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  • Open Access

    ARTICLE

    Optimal Shape Factor and Fictitious Radius in the MQ-RBF: Solving Ill-Posed Laplacian Problems

    Chein-Shan Liu1, Chung-Lun Kuo1, Chih-Wen Chang2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.3, pp. 3189-3208, 2024, DOI:10.32604/cmes.2023.046002

    Abstract To solve the Laplacian problems, we adopt a meshless method with the multiquadric radial basis function (MQ-RBF) as a basis whose center is distributed inside a circle with a fictitious radius. A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function. A sample function is interpolated by the MQ-RBF to provide a trial coefficient vector to compute the merit function. We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm. The novel method provides the optimal values of parameters and,… More >

  • Open Access

    ARTICLE

    Novel Investigation of Stochastic Fractional Differential Equations Measles Model via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel

    Saima Rashid1,2,*, Fahd Jarad3,4

    CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.3, pp. 2289-2327, 2024, DOI:10.32604/cmes.2023.028773

    Abstract Because of the features involved with their varied kernels, differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues. In this paper, we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels. In this approach, the overall population was separated into five cohorts. Furthermore, the descriptive behavior of the system was investigated, including prerequisites for the positivity of solutions, invariant domain of the solution, presence and stability of equilibrium points, and sensitivity analysis. We included a stochastic element in every cohort and… More >

  • Open Access

    ARTICLE

    Improving Video Watermarking through Galois Field GF(24) Multiplication Tables with Diverse Irreducible Polynomials and Adaptive Techniques

    Yasmin Alaa Hassan1,*, Abdul Monem S. Rahma2

    CMC-Computers, Materials & Continua, Vol.78, No.1, pp. 1423-1442, 2024, DOI:10.32604/cmc.2023.046149

    Abstract Video watermarking plays a crucial role in protecting intellectual property rights and ensuring content authenticity. This study delves into the integration of Galois Field (GF) multiplication tables, especially GF(24), and their interaction with distinct irreducible polynomials. The primary aim is to enhance watermarking techniques for achieving imperceptibility, robustness, and efficient execution time. The research employs scene selection and adaptive thresholding techniques to streamline the watermarking process. Scene selection is used strategically to embed watermarks in the most vital frames of the video, while adaptive thresholding methods ensure that the watermarking process adheres to imperceptibility criteria, maintaining the video’s visual quality.… More >

  • Open Access

    ARTICLE

    A Novel Method for Linear Systems of Fractional Ordinary Differential Equations with Applications to Time-Fractional PDEs

    Sergiy Reutskiy1, Yuhui Zhang2,*, Jun Lu3,*, Ciren Pubu4

    CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.2, pp. 1583-1612, 2024, DOI:10.32604/cmes.2023.044878

    Abstract This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations (FODEs) which have been widely used in modeling various phenomena in engineering and science. An approximate solution of the system is sought in the form of the finite series over the Müntz polynomials. By using the collocation procedure in the time interval, one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure. This technique also serves as the basis for solving the time-fractional partial differential equations (PDEs). The modified radial basis… More >

  • Open Access

    PROCEEDINGS

    The Method of Moments for Electromagnetic Scattering Analysis Accelerated by the Polynomial Chaos Expansion in Infinite Domains

    Yujing Ma1,*, Leilei Chen2,3, Haojie Lian3,4, Zhongwang Wang2,3

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.28, No.1, pp. 1-1, 2023, DOI:10.32604/icces.2023.010585

    Abstract An efficient method of moments (MoM) based on polynomial chaos expansion(PCE) is applied to quickly calculate the electromagnetic scattering problems. The triangle basic functions are used to discretize the surface integral equations. The PCE is utilized to accelerate the MoM by constructing a surrogate model for univariate and bivariate analysis[1]. The mathematical expressions of the surrogate model for the radar cross-section (RCS) are established by considering uncertain parameters such as bistatic angle, incident frequency, and dielectric constant[2,3]. By using the example of a scattering cylinder with analytical solution, it is verified that the MoM accelerated by PCE presents a considerable… More >

  • Open Access

    PROCEEDINGS

    Fragile Points Method for Modeling Complex Structural Failure

    Mingjing Li1,*, Leiting Dong1, Satya N. Atluri2

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.4, pp. 1-2, 2023, DOI:10.32604/icces.2023.09689

    Abstract The Fragile Points Method (FPM) is a discontinuous meshless method based on the Galerkin weak form [1]. In the FPM, the problem domain is discretized by spatial points and subdomains, and the displacement trial function of each subdomain is derived based on the points within the support domain. For this reason, the FPM doesn’t suffer from the mesh distortion and is suitable to model complex structural deformations. Furthermore, similar to the discontinuous Galerkin finite element method, the displacement trial functions used in the FPM is piece-wise continuous, and the numerical flux is introduced across each interior interface to guarantee the… 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

    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 >

  • Open Access

    PROCEEDINGS

    Robust Shape Optimization of Sound Barriers Based on Isogeometric Boundary Element Method and Polynomial Chaos Expansion

    Xuhang Lin1, Haibo Chen1,*

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.1, pp. 1-1, 2023, DOI:10.32604/icces.2023.09388

    Abstract As an important and useful tool for reducing noise, the sound barrier is of practical significance. The sound barrier has different noise reduction effects for different sizes, shapes and properties of the sound absorbing material. Liu et al. [1] have performed shape optimization of sound barriers by using isogeometric boundary element method and method of moving asymptotes (MMA). However, in engineering practice, it is difficult to determine some parameters accurately such as material properties, geometries, external loads. Therefore, it is necessary to consider these uncertainty conditions in order to ensure the rationality of the numerical calculation of engineering problems. In… More >

  • Open Access

    ARTICLE

    A CHEBYSHEV SPECTRAL METHOD FOR HEAT AND MASS TRANSFER IN MHD NANOFLUID FLOW WITH SPACE FRACTIONAL CONSTITUTIVE MODEL

    Shina D. Oloniiju , Sicelo P. Goqo, Precious Sibanda

    Frontiers in Heat and Mass Transfer, Vol.13, pp. 1-8, 2019, DOI:10.5098/hmt.13.19

    Abstract In some recent studies, it has been suggested that non–Newtonian fluid flow can be modeled by a spatially non–local velocity, whose dynamics are described by a fractional derivative. In this study, we use the space fractional constitutive relation to model heat and mass transfer in a nanofluid. We present a numerically accurate algorithm for approximating solutions of the system of fractional ordinary differential equations describing the nanofluid flow. We present numerically stable differentiation matrices for both integer and fractional order derivatives defined by the one–sided Caputo derivative. The differentiation matrices are based on the series expansion of the unknown functions… More >

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