Numerical Simulation of the Generalized Wave Equation Using an Improved Adaptive Differential Evolution–Optimized Staggered-Grid Finite-Difference Scheme

Numerical Simulation of the Generalized Wave Equation Using an Improved Adaptive Differential Evolution–Optimized Staggered-Grid Finite-Difference Scheme | 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 Numerical Simulation of the Generalized Wave Equation Using an Improved Adaptive Differential Evolution–Optimized Staggered-Grid Finite-Difference Scheme Jun Qi Zhang, wenlei Bai, chengfang Zhang, zhiyang Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8019691/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 The generalized wave equation expands traditional elastic wave theory by incorporating couple-stress and strain-gradient effects, providing a more comprehensive description of subsurface mechanical behavior. This formulation is particularly suited for capturing rotational motion and scale-dependent phenomena induced by microstructural heterogeneity. In this study, the generalized wave equation with couple-stress and strain-gradient terms is derived and numerically solved using a finite-difference (FD) approach, selected for its simplicity, efficiency, and parallelizability. However, traditional FD schemes often exhibit numerical dispersion. To address this, we develop an optimized staggered-grid finite-difference operator guided by an enhanced self-adaptive differential evolution (SADE) algorithm. The algorithm employs a multi-strategy adaptive mutation mechanism and a dynamically updated strategy pool to balance global exploration with local exploitation. The resulting first-order spatial derivative operators achieve high accuracy, markedly reducing numerical dispersion. Numerical tests on layered and Marmousi models confirm that the proposed method more faithfully reproduces wavefield phase and amplitude characteristics than traditional FD method and other metaheuristic optimization techniques. This work not only establishes a novel numerical optimization framework but also provides an effective computational tool for high-fidelity, seismic wave simulation, imaging, and inversion. Generalized Wave Equation Differential Evolution Algorithm Finite-difference Numerical Simulation Full Text 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. 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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-8019691","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":546651962,"identity":"e76828ff-f36a-4a15-92cf-179eafb10004","order_by":0,"name":"Jun Qi 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This formulation is particularly suited for capturing rotational motion and scale-dependent phenomena induced by microstructural heterogeneity. In this study, the generalized wave equation with couple-stress and strain-gradient terms is derived and numerically solved using a finite-difference (FD) approach, selected for its simplicity, efficiency, and parallelizability. However, traditional FD schemes often exhibit numerical dispersion. To address this, we develop an optimized staggered-grid finite-difference operator guided by an enhanced self-adaptive differential evolution (SADE) algorithm. The algorithm employs a multi-strategy adaptive mutation mechanism and a dynamically updated strategy pool to balance global exploration with local exploitation. The resulting first-order spatial derivative operators achieve high accuracy, markedly reducing numerical dispersion. 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