Hierarchical RBFs Methods for the interface problem of the Maxwell equations in complex domains

Hierarchical RBFs Methods for the interface problem of the Maxwell equations in complex domains | 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 Hierarchical RBFs Methods for the interface problem of the Maxwell equations in complex domains Yi Liu, Qiuyan Xu, Zhiyong Liu, Jiye Yang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8006255/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 transverse electric and transverse magnetic modes of Maxwell equations are two fundamental polarization patterns for electromagnetic wave propagation in waveguides or at medium interfaces. This paper addresses interface problems of Maxwell equations in complex domains by proposing a high precision numerical method based on hierarchical radial basis functions (H-RBFs). Through separate analysis of transverse electric and transverse magnetic fields, two H-RBFs based modes are established, with detailed algorithmic implementation provided. The numerical experiments demonstrate the effectiveness of the presented method, which is show high precision in complex domains, thus offering a reliable numerical tool for electromagnetic interface problems. Maxwell equations Discontinuous interface Hierarchical radial basis function Transverse electric and Transverse magnetic modes Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 08 Feb, 2026 Reviewers agreed at journal 25 Jan, 2026 Reviewers agreed at journal 10 Nov, 2025 Reviewers invited by journal 09 Nov, 2025 Editor assigned by journal 02 Nov, 2025 Submission checks completed at journal 02 Nov, 2025 First submitted to journal 01 Nov, 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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