Explicit Time Integration Method Based on Uniform Trigonometric B-Spline Function for Transient Heat Conduction Analysis by Zixu Li, Yongyu Hong, Pan Wang, Weibin Wen

“…In this paper, a new explicit time integration method for transient heat conduction analysis is proposed based on the uniform trigonometric B-spline function. …”
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APPLICATIONS OF QUASI-STATIC METHOD IN STATIC FAILURE SIMULATION FOR LARGE AIRCRAFT WINGBOX by YU Ming, LING XiaoTao, WANG QianPing

“…The strength problems of large-aircraft wingbox is complex.Studying the bearing characteristics of wingbox,plays an important role in wing structure refined design,weight optimization and development cost saving.Based on the explicit time integration,this paper simulated the static loading process of typical wingbox section until failure in quasi-static limits,while taking the material nonlinearity and damage characteristics into consideration.Both the strain distribution and the strength prediction agree well with the experimental results.The study provides a reference for evaluating the ultimate strength of aircraft assembly.…”
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Dynamics Characteristic Analysis of Ball Screw Under High Load by Yang Wuxu, Fan Yuanxun, Liu Minghui, Dong Huili

“…To research the dynamics characteristic of high load ball screw under angular vibration driving velocity，a flexible body dynamic model and a control model considering the process of ball entering and leaving the re-circulating mechanism are built based on explicit time integration. The comparison of dynamic responses and other characteristics shows that the ball screw under high load has a certain probability of transient stuck originated from the impact between the balls in the groove and the balls in the deflector，this phenomenon stems from the collision between the ball in the raceway and the ball in the reverser，and the common action of the normal force loading and unloading when balls enter and leave the re-circulating mechanism，etc. …”
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Towards Numerical Method-Informed Neural Networks for PDE Learning by Pasquale De Luca, Livia Marcellino

“…This paper addresses these limitations by embedding the mathematical structure of implicit–explicit time integration schemes directly into neural network architectures. …”
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Adaptively Implicit Advection for Atmospheric Flows by Hilary Weller, Christian Kühnlein, Piotr K. Smolarkiewicz

“…The demonstration in this paper uses the second‐order Runge‐Kutta implicit/explicit time integration in combination with a second/third‐order finite‐volume spatial discretization and is tested using deformation flow tracer advection on the sphere and a fully compressible model for atmospheric flows. …”
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Comparative Study of Different Linear Analysis for Seismic Resistance of Buildings According to Eurocode 8 by Ivelin Ivanov, Dimitar Velchev

“…Using an artificial diagram, three approaches in finite element methods exist: explicit time integration, implicit time integration, and modal dynamics. …”
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Comparative Analysis of ALE Method Implementation in Time Integration Schemes for Pile Penetration Modeling by Ihab Bendida Bourokba, Abdelmadjid Berga, Patrick Staubach, Nazihe Terfaya

“…Comparative analysis revealed the explicit time integration method as more robust and computationally efficient, particularly for complex soil–pile interactions with higher friction coefficients.…”
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A comparative study of explicit and implicit Large Eddy simulations using a high-order discontinuous Galerkin solver: Application to a Formula 1 front wing by Gerasimos Ntoukas, Gonzalo Rubio, Oscar Marino, Alexandra Liosi, Francesco Bottone, Julien Hoessler, Esteban Ferrer

“…This formulation employs Gauss-Lobatto points, which downgrades the accuracy of integration but allows for larger time steps in explicit time integration.We compare our results to Nektar++, by Slaughter et al. in Flow, Turbulence and Combustion 110, 917–944 (2023), showing that both LES techniques provide results that agree well with the reference values. …”
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Second order algorithm with convergence analysis for viscoelastic flow model by Chinedu Nwaigwe, Sanda Micula

“…The high-degree term is discretized with central difference spatial scheme and implicit-explicit time integrator, while the unsteady and external source terms are discretized implicitly. …”
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