Xuechuan Wang¹, Wei He^1,*, 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

Shuo Yang¹, Yongxing Shen^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.26, No.4, pp. 1-1, 2023, DOI:10.32604/icces.2023.09207

Abstract Fatigue refers to repeated cyclic loading well below the ultimate failure stress of the structure. It accounts for most mechanical failures, and thus deserves serious consideration in engineering practice. Phase field approach is a powerful tool for fracture simulation, which tracks arbitrary and complicated crack paths without extra criterion. This approach has been widely applied to various cracking problems, such as shell fracture, beam fracture , etc. The phase field approach for fracture has been adapted for fatigue fracture in recent years. Due to the mesh requirement of the phase field approach and the large amount of load steps of… More >

Pushpendra Kumar^1,*, Vedat Suat Erturk², V. Govindaraj¹, Dumitru Baleanu^3,4,5

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 2487-2506, 2023, DOI:10.32604/cmes.2023.026009

Abstract In this article, we introduce a nonlinear Caputo-type snakebite envenoming model with memory. The well-known Caputo fractional derivative is used to generalize the previously presented integer-order model into a fractional-order sense. The numerical solution of the model is derived from a novel implementation of a finite-difference predictor-corrector (L1-PC) scheme with error estimation and stability analysis. The proof of the existence and positivity of the solution is given by using the fixed point theory. From the necessary simulations, we justify that the first-time implementation of the proposed method on an epidemic model shows that the scheme is fully suitable and time-efficient… More >

M. F. Elettreby^{1, 2, *}, Ali S. Alqahtani¹, E. Ahmed²

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 665-682, 2020, DOI:10.32604/cmes.2020.09194

Abstract Drug resistance is one of the most serious phenomena in financial, economic and medical terms. The present paper proposes and investigates a simple mathematical fractional-order model for the phenomenon of multi-drug antimicrobial resistance. The model describes the dynamics of the susceptible and three kinds of infected populations. The first class of the infected society responds to the first antimicrobial drug but resists to the second one. The second infected individuals react to the second antimicrobial drug but resist to the first one. The third class shows resistance to both of the two drugs. We formulate the model and associate it… More >

Ali Maghami¹, Farzad Shahabian¹, Seyed Mahmoud Hosseini^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.121, No.3, pp. 877-907, 2019, DOI:10.32604/cmes.2019.08019

Abstract The suitability of six higher order root solvers is examined for solving the nonlinear equilibrium equations in large deformation analysis of structures. The applied methods have a better convergence rate than the quadratic Newton-Raphson method. These six methods do not require higher order derivatives to achieve a higher convergence rate. Six algorithms are developed to use the higher order methods in place of the NewtonRaphson method to solve the nonlinear equilibrium equations in geometrically nonlinear analysis of structures. The higher order methods are applied to both continuum and discrete problems (spherical shell and dome truss). The computational cost and the… More >

H. Theilig¹

Structural Durability & Health Monitoring, Vol.6, No.3&4, pp. 239-272, 2010, DOI:10.3970/sdhm.2010.006.239

Abstract The aim of this paper is to give an overview to some problems and solutions of the fracture analysis of 2D structures. It will be shown that the common computer-aided two-dimensional fatigue crack path simulation can be considerably improved in accuracy by using a predictor-corrector procedure in combination with the modified virtual crack closure integral (MVCCI) method. Furthermore the paper presents an improved finite element technique for the calculation of stress intensity factors of mixed mode problems by the MVCCI Method. The procedure is devised to compute the separated strain energy release rates by using the convergence of two separate… More >

Ali Shokri¹, Mehdi Dehghan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.4, pp. 333-358, 2012, DOI:10.3970/cmes.2012.084.333

Abstract The Ginzburg-Landau equation has been used as a mathematical model for various pattern formation systems in mechanics, physics and chemistry. In this paper, we study the complex Ginzburg-Landau equation in two spatial dimensions with periodical boundary conditions. The method numerically approximates the solution by collocation method based on radial basis functions (RBFs). To improve the numerical results we use a predictor-corrector scheme. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the accuracy and efficiency of the presented method. More >