/\/doi.org\/10.1007\/s40314-019-0767-y","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,19]]},"assertion":[{"value":"18 June 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 August 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 September 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 January 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"1"}}