Quadrature method and extrapolation algorithm for solving the boundary integral equations of the acoustic wave scattering problems

Quadrature method and extrapolation algorithm for solving the boundary integral equations of the acoustic wave scattering problems | 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 Quadrature method and extrapolation algorithm for solving the boundary integral equations of the acoustic wave scattering problems Hong Guo, Jin Huang, Hu Li, Zhaoxing Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4230474/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 This paper studies the time domain acoustic wave scattering problems of a bounded obstacle or a smooth open arc in the unbounded domain, where the obstacle has the smooth and closed boundary. Due to the potential theories, the first kind retarded single-layer potential boundary integral equations of the above problems can be obtained and they are solved by two steps, we get the temporal discretization by the convolution quadrature method firstly, and then the first kind boundary integral equations in space are solved by the quadrature method. Meanwhile, the scattered field can be computed in terms of the trapezoidal rule. The existence and uniqueness of the numerical solution are proved, the convergence of the approximate solution is also analysed and the error bound is got. The asymptotic expansion of the error in space shows that the convergence rate is O(h3). Moreover, the extrapolation algorithm is used to improve the accuracy of the numerical solution. The posteriori error estimate is also obtained, which is helpful for designing the self-adaptive algorithm. Some numerical experiments are implemented to show the effectiveness of our method. Acoustic wave time domain retarded single-layer potential convolution quadrature quadrature method extrapolation algorithm 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. 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-4230474","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":292882675,"identity":"5779ac37-6f62-4319-92f7-cd1219a7bc97","order_by":0,"name":"Hong Guo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA90lEQVRIiWNgGAWjYHACNhAhB8QGcCEJYrQYAykDuGqitCQ2EK1FPiL52IOPO2rT589v3sDMU1FXx9/AfPA2D4NdHi4thjfS0g1nnjmeu+EYWwEzz5nDEhIH2JKteRiSi3FqmZFjJs3bdix3AxuPATNv2wEJAwYeM2kehgOJDQS0pMu3gbT8qwNq4f+GV4u8BFhLTQLDMZCWBmaQLWx4tRjwPEuTnNl2wHDDsbSCg3OOHZaccZjN2HKOQTJuW9qTj0l8bKuTl28+vPHBm5o6fv725oc33lTY4bblAJg6DCYhbGawOA71IFsgZtXhVjEKRsEoGAWjAAB84U5/+rP6TAAAAABJRU5ErkJggg==","orcid":"","institution":"University of Electronic Science and Technology of China","correspondingAuthor":true,"prefix":"","firstName":"Hong","middleName":"","lastName":"Guo","suffix":""},{"id":292882677,"identity":"48e0b804-43de-40d6-98d6-9ab56df1f67a","order_by":1,"name":"Jin Huang","email":"","orcid":"","institution":"University of Electronic Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Jin","middleName":"","lastName":"Huang","suffix":""},{"id":292882678,"identity":"454c9192-7a79-4d10-a222-88934e415609","order_by":2,"name":"Hu Li","email":"","orcid":"","institution":"Chengdu Normal University","correspondingAuthor":false,"prefix":"","firstName":"Hu","middleName":"","lastName":"Li","suffix":""},{"id":292882679,"identity":"92b2733a-80f5-4898-bb69-7b6b5905ef33","order_by":3,"name":"Zhaoxing Li","email":"","orcid":"","institution":"North China University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Zhaoxing","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2024-04-07 08:44:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4230474/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4230474/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":60654669,"identity":"2ad8e62a-8792-4cd0-864e-213ee5015638","added_by":"auto","created_at":"2024-07-19 07:14:39","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2787399,"visible":true,"origin":"","legend":"","description":"","filename":"Timedomain.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4230474/v1_covered_ab864a57-4af8-4d7c-8e2b-12d6a64e5900.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Quadrature method and extrapolation algorithm for solving the boundary integral equations of the acoustic wave scattering problems","fulltext":[],"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":true,"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":"Acoustic wave, time domain, retarded single-layer potential, convolution quadrature, quadrature method, extrapolation algorithm","lastPublishedDoi":"10.21203/rs.3.rs-4230474/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4230474/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper studies the time domain acoustic wave scattering problems of a bounded obstacle or a smooth open arc in the unbounded domain, where the obstacle has the smooth and closed boundary. Due to the potential theories, the first kind retarded single-layer potential boundary integral equations of the above problems can be obtained and they are solved by two steps, we get the temporal discretization by the convolution quadrature method firstly, and then the first kind boundary integral equations in space are solved by the quadrature method. Meanwhile, the scattered field can be computed in terms of the trapezoidal rule. The existence and uniqueness of the numerical solution are proved, the convergence of the approximate solution is also analysed and the error bound is got. The asymptotic expansion of the error in space shows that the convergence rate is O(h3). Moreover, the extrapolation algorithm is used to improve the accuracy of the numerical solution. The posteriori error estimate is also obtained, which is helpful for designing the self-adaptive algorithm. 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