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  • Open Access

    ARTICLE

    Fast and Accurate Predictor-Corrector Methods Using Feedback-Accelerated Picard Iteration for Strongly Nonlinear Problems

    Xuechuan Wang1, Wei He1,*, Haoyang Feng1, Satya N. Atluri2

    CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.2, pp. 1263-1294, 2024, DOI:10.32604/cmes.2023.043068

    Abstract Although predictor-corrector methods have been extensively applied, they might not meet the requirements of practical applications and engineering tasks, particularly when high accuracy and efficiency are necessary. A novel class of correctors based on feedback-accelerated Picard iteration (FAPI) is proposed to further enhance computational performance. With optimal feedback terms that do not require inversion of matrices, significantly faster convergence speed and higher numerical accuracy are achieved by these correctors compared with their counterparts; however, the computational complexities are comparably low. These advantages enable nonlinear engineering problems to be solved quickly and accurately, even with rough initial guesses from elementary predictors.… More > Graphic Abstract

    Fast and Accurate Predictor-Corrector Methods Using Feedback-Accelerated Picard Iteration for Strongly Nonlinear Problems

  • Open Access

    ARTICLE

    Highly Accurate Golden Section Search Algorithms and Fictitious Time Integration Method for Solving Nonlinear Eigenvalue Problems

    Chein-Shan Liu1, Jian-Hung Shen2, Chung-Lun Kuo1, Yung-Wei Chen2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.2, pp. 1317-1335, 2024, DOI:10.32604/cmes.2023.030618

    Abstract This study sets up two new merit functions, which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems. For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less, where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector. 1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues. Simultaneously, the real… More >

  • Open Access

    ARTICLE

    Nonlinear Flap-Wise Vibration Characteristics of Wind Turbine Blades Based on Multi-Scale Analysis Method

    Qifa Lang, Yuqiao Zheng*, Tiancai Cui, Chenglong Shi, Heyu Zhang

    Energy Engineering, Vol.121, No.2, pp. 483-498, 2024, DOI:10.32604/ee.2023.042437

    Abstract This work presents a novel approach to achieve nonlinear vibration response based on the Hamilton principle. We chose the 5-MW reference wind turbine which was established by the National Renewable Energy Laboratory (NREL), to research the effects of the nonlinear flap-wise vibration characteristics. The turbine wheel is simplified by treating the blade of a wind turbine as an Euler-Bernoulli beam, and the nonlinear flap-wise vibration characteristics of the wind turbine blades are discussed based on the simplification first. Then, the blade’s large-deflection flap-wise vibration governing equation is established by considering the nonlinear term involving the centrifugal force. Lastly, it is… More >

  • Open Access

    ARTICLE

    Nonlinear Components of a Block Cipher over Eisenstein Integers

    Mohammad Mazyad Hazzazi1, Muhammad Sajjad2, Zaid Bassfar3, Tariq Shah2,*, Ashwag Albakri4

    CMC-Computers, Materials & Continua, Vol.77, No.3, pp. 3659-3675, 2023, DOI:10.32604/cmc.2023.039013

    Abstract In block ciphers, the nonlinear components, also known as substitution boxes (S-boxes), are used with the purpose to induce confusion in cryptosystems. For the last decade, most of the work on designing S-boxes over the points of elliptic curves, chaotic maps, and Gaussian integers has been published. The main purpose of these studies is to hide data and improve the security levels of crypto algorithms. In this work, we design pair of nonlinear components of a block cipher over the residue class of Eisenstein integers (EI). The fascinating features of this structure provide S-boxes pair at a time by fixing… More >

  • Open Access

    ARTICLE

    Modeling Geometrically Nonlinear FG Plates: A Fast and Accurate Alternative to IGA Method Based on Deep Learning

    Se Li1, Tiantang Yu1,*, Tinh Quoc Bui2

    CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.3, pp. 2793-2808, 2024, DOI:10.32604/cmes.2023.030278

    Abstract Isogeometric analysis (IGA) is known to show advanced features compared to traditional finite element approaches. Using IGA one may accurately obtain the geometrically nonlinear bending behavior of plates with functional grading (FG). However, the procedure is usually complex and often is time-consuming. We thus put forward a deep learning method to model the geometrically nonlinear bending behavior of FG plates, bypassing the complex IGA simulation process. A long bidirectional short-term memory (BLSTM) recurrent neural network is trained using the load and gradient index as inputs and the displacement responses as outputs. The nonlinear relationship between the outputs and the inputs… More >

  • Open Access

    ARTICLE

    DUAL SOLUTIONS FOR HEAT AND MASS TRANSFER IN MHD JEFFREY FLUID IN THE PRESENCE OF HOMOGENEOUSHETEROGENEOUS REACTIONS

    C. S. K. Rajua , N. Sandeepa, J. Prakashb,1

    Frontiers in Heat and Mass Transfer, Vol.7, pp. 1-8, 2016, DOI:10.5098/hmt.7.14

    Abstract In this study, we analyzed the effects of nonlinear thermal radiation and induced magnetic field on steady two-dimensional incompressible flow of Jeffrey fluid flow past a stretching/shrinking surface in the presence of homogeneous-heterogeneous reactions. For physical relevance in this study we analyzed the behavior of homogeneous and heterogeneous profiles individually. The transformed governing equations with the help of similarity variables are solved numerically via Runge-Kutta and Newton’s method. We obtained better accuracy of the present results by differentiating with the existed published literature. The effect of pertinent parameters on velocity, induced magnetic field, temperature and concentration profiles along with the… More >

  • Open Access

    ARTICLE

    Influence of Vertical Irregularity on the Seismic Behavior of Base Isolated RC Structures with Lead Rubber Bearings under Pulse-Like Earthquakes

    Ali Mahamied1, Amjad A. Yasin1, Yazan Alzubi1,*, Jamal Al Adwan1, Issa Mahamied2

    Structural Durability & Health Monitoring, Vol.17, No.6, pp. 501-519, 2023, DOI:10.32604/sdhm.2023.028686

    Abstract Nowadays, an extensive number of studies related to the performance of base isolation systems implemented in regular reinforced concrete structures subjected to various types of earthquakes can be found in the literature. On the other hand, investigations regarding the irregular base-isolated reinforced concrete structures’ performance when subjected to pulse-like earthquakes are very scarce. The severity of pulse-like earthquakes emerges from their ability to destabilize the base-isolated structure by remarkably increasing the displacement demands. Thus, this study is intended to investigate the effects of pulse-like earthquake characteristics on the behavior of low-rise irregular base-isolated reinforced concrete structures. Within the study scope,… More >

  • Open Access

    ARTICLE

    A Novel Accurate Method for Multi-Term Time-Fractional Nonlinear Diffusion Equations in Arbitrary Domains

    Tao Hu1, Cheng Huang2, Sergiy Reutskiy3,*, Jun Lu4, Ji Lin5,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.2, pp. 1521-1548, 2024, DOI:10.32604/cmes.2023.030449

    Abstract A novel accurate method is proposed to solve a broad variety of linear and nonlinear (1+1)-dimensional and (2+1)- dimensional multi-term time-fractional partial differential equations with spatial operators of anisotropic diffusivity. For (1+1)-dimensional problems, analytical solutions that satisfy the boundary requirements are derived. Such solutions are numerically calculated using the trigonometric basis approximation for (2+1)-dimensional problems. With the aid of these analytical or numerical approximations, the original problems can be converted into the fractional ordinary differential equations, and solutions to the fractional ordinary differential equations are approximated by modified radial basis functions with time-dependent coefficients. An efficient backward substitution strategy that… More >

  • Open Access

    ARTICLE

    Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

    Muhammad Shoaib Arif1,2,*, Kamaleldin Abodayeh1, Yasir Nawaz2

    CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.2, pp. 1405-1425, 2024, DOI:10.32604/cmes.2023.028946

    Abstract This work aimed to construct an epidemic model with fuzzy parameters. Since the classical epidemic model does not elaborate on the successful interaction of susceptible and infective people, the constructed fuzzy epidemic model discusses the more detailed versions of the interactions between infective and susceptible people. The next-generation matrix approach is employed to find the reproduction number of a deterministic model. The sensitivity analysis and local stability analysis of the system are also provided. For solving the fuzzy epidemic model, a numerical scheme is constructed which consists of three time levels. The numerical scheme has an advantage over the existing… More >

  • Open Access

    ARTICLE

    Bifurcation Analysis of a Nonlinear Vibro-Impact System with an Uncertain Parameter via OPA Method

    Dongmei Huang1, Dang Hong2, Wei Li1,*, Guidong Yang1, Vesna Rajic3

    CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.1, pp. 509-524, 2024, DOI:10.32604/cmes.2023.029215

    Abstract In this paper, the bifurcation properties of the vibro-impact systems with an uncertain parameter under the impulse and harmonic excitations are investigated. Firstly, by means of the orthogonal polynomial approximation (OPA) method, the nonlinear damping and stiffness are expanded into the linear combination of the state variable. The condition for the appearance of the vibro-impact phenomenon is to be transformed based on the calculation of the mean value. Afterwards, the stochastic vibro-impact system can be turned into an equivalent high-dimensional deterministic non-smooth system. Two different Poincaré sections are chosen to analyze the bifurcation properties and the impact numbers are identified… More >

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