An electromagnetic shape optimisation for perfectly electric conductors by the time-domain boundary integral equations

An electromagnetic shape optimisation for perfectly electric conductors by the time-domain boundary integral equations | 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 An electromagnetic shape optimisation for perfectly electric conductors by the time-domain boundary integral equations Toru Takahashi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3865606/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 This study proposes a shape optimisation framework for unsteady electromagnetic scattering problems on the basis of the time-domain boundary integral equation method, focusing on the perfectly electric conductors (PECs). The boundary-only formulation is ideal for treating a shape optimisation problem in exterior domains. However, the electromagnetic shape optimisation in concern has been unrealised with the boundary integral approach regardless of the fact that the boundary-type shape derivative has been known in the literature. The first contribution of the present study is to derive a novel expression of the shape derivative in terms of the surface current densities of the primary and adjoint problems, by considering that the surface current density is handled by usual integral equations methods. The second contribution is to clarify the integral representations and equations of the adjoint electromagnetic fields in terms of the reversal time. These theoretical achievements possess a high affinity with the standard spatial discretising approach (i.e. RWG basis) whenever the temporal basis is sufficiently smooth. The numerical experiments confirmed the reliability of the proposed shape optimisation methodology and indicated the capability to deal with scientific and engineering applications. Shape optimisation Electromagnetics Boundary integral equation Boundary element method Shape derivative Adjoint variable method Time domain Perfectly electric conductors NURBS Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 18 Mar, 2024 Reviews received at journal 18 Jan, 2024 Reviewers agreed at journal 17 Jan, 2024 Reviewers invited by journal 17 Jan, 2024 Editor assigned by journal 16 Jan, 2024 Submission checks completed at journal 16 Jan, 2024 First submitted to journal 15 Jan, 2024 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-3865606","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":267571812,"identity":"589220ab-07bf-4e83-815c-a7d62dacc1d7","order_by":0,"name":"Toru Takahashi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABSklEQVRIie2RMUvDQBTHXzhIlitdr8TiV7hSiApHi5/DJSGQLg10crHggZAura4FIf0KDX6BQCBZiq4HCm0RnDoIWYKkYCoqJLaom0h+w3GP43f/d/cASkr+MBQIAALKvh6hQo3fVv1TsX6tQPB9Q21l9ESkpNWsXl88xr3e3Ul1wOVF8sKMK44pJH1QDgopONII6KZGHkJNHdN7ezzzlcbo0jLGPqbSMAR0xPMKseRMQQyEriGcKVzoMqkMA4PPVxQqHBD1tynnbF904hjTW3syX8i1daZMNinrnUqgUdGlKqa+PRUgqzgJjGmmoG0psxAd6lbUbIjuaaaYtjczHLXOrabny71gLyTFtygDRxLP7Kzhis5NjNOW7UZBWFulrO76yFuu+sws/Nj7WHJIHCQHjjd3Zy0Rk+4cUY4U2h/b1g+VkpKSkn/LK24tcI89vHi1AAAAAElFTkSuQmCC","orcid":"","institution":"Nagoya Uinversity","correspondingAuthor":true,"prefix":"","firstName":"Toru","middleName":"","lastName":"Takahashi","suffix":""}],"badges":[],"createdAt":"2024-01-15 06:44:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3865606/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3865606/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":49765114,"identity":"7fa2943f-026e-49fb-b8ef-7c4752d63a50","added_by":"auto","created_at":"2024-01-17 16:41:24","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4847642,"visible":true,"origin":"","legend":"","description":"","filename":"ms.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3865606/v1_covered_5a795fd6-bf29-4c50-acf5-ace9cc6bf72e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An electromagnetic shape optimisation for perfectly electric conductors by the time-domain boundary integral equations","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"engineering-with-computers","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ewco","sideBox":"Learn more about [Engineering with Computers](http://link.springer.com/journal/366)","snPcode":"366","submissionUrl":"https://submission.nature.com/new-submission/366/3","title":"Engineering with Computers","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Shape optimisation, Electromagnetics, Boundary integral equation, Boundary element method, Shape derivative, Adjoint variable method, Time domain, Perfectly electric conductors, NURBS","lastPublishedDoi":"10.21203/rs.3.rs-3865606/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3865606/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study proposes a shape optimisation framework for unsteady electromagnetic scattering problems on the basis of the time-domain boundary integral equation method, focusing on the perfectly electric conductors (PECs). 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