Article
Mathematics, Applied
Lijuan Nong, An Chen
Summary: This paper discusses an efficient difference scheme for solving time-fractional equations in two space dimensions, utilizing the modified L1 method and fast discrete sine transform technique. A fast Crank-Nicolson compact difference scheme is developed, proven to be stable and accurate, with the method of adding correction terms to handle nonsmooth problems efficiently. Numerical examples are provided to demonstrate the effectiveness of the proposed scheme.
JOURNAL OF FUNCTION SPACES
(2021)
Article
Mathematics, Applied
An Chen
Summary: This paper presents two robust fully discrete finite element methods for the numerical approximation of the modified anomalous subdiffusion model. The error estimates for semidiscrete and fully discrete schemes are investigated with respect to data regularity. Numerical comparisons with a Crank-Nicolson finite element method demonstrate the efficiency of the proposed methods and validate the theoretical results.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2021)
Article
Mathematics, Applied
Huaming Yi, Yanping Chen, Yang Wang, Yunqing Huang
Summary: The article proposes and analyzes the optimal error estimates of a second-order backward difference formula (BDF2) numerical scheme for the semi-linear parabolic interface problems. The partially penalized immersed finite element (PPIFE) methods are used for the spatial discretization to resolve the discontinuity of the diffusion coefficient across the interface. The classical extrapolation method is adopted to treat the nonlinear term, which effectively avoids the complicated numerical calculation of the nonlinearity. The error analysis is based on the corresponding time-discrete system, which neatly splits the error into two parts: the temporal discretization error and the spatial discretization error. The optimal error estimates in both L2 norm and semi-H1 norm can be unconditionally derived without the coupling condition of time step and space size. Numerical experiments are conducted to confirm the theoretical analysis.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Correction
Mathematics, Applied
Jiankang Shi, Minghua Chen, Yubin Yan, Jianxiong Cao
Summary: This paper discusses subdiffusion equations with a Caputo fractional derivative and develops a correction scheme to improve the approximation of interpolation. By calculating the coefficients of the correction approximation and using the Bose-Einstein integral method, a higher convergence rate can be achieved.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Dietmar Gallistl, Ngoc Tien Tran
Summary: This paper analyzes a regularization scheme for the Monge-Ampere equation and proposes stability estimates and convergence results. The main application is to provide guaranteed a posteriori error bounds in continuously differentiable finite element approximations.
NUMERISCHE MATHEMATIK
(2023)
Article
Computer Science, Interdisciplinary Applications
Arttu Polojarvi
Summary: This paper introduces a model for describing the three-dimensional continuous failure process of an ice sheet, based on the combined finite-discrete element method. The model is carefully validated against experimental results, showing convincing agreement between the modelled and experimental failure processes.
COMPUTERS & STRUCTURES
(2022)
Article
Mathematics, Applied
Surendra Nepal, Yosief Wondmagegne, Adrian Muntean
Summary: We propose a fully discrete scheme for the numerical approximation of a moving-boundary problem involving diffusants penetration into rubber. The scheme combines the Galerkin finite element method for space discretization with the backward Euler method for time discretization. In addition to addressing the existence and uniqueness of solutions, we assume sufficient regularity of the moving boundary problem's solution and derive a priori error estimates for the concentration of diffusants and the position of the moving boundary. Our numerical results demonstrate the theoretical order of convergence in different physical parameter regimes. (c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mechanics
Wei Guan, Ying Dai, Wenxiao Li, Yang Qu, Pengfei He
Summary: This study investigated the impact of the geometry of textile composite reinforcements on the mechanical properties of the final part, proposed an improved semi-discrete simulation method, and conducted experiments to validate the results, showing a good agreement between simulation and experimental results.
COMPOSITE STRUCTURES
(2022)
Article
Mathematics, Applied
Yun-Shun Wu, Wen-Tao Cheng, Wei-Ping Zhou, Lun-Zhi Deng
Summary: This paper focuses on constructing new modified Gamma operators using the second central moment of classic Gamma operators and investigating their quantitative properties. Global results are established in certain weighted spaces, including Voronovskaya-type asymptotic formula and point-wise estimates. Weighted approximation of these operators is also discussed, along with quantitative Voronovskaya-type asymptotic formula and Gruss Voronovskaya-type approximation.
JOURNAL OF FUNCTION SPACES
(2021)
Article
Mathematics, Applied
Luigi C. Berselli, Michael Ruzicka
Summary: In this paper, we study parabolic problems with stress tensor depending only on the symmetric gradient and develop a new approximation method to obtain global regularity results for general potential operators. We prove natural second order spatial regularity up to the boundary under homogeneous Dirichlet boundary conditions. The same method also yields regularity results in the elliptic case and for 1 < p <= 2, confirming known results in a different way.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Engineering, Civil
Armin Yousefi Kanani, Xing-Er Wang, Xiaonan Hou, Allan E. W. Rennie, Jianqiao Ye
Summary: The research in this paper used an innovative method to modify adhesively bonded joints for improved mechanical performance. Additive manufacturing was employed to produce sacrificial support structures, which allowed for accurate fillet formation at the end of the bond line. Finite element and discrete element methods were also used to study stress distribution and joint failure load, which showed significant improvements in mechanical performance.
ENGINEERING STRUCTURES
(2023)
Article
Computer Science, Artificial Intelligence
Judy Yangjun Lin, Shaoyan Guo, Longhan Xie, Ruxu Du, Gu Xu
Summary: In this study, the issue of initializing dual weight vectors in the semi-discrete optimal transport setting was addressed by discretizing the domain of the source distribution, approximating Laguerre cells, and utilizing local perturbation and boundary methods. Theoretical results of the computation process were investigated and an efficient algorithm was provided to ensure successful computation.
KNOWLEDGE-BASED SYSTEMS
(2021)
Article
Computer Science, Interdisciplinary Applications
O. Nikan, Z. Avazzadeh, J. A. Tenreiro Machado
Summary: This paper introduces a meshless method for approximating solutions of nonlinear reaction-diffusion models. Time discretization is done using a weighted discrete scheme, while spatial discretization employs RBF-FD. The approach benefits from a local collocation technique for estimating the differential operators, enhancing computational efficiency.
JOURNAL OF COMPUTATIONAL SCIENCE
(2021)
Article
Automation & Control Systems
Bangti Jin, Zhi Zhou
Summary: This work focuses on the numerical recovery of a spatially dependent diffusion coefficient in a subdiffusion model from distributed observations. The study establishes the well-posedness of the continuous formulation and proves the convergence of the discrete solutions to the continuous problem as discretization parameters tend to zero. Convergence rates for discrete approximations to the exact coefficient are derived under additional regularity conditions, supported by illustrative numerical results.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2021)
Article
Mathematics, Applied
Yanping Chen, Huaming Yi, Yang Wang, Yunqing Huang
Summary: In this paper, we propose and analyze the two-grid immersed finite element methods for semi-linear parabolic interface problems with discontinuous diffusion coefficients. The methods use immersed finite element methods for spatial discretization and allow meshes that are not aligned with the interface. Optimal error estimates are derived for both spatially semi-discrete schemes and fully discrete schemes. The two-grid algorithms based on the Newton methods are used to handle the nonlinear term. Theoretical and numerical results demonstrate that the two-grid immersed finite element methods can achieve optimal convergence order when the coarse mesh satisfies certain conditions.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Mathematics, Applied
Shujun Shen, Fawang Liu, Vo V. Anh
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2019)
Article
Mathematics, Applied
Ruige Chen, Fawang Liu, Vo Anh
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2019)
Article
Mathematics, Applied
Zeting Liu, Fawang Liu, Fanhai Zeng
APPLIED NUMERICAL MATHEMATICS
(2019)
Article
Mathematics, Applied
Fawang Liu, Libo Feng, Vo Anh, Jing Li
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2019)
Article
Mathematics, Applied
Mengchen Zhang, Ming Shen, Fawang Liu, Hongmei Zhang
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2019)
Article
Mathematics, Applied
Jinghua Zhang, Fawang Liu, Vo V. Anh
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2019)
Article
Mathematics, Applied
Libo Feng, Fawang Liu, Ian Turner
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2019)
Article
Mathematics, Applied
Chunyan Liu, Liancun Zheng, Mingyang Pan, Ping Lin, Fawang Liu
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2019)
Article
Mathematics, Applied
Ruige Chen, Fawang Liu, Vo Anh
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2019)
Article
Engineering, Multidisciplinary
Y. H. Shi, F. Liu, Y. M. Zhao, F. L. Wang, I. Turner
APPLIED MATHEMATICAL MODELLING
(2019)
Article
Physics, Multidisciplinary
Chunyan Liu, Liancun Zheng, Ping Lin, Mingyang Pan, Fawang Liu
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2019)
Article
Mathematics, Applied
Minling Zheng, Fawang Liu, Zhengmeng Jin
APPLIED MATHEMATICS AND COMPUTATION
(2020)
Article
Mathematics, Applied
Libo Feng, Fawang Liu, Ian Turner
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2020)
Article
Engineering, Multidisciplinary
A. A. Aganin, A. I. Davletshin
Summary: A mathematical model of interaction of weakly non-spherical gas bubbles in liquid is proposed in this paper. The model equations are more accurate and compact compared to existing analogs. Five problems are considered for validation, and the results show good agreement with experimental data and numerical solutions. The model is also used to analyze the behavior of bubbles in different clusters, providing meaningful insights.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Hao Wu, Jie Sun, Wen Peng, Lei Jin, Dianhua Zhang
Summary: This study establishes an analytical model for the coupling of temperature, deformation, and residual stress to explore the mechanism of residual stress formation in hot-rolled strip and how to control it. The accuracy of the model is verified by comparing it with a finite element model, and a method to calculate the critical exit crown ratio to maintain strip flatness is proposed.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Shengwen Tu, Naoki Morita, Tsutomu Fukui, Kazuki Shibanuma
Summary: This study aimed to extend the finite element method to cope with elastic-plastic problems by introducing the s-version FEM. The s-version FEM, which overlays a set of local mesh with fine element size on the conventional FE mesh, simplifies domain discretisation and provides accurate numerical predictions. Previous applications of the s-version FEM were limited to elastic problems, lacking instructions for stress update in plasticity. This study presents detailed instructions and formulations for addressing plasticity problems with the s-version FEM and analyzes a stress concentration problem with linear/nonlinear material properties.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Bo Fan, Zhongmin Wang
Summary: A 3D rotating hyperelastic composite REF model was proposed to analyze the influence of tread structure and rotating angular speed on the vibration characteristics of radial tire. Nonlinear dynamic differential equations and modal equations were established to study the effects of internal pressure, tread pressure sharing ratio, belt structure, and rotating angular speed on the vibration characteristics.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
X. W. Chen, Z. Q. Yue, Wendal Victor Yue
Summary: This paper examines the axisymmetric problem of a flat mixed-mode annular crack near and parallel to an arbitrarily graded interface in functionally graded materials (FGMs). The crack is modeled as plane circular dislocation loop and an efficient solution for dislocation in FGMs is used to calculate the stress field at the crack plane. The analytical solutions of the stress intensity factors are obtained and numerical study is conducted to investigate the fracture mechanics of annular crack in FGMs.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Xumin Guo, Jianfei Gu, Hui Li, Kaihua Sun, Xin Wang, Bingjie Zhang, Rangwei Zhang, Dongwu Gao, Junzhe Lin, Bo Wang, Zhong Luo, Wei Sun, Hui Ma
Summary: In this study, a novel approach combining the transfer matrix method and lumped parameter method is proposed to analyze the vibration response of aero-engine pipelines under base harmonic and random excitations. The characteristics of the pipelines are investigated through simulation and experiments, validating the effectiveness of the proposed method.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Xiangyu Sha, Aizhong Lu, Ning Zhang
Summary: This paper investigates the stress and displacement of a layered soil with a fractional-order viscoelastic model under time-varying loads. The correctness of the solutions is validated using numerical methods and comparison with existing literature. The research findings are of significant importance for exploring soil behavior and its engineering applications under time-varying loads.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Thuy Dong Dang, Thi Kieu My Do, Minh Duc Vu, Ngoc Ly Le, Tho Hung Vu, Hoai Nam Vu
Summary: This paper investigates the nonlinear torsional buckling of corrugated core sandwich toroidal shell segments with functionally graded graphene-reinforced composite (FG-GRC) laminated coatings in temperature change using the Ritz energy method. The results show the significant beneficial effects of FG-GRC laminated coatings and corrugated core on the nonlinear buckling responses of structures.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Zhihao Zhai, Chengbiao Cai, Qinglai Zhang, Shengyang Zhu
Summary: This paper investigates the effect of localized cracks induced by environmental factors on the dynamic performance and service life of ballastless track in high-speed railways. A mathematical approach for forced vibrations of Mindlin plates with a side crack is derived and implemented into a train-track coupled dynamic system. The accuracy of this approach is verified by comparing with simulation and experimental results, and the dynamic behavior of the side crack under different conditions is analyzed.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
James Vidler, Andrei Kotousov, Ching-Tai Ng
Summary: The far-field methodology, developed by J.C. Maxwell, is utilized to estimate the effective third order elastic constants of composite media containing random distribution of spherical particles. The results agree with previous studies and can be applied to homogenization problems in other fields.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Kim Q. Tran, Tien-Dat Hoang, Jaehong Lee, H. Nguyen-Xuan
Summary: This study presents novel frameworks for graphene platelets reinforced functionally graded triply periodic minimal surface (GPLR-FG-TPMS) plates and investigates their performance through static and free vibration analyses. The results show that the mass density framework has potential for comparing different porous cores and provides a low weight and high stiffness-to-weight ratio. Primitive plates exhibit superior performance among thick plates.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Bence Hauck, Andras Szekrenyes
Summary: This study explores several methods for computing the J-integral in laminated composite plate structures with delamination. It introduces two special types of plate finite elements and a numerical algorithm. The study presents compact formulations for calculating the J-integral and applies matrix multiplication to take advantage of plate transition elements. The models and algorithms are applied to case studies and compared with analytical and previously used finite element solutions.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Wu Ce Xing, Jiaxing Wang, Yan Qing Wang
Summary: This paper proposes an effective mathematical model for bolted flange joints to study their vibration characteristics. By modeling the flange and bolted joints, governing equations are derived. Experimental studies confirm that the model can accurately predict the vibration characteristics of multiple-plate structures.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Pingchao Yu, Li Hou, Ke Jiang, Zihan Jiang, Xuanjun Tao
Summary: This paper investigates the imbalance problem in rotating machinery and finds that mass imbalance can induce lateral-torsional coupling vibration. By developing a model and conducting detailed analysis, it is discovered that mass imbalance leads to nonlinear time-varying characteristics and there is no steady-state torsional vibration in small unbalanced rotors. Under largely unbalanced conditions, both resonant and unstable behavior can be observed, and increasing lateral damping can suppress instability and reduce lateral amplitude in the resonance region.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Yong Cao, Ziwen Guo, Yilin Qu
Summary: This paper investigates the mechanically induced electric potential and charge redistribution in a piezoelectric semiconductor cylindrical shell. The results show that doping levels can affect the electric potentials and mechanical displacements, and alter the peak position of the zeroth-order electric potential. The doping level also has an inhibiting effect on the first natural frequency. These findings are crucial for optimizing the design and performance of cylindrical shell-shaped sensors and energy harvesters.
APPLIED MATHEMATICAL MODELLING
(2024)
