Research on Newton-Krylov Method for Multi-component Flow Heat Transfer Coupled System of High-temperature Gas-cooled Reactor by TANG Huanran, ZHANG Han, LIU Lixun, PENG Xinru, WU Yingjie, GUO Jiong, LI Fu

“…In this paper, a multi-component gas flow coupling calculation program for the characteristics of HTGRs was developed based on NK method. Among the two variants of the NK method, finite-Difference Jacobian Newton-Krylov method (DJNK) which explicitly constructs the Jacobian was chosen as the solution method. …”

Computational study of fluid forces over a cylinder attached with elastic beam: A finite element-based simulations by Yasir Arif, Rashid Mahmood, Mehdi Tlija, Afraz Hussain Majeed, Kamran Usman, Ehab Seif Ghith

“…The discrete systems are solved using a Newton method that employs split differences to explicitly generate the Jacobian matrices. …”
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Finite-Time Synchronization and Practical Synchronization for Caputo Fractional-Order Fuzzy Cellular Neural Networks with Transmission Delays and Uncertainties via Information Feed... by Hongguang Fan, Hui Wen, Kaibo Shi, Anran Zhou

“…Namely, changing one of the feedback terms from positive to negative can cause PFT synchronization to switch to FT synchronization via adjusted control parameters, making our control methods applicable to different scenarios. The settling time depends explicitly on feedback coefficients, initial conditions, and fractional order.…”
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Analysis of Fatigue Performance of Metallic Components with Gradient Microstructures by Pandi Zhao, Liheng Tuo, Hongrui Zhang, Zhiyan Sun, Shuai Ren, Gaihuan Yuan, Zebang Zheng

“…Based on this method, a macroscopic finite element model was developed to simulate the plastic strain accumulation and springback of the sealing ring in service. …”
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DYNAMIC CHARACTERISTICS OF INTERNAL CONTACT OF ROLLING BEARINGS UNDER DIFFERENT DEGREES OF FAILURE by TU WenBing, YANG JinWen, LUO Ya, REN JiWen

“…The effectiveness of the model was verified by the experiment on the outer ring fault of the rolling bearing. Based on the explicit dynamics method,the dynamic contact force between the rolling element and each component and the contact strain of the fault area was analyzed,then the influence law of different fault degrees on the internal dynamic characteristics of the bearing and the change law of the contact deformation under the fault condition were revealed. …”
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Akhmediev Breathers and Kuznetsov–Ma Solitons in the Cubic-Quintic Nonlinear Schrödinger Equation by Changchang Pan, Gangzhou Wu, Lei Zhang, Huicong Zhang

“…We used the Darboux transformation method to obtain explicit analytical solutions for the Akhmediev breather, the Kuznetsov-Ma soliton, and the Peregrine soliton of the cubic-quintic nonlinear Schrödinger equation. …”
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DEVELOPMENT OF A DISCRETE MATHEMATICAL MODEL OF THE HYDROTREATING DIESEL FUEL REACTOR by Ksenia Igorevna Netsvetaeva

“…The article gives an example of the transformation of the initial mathematical model of the hydrotreating diesel fuel reactor which is a system of algebraic equations into its discrete analogue, using the method of "nets" (finite difference method). The transformation of the original system was made because of the complexity of solving it explicitly and the need to obtain the most accurate values of the variables.…”
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Size-dependent nonlinear bending of microbeams based on a third-order shear deformation theory by Ngoc Duyen Dang, Dinh Kien Nguyen, Cong Ich Le

“…Nonlinear bending of microbeams under different mechanical loading is predicted with the aid of Newton–Raphson iterative method. …”
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Structure-based modeling of artificial leather used in sports with non-symmetric fiber distribution by Tonghuan QU, Akihiro MATSUDA

“…The mechanical behavior of artificial leather specimens under uniaxial extension at various tensile angles was simulated through finite element computations. The differences in mechanical response in two axisymmetric directions about the main direction of the fiber family were captured, breaking through the limitations of the currently applied fiber dispersion models. …”
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Simulation of a Custom-Made Temporomandibular Joint—An Academic View on an Industrial Workflow by Annchristin Andres, Kerstin Wickert, Elena Gneiting, Franziska Binmoeller, Stefan Diebels, Michael Roland

“…In this study, we compare two finite element method-based simulation workflows from both academic and industrial perspectives, focusing on a patient-specific case involving a custom-made temporomandibular joint prosthesis. …”
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The study of seismic resistance of rubber-metal supports by G.A. Dzhinchvelashvili, O.V. Mkrtychev

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A numerical framework for simulating fluid-structure interaction phenomena by A. De Rosis, S. de Miranda, C. Burrafato, F. Ubertini

“…The lattice Boltzmann method is used to compute fluid dynamics, while the corotational finite element formulation together with the Time Discontinuous Galerkin method are adopted to predict structure dynamics. …”
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Simulation Analysis of the Dynamic Performance of Multi Tooth Meshing of Filtering Reducer based on ANSYS- LS / DYNA by Lei Xiaochun, Yang Rongsong, Zhu Bingfeng, Liu Qiang, Chen Zhiliang

“…The filtering reducer structure principle and multi tooth elastic meshing effect are introduced,with the help of explicit dynamics software ANSYS / LS- DYNA,the three- dimensional nonlinear finite element contact analysis model is established,the dynamic meshing simulation of gear transmission mechanism under a certain speed and different load torque is carried out,the tooth surface contact stress,tooth root bending stress distribution and the rules of contact force changes under the condition of multi tooth contact with time are obtained,a theoretical basis for further filter reducer gear strength analysis and fatigue life calculation is provided by this method.…”
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The Higher Accuracy Fourth-Order IADE Algorithm by N. Abu Mansor, A. K. Zulkifle, N. Alias, M. K. Hasan, M. J. N. Boyce

“…This study develops the novel fourth-order iterative alternating decomposition explicit (IADE) method of Mitchell and Fairweather (IADEMF4) algorithm for the solution of the one-dimensional linear heat equation with Dirichlet boundary conditions. …”
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Numerical Simulations for the Space-Time Variable Order Nonlinear Fractional Wave Equation by Nasser Hassan Sweilam, Taghreed Abdul Rahman Assiri

“…The explicit finite-difference method for solving variable order fractional space-time wave equation with a nonlinear source term is considered. …”
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Symbolic Regression-Based Modeling for Aerodynamic Ground-to-Flight Deviation Laws of Aerospace Vehicles by Di Ding, Qing Wang, Qin Chen, Lei He

“…This study provides valuable insight for modeling problems with finite data samples and explicit physical meanings.…”
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NUMERICAL MODELING OF HYDRODYNAMIC PROCESSES IN AQUIFERS by Maxim Alexandrovich Sixtus

“…The mathematical model of the object is represented as a system of differential equations in partial derivatives that can be solved by the explicit scheme of finite difference method. Geometric parameters of the object are described by functions of two variables, it is a distinctive feature ofproposed method of mathematical modeling. …”
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Study on the Effect of the Groove Surface on Clutch Engagement Character by Chai Mengjiang

“…Based on the transient dynamics principle,a finite element model of a friction clutch system is established by using explicit dynamics method of software ABAQUS. …”
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Implicit analysis of the transient water flow with dissolved air by J. Twyman

“…The implicit finite-difference method (IFDM) for solving a system that transports water with dissolved air using a fixed (or variable) rectangular space-time mesh defined by the specified time step method is applied. …”
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Unified Description of the Mechanical Properties of Typical Marine Soil and Its Application by Yongqiang Li, Gang Wang, Liping Jing, Lei Zhang, Xinjun Cheng

“…This model can describe the unified behaviour of unsaturated soil and saturated soil using independent state variables and can uniquely describe the multiple mechanical properties of soils under general stress states, without changing the parameter values using the transform stress method. An effective stress-based, fully coupled, explicit finite element–finite difference method was established based on this model and three-phase field theory. …”
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