A Non-intrusive Approach for the Imposition of Strong Dirichlet Boundary Conditions in Unfitted Boundary Meshes

A Non-intrusive Approach for the Imposition of Strong Dirichlet Boundary Conditions in Unfitted Boundary Meshes | 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 A Non-intrusive Approach for the Imposition of Strong Dirichlet Boundary Conditions in Unfitted Boundary Meshes Juan Ignacio Camarotti, Ricky Aristio, Riccardo Rossi, Rubén Zorrilla, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6809603/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 23 Sep, 2025 Read the published version in Engineering with Computers → Version 1 posted 9 You are reading this latest preprint version Abstract The enforcement of essential boundary conditions is a fundamental challenge in unfitted boundary methods. This paper presents a non-intrusive, black-box strategy for imposing such conditions in unfitted meshes. The approach is intended for situations where the user does not have access to the solver’s source code or its mathematical formulation, which is often the case when using commercial software. The proposed algorithm allows solvers originally designed for body-fitted meshes to be used in unfitted cases, provided that four conditions are satisfied: (i) the solver must support user scripting, (ii) allow the imposition of Dirichlet boundary conditions at the node level through scripting, (iii) permit the deactivation of elements outside the physical domain, and (iv) provide access to the solution gradient within active elements. In the current work, we show the application of this non-intrusive algorithm in the context of the Finite Element Method (FEM) and Isogeometric Analysis (IGA), demonstrating optimal L2-norm error convergence.This is demonstrated using the Kratos Multiphysics code (release v10.1) from the user API, simply leveraging the capabilities mentioned above. Unfitted boundary methods Black-box solver Strong dirichlet boundary conditions Finite element method (FEM) Isogeometric Analysis (IGA) Trimmed domain Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 23 Sep, 2025 Read the published version in Engineering with Computers → Version 1 posted Editorial decision: Revision requested 31 Jul, 2025 Reviews received at journal 31 Jul, 2025 Reviews received at journal 30 Jun, 2025 Reviewers agreed at journal 23 Jun, 2025 Reviewers agreed at journal 20 Jun, 2025 Reviewers invited by journal 20 Jun, 2025 Editor assigned by journal 04 Jun, 2025 Submission checks completed at journal 04 Jun, 2025 First submitted to journal 03 Jun, 2025 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. 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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-6809603","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":466219901,"identity":"5c61d737-0c55-4bf2-a3a1-b62a7cfe092e","order_by":0,"name":"Juan Ignacio Camarotti","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3klEQVRIiWNgGAWjYBACxgYUroENmJIgVgtjwwGDNAmCWlC1H2A4TFgL84zkZw8Yauyi+WcfPv74Q8H5OoNrBxhvfMBn8ow0cwOGY8m5M86lJQIddlvC4HYCs+UMvFoSzCQYG5hzG87wGMK0sEnz4NWS/g2opT53PkTLOYiWP3i15IBsOZy7AaLlAEQLPu8z9rwpk0g4djx34xm2xBlnDJIlZ95ObLbswaPFsD19m8SHmurceWeYD3yo+GPHz3c7+eCNH/i0NACJBDSbG/C5i0Eer+woGAWjYBSMAhAAAE0EUSYCH9z7AAAAAElFTkSuQmCC","orcid":"","institution":"Technical University of Munich","correspondingAuthor":true,"prefix":"","firstName":"Juan","middleName":"Ignacio","lastName":"Camarotti","suffix":""},{"id":466219903,"identity":"c216bfeb-52c9-48ca-b4b1-fe0267dc291d","order_by":1,"name":"Ricky Aristio","email":"","orcid":"","institution":"Technical University of Munich","correspondingAuthor":false,"prefix":"","firstName":"Ricky","middleName":"","lastName":"Aristio","suffix":""},{"id":466219904,"identity":"3fc4ac52-5ce0-4334-8e17-518a521c1c1d","order_by":2,"name":"Riccardo Rossi","email":"","orcid":"","institution":"Universitat Politècnica de Catalunya","correspondingAuthor":false,"prefix":"","firstName":"Riccardo","middleName":"","lastName":"Rossi","suffix":""},{"id":466219905,"identity":"816c8e19-fb0d-4910-8eee-118e8fd2342b","order_by":3,"name":"Rubén Zorrilla","email":"","orcid":"","institution":"Universitat Politècnica de Catalunya","correspondingAuthor":false,"prefix":"","firstName":"Rubén","middleName":"","lastName":"Zorrilla","suffix":""},{"id":466219906,"identity":"7c954f1f-97de-44f5-8006-d6a38dd6008b","order_by":4,"name":"Roland Wüchner","email":"","orcid":"","institution":"Technical University of Munich","correspondingAuthor":false,"prefix":"","firstName":"Roland","middleName":"","lastName":"Wüchner","suffix":""}],"badges":[],"createdAt":"2025-06-03 09:38:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6809603/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6809603/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00366-025-02207-y","type":"published","date":"2025-09-23T15:58:23+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":92430951,"identity":"2a315609-24de-4ce5-9f8f-3a5f010cab9f","added_by":"auto","created_at":"2025-09-29 16:08:11","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3354455,"visible":true,"origin":"","legend":"","description":"","filename":"camarottipaperspringer.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6809603/v1_covered_5c518dc9-c75e-482c-9818-307209e3383e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Non-intrusive Approach for the Imposition of Strong Dirichlet Boundary Conditions in Unfitted Boundary Meshes","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Unfitted boundary methods, Black-box solver, Strong dirichlet boundary conditions, Finite element method (FEM), Isogeometric Analysis (IGA), Trimmed domain","lastPublishedDoi":"10.21203/rs.3.rs-6809603/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6809603/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The enforcement of essential boundary conditions is a fundamental challenge in unfitted boundary methods. 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