The inverse design of a linear transport equation using the gradient-adjoint and MMOC schemes

The inverse design of a linear transport equation using the gradient-adjoint and MMOC schemes | 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 The inverse design of a linear transport equation using the gradient-adjoint and MMOC schemes Alexandre Santos Francisco, Welbe Corlindo, Panters Rodriguez Bermudez This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9151955/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract The inverse design of transport equations can be approached using a gradient-adjoint methodology. In this methodology, the numerical schemes used for solving the adjoint problem determine the direction of descent in the iterative algorithm, which ultimately affects the CPU time consumed during the inverse design process. As the CPU time represents a significant bottleneck, it is essential to use efficient and accurate schemes for the adjoint problem. We proposed the use of the Modified Method of Characteristics (MMOC). Although the MMOC fails to preserve certain integral identities satisfied by the solution of the differential equations, it remains computationally competitive. In this work, we evaluated the computational performance of the MMOC in comparison with the Lax-Friedrichs and Lax-Wendroff schemes, in the context of the inverse design. By testing the Doswell frontogenesis equation, we observed that the MMOC can offer more efficient and accurate computations under more severe simulation configurations. 2020 MSC: 00-01, 99-00 Characteristics-based method inverse design Doswell frontogenesis Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 18 May, 2026 Reviewers agreed at journal 05 Apr, 2026 Reviewers agreed at journal 03 Apr, 2026 Reviewers invited by journal 03 Apr, 2026 Editor assigned by journal 21 Mar, 2026 Submission checks completed at journal 18 Mar, 2026 First submitted to journal 17 Mar, 2026 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-9151955","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":617751435,"identity":"ed272233-1d17-42d3-b62b-5ecf6c17615f","order_by":0,"name":"Alexandre Santos Francisco","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYDAC5gMgUgLMOsDDwMDP3sBDQAtbAkwLWwJIi2TPAeK0gACPAQNRWvjbeB9+LqixsOdv7/l44A3DYQkeBt5jH/BpkTjGbiw945hE4owzZzccnAPWwpc8A68199sYpHkbJBIMJHI3HOZhOFxnz8BjjFeH/DE25t9ALfYGEjkPQFqAthDQYnCMjQ1kC+MGiRwG4rQYArVY84D9cszg4ByDdAkeZr5kvFrkgA67zVNTBwyx5scf3lRYS/Cw9x7GqwXdnUDMTIqGUTAKRsEoGAVYAQA4fj42bqqC1wAAAABJRU5ErkJggg==","orcid":"","institution":"Fluminense Federal University","correspondingAuthor":true,"prefix":"","firstName":"Alexandre","middleName":"Santos","lastName":"Francisco","suffix":""},{"id":617751436,"identity":"7cde6ae7-8fce-4088-8d9a-dbce7b87f802","order_by":1,"name":"Welbe Corlindo","email":"","orcid":"","institution":"Fluminense Federal University","correspondingAuthor":false,"prefix":"","firstName":"Welbe","middleName":"","lastName":"Corlindo","suffix":""},{"id":617751437,"identity":"0d88aeab-9e51-4979-995d-b473b7cef73b","order_by":2,"name":"Panters Rodriguez Bermudez","email":"","orcid":"","institution":"Fluminense Federal University","correspondingAuthor":false,"prefix":"","firstName":"Panters","middleName":"Rodriguez","lastName":"Bermudez","suffix":""}],"badges":[],"createdAt":"2026-03-17 19:08:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9151955/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9151955/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106503347,"identity":"5ca7c108-a118-4329-a065-3f3ca835575c","added_by":"auto","created_at":"2026-04-09 09:29:34","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":552617,"visible":true,"origin":"","legend":"","description":"","filename":"Bilbao3.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9151955/v1_covered_fe0423e8-77a7-4327-bd40-c8b3900ce611.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The inverse design of a linear transport equation using the gradient-adjoint and MMOC schemes","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"international-journal-of-applied-and-computational-mathematics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [International Journal of Applied and Computational Mathematics](https://link.springer.com/journal/40819)","snPcode":"40819","submissionUrl":"https://submission.nature.com/new-submission/40819/3","title":"International Journal of Applied and Computational Mathematics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Characteristics-based method, inverse design, Doswell frontogenesis","lastPublishedDoi":"10.21203/rs.3.rs-9151955/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9151955/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe inverse design of transport equations can be approached using a gradient-adjoint methodology. 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