Two efficient block preconditioners for the mass-conserved Ohta-Kawasaki equation

Two efficient block preconditioners for the mass-conserved Ohta-Kawasaki equation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Two efficient block preconditioners for the mass-conserved Ohta-Kawasaki equation Juan Zhang, shifeng Li, Kai Jiang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1996000/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this paper, we propose two efficient block preconditioners to solve the mass-conserved Ohta-Kawasaki equation with finite element dis-cretization. We also study the spectral distribution of these two pre-conditioners, i.e., Schur complement preconditioner and the modified Hermitian and skew-Hermitian splitting (MHSS in short) preconditioner. Besides, the Newton method and its variant are used to address the implicitly nonlinear term. We rigorously analyze the convergence of the Newton iteration methods. Finally, we offer numerical examples to support the theoretical analysis and indicate the efficiency of the proposed preconditioners for the mass-conserved Ohta-Kawasaki equation. Mass-conserved Ohta-Kawasaki equation Newton method Schur complement preconditioner MHSS preconditioner Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-1996000","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":131918157,"identity":"f3c24f9c-6bef-4255-8e3a-64474de3b8c6","order_by":0,"name":"Juan Zhang","email":"","orcid":"","institution":"Xiangtan University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Juan","middleName":"","lastName":"Zhang","suffix":""},{"id":131918158,"identity":"6b45a287-8bed-44f5-9e7b-7e5d70fbba6e","order_by":1,"name":"shifeng Li","email":"","orcid":"","institution":"Xiangtan University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"shifeng","middleName":"","lastName":"Li","suffix":""},{"id":131918159,"identity":"444b9815-91d6-450e-8962-0217ac392700","order_by":2,"name":"Kai Jiang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3klEQVRIiWNgGAWjYBACCQbGBoMEIIMfwmcmQYtkAzPRWqDA4ACxWiTbDzcUPKi5Y7f5Rv4xCYYK68QG9rMH8GqR5kkEOuzYs+RtZw6zSTCcSU9s4MlLwKtFjgGkhe1wstnxZjYJxrbDiQ0SPAb4tfA/BGr5dzjZuJkZqOUfEVqkJYC2JLYdtjNgB9nSQIQWyRlAWxL7DidInDlsbJFwLN24jScHvxaJ8+nPDH98O2zPPyPx4Y0PNday/exn8GsBAjaQisQGEDMBxCWkHgiYHwAJeyIUjoJRMApGwUgFAONVRJeK/C3cAAAAAElFTkSuQmCC","orcid":"","institution":"Xiangtan University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Kai","middleName":"","lastName":"Jiang","suffix":""}],"badges":[],"createdAt":"2022-08-25 03:44:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1996000/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1996000/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":25852775,"identity":"00005384-9b13-4aa2-8535-eae776a4ed47","added_by":"auto","created_at":"2022-08-30 16:41:21","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1011367,"visible":true,"origin":"","legend":"","description":"","filename":"NumerMethodsOKequationNA.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1996000/v1_covered.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Two efficient block preconditioners for the mass-conserved Ohta-Kawasaki equation","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-1996000/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Mass-conserved Ohta-Kawasaki equation, Newton method, Schur complement preconditioner, MHSS preconditioner","lastPublishedDoi":"10.21203/rs.3.rs-1996000/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1996000/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this paper, we propose two efficient block preconditioners to solve the mass-conserved Ohta-Kawasaki equation with finite element dis-cretization. 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