First Order Explicit Time Integration Scheme with Large Time Steps for Parabolic Problems Using Irregular Grids

First Order Explicit Time Integration Scheme with Large Time Steps for Parabolic Problems Using Irregular Grids | 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 First Order Explicit Time Integration Scheme with Large Time Steps for Parabolic Problems Using Irregular Grids Eugenio Oñate, Francisco Zarate, Juan M. Gimenez, Sergio R. Idelsohn This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6176685/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 14 Oct, 2025 Read the published version in Advanced Modeling and Simulation in Engineering Sciences → Version 1 posted 4 You are reading this latest preprint version Abstract We present a fast first order explicit time integration scheme for solving parabolic problems in mechanics via standard numerical methods in space using irregular grids, such as unstructured finite element meshes, or grids containing elements or cells of very different sizes. The new scheme extends one of the explicit FIC-Time (EFT) integration methods derived by the authors in a previous publication that allow considerable larger time steps than the forward-Euler (FE) scheme. The new EFT scheme overcomes the limitations in the time step size of explicit time integration schemes for irregular grids containing large and small elements. A variable time step is used for eliminating the oscillations near Dirichlet boundaries when large time steps are used. The advantages of the new EFT scheme versus the FE scheme are shown in one-, two- and three-dimensional transient heat conduction problems using irregular finite element grids Explicit time integration schemes parabolic equation large time steps irregular grid finite increment calculus FIC-Time Full Text Supplementary Files con360.tex Cite Share Download PDF Status: Published Journal Publication published 14 Oct, 2025 Read the published version in Advanced Modeling and Simulation in Engineering Sciences → Version 1 posted Reviewers agreed at journal 20 Mar, 2025 Reviewers invited by journal 20 Mar, 2025 Editor assigned by journal 20 Mar, 2025 First submitted to journal 06 Mar, 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. 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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-6176685","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":431516264,"identity":"74c2d8e7-9a05-4970-864e-f1a093bb28b3","order_by":0,"name":"Eugenio Oñate","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0UlEQVRIiWNgGAWjYNCCCgYeJF4CQfWMDQxnSNbC2IYiQEALv3Tz8wcf59nJ6M5uPsDMu8OOgZ89xwCvFsk5xwwbZ25L5jG7cyyBmfdMMoNkzxv8WgxuJBg28247wGN2I8eAmbftAFCEgC0GN9I/Nv+dA9KS/wGsxZ6wlhzDZsYGsC0MEFskCPllRk7hzJ5jQL/cSDM4OPdMMo/EmWcFeLXwS6Rv+PCjxs7e7Ebywwdvd9jJ8bcnb8CrBQUcAMYqD2FlKACoZRSMglEwCkYBBgAAhbFGp8hox1MAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-0804-7095","institution":"Centre Internacional de Metodes Numerics en Enginyeria - CIMNE","correspondingAuthor":true,"prefix":"","firstName":"Eugenio","middleName":"","lastName":"Oñate","suffix":""},{"id":431516265,"identity":"4a35e4d9-67a8-45c2-b16a-cfb0f154ce2f","order_by":1,"name":"Francisco Zarate","email":"","orcid":"","institution":"Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE)","correspondingAuthor":false,"prefix":"","firstName":"Francisco","middleName":"","lastName":"Zarate","suffix":""},{"id":431516266,"identity":"2e9a24a7-c9d8-44aa-9a75-8842c9cc3c08","order_by":2,"name":"Juan M. 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