Article
Engineering, Multidisciplinary
Q. G. Liu, C. M. Fan, B. Sarler
Summary: The paper introduces a Localized Method of Fundamental Solutions (LMFS) for solving two-dimensional anisotropic elasticity problems by dividing the computational domain into overlapping subdomains and combining the classical Method of Fundamental Solutions (MFS) to achieve expression and calculation of the solution.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Mathematics
Junli Zhang, Hui Zheng, Chia-Ming Fan, Ming-Fu Fu
Summary: Due to the employment of fundamental solutions as basis functions, the localized method of fundamental solution can obtain more accurate numerical results than other localized methods in homogeneous problems. In this work, the LMFS is proposed for the analysis of inhomogeneous inverse Cauchy problems, where the recursive composite multiple reciprocity method is adopted to transform the original inhomogeneous problem into a higher-order homogeneous problem that can be solved directly by the LMFS.
Article
Mathematics, Applied
Yan Gu, Chia-Ming Fan, Zhuojia Fu
Summary: The LMFS method proposed in this paper is a numerical solution approach for three-dimensional elasticity problems. It combines the advantages of localized discretization schemes and the classical MFS formulation, allowing for easy handling of numerical examples with up to 100,000 unknowns on a personal computer. The advantages, disadvantages, and potential applications of the LMFS method in comparison to the classical MFS and BEM are discussed.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2021)
Article
Mathematics, Applied
Weiwei Li
Summary: In this paper, a localized version of the method of fundamental solutions (MFS) named as the localized MFS (LMFS) is applied to 2D harmonic elastic wave problems. By dividing the domain into small subdomains, LMFS can effectively solve large-scale problems in a sparse and banded system of linear equations.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Engineering, Multidisciplinary
Quan Jiang, Zhidong Zhou, Jubing Chen, Fengpeng Yang
Summary: This paper presents a new version of the method of fundamental solutions (MFS) for two-dimensional linear elasticity problems based on the stress function, deriving displacement compatibilities and boundary conditions in derivative forms. The interpolation equations are reconstructed based on the single-valuedness conditions of displacements. Numerical examples show that the proposed method is effective and has high accuracy under various boundary conditions.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Mechanics
Yan Gu, Mikhail Golub, Chia-Ming Fan
Summary: The paper introduces a new localized method of fundamental solutions (LMFS) for the numerical solution of problems with cracks in linear elastic fracture mechanics. The method divides the computational domain into sub-domains and uses local system of equations to improve computational efficiency and accuracy.
ENGINEERING FRACTURE MECHANICS
(2021)
Article
Engineering, Multidisciplinary
Aly R. El-metwaly, M. A. Kamal, Youssef F. Rashed, Hany Nasry Zaky, Ahmed S. Ismail
Summary: This paper develops a meshless method of fundamental solutions to solve couple stress problems, even in the presence of body forces. It derives suitable new particular solutions that maintain the meshless nature of the technique. The paper discusses in detail the derivation of the new particular solutions for generalizing displacements and tractions. Several examples, including stress concentration and problems with body forces, are tested to demonstrate the efficiency and strength of the derived formulation.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Shuainan Liu, Po-Wei Li, Chia-Ming Fan, Yan Gu
Summary: This paper explores the use of LMFS for numerically solving general transient convection-diffusion-reaction equations in 2D and 3D materials. The method utilizes CN time-stepping technology and CCS approximation for solving boundary value problems efficiently.Various benchmark examples demonstrate the effectiveness and feasibility of the approach compared to traditional methods like MFS and BEM.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Mathematics, Applied
Shuainan Liu, Zhuojia Fu, Yan Gu
Summary: This paper presents the first attempt to apply the localized method of fundamental solutions (LMFS) and domain-decomposition technique for solving steady-state heat conduction problems in two-dimensional anisotropic layered materials. The proposed algorithm is accurate, stable, and computationally efficient for large-scale multi-layered materials.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2022)
Article
Mathematics, Applied
Yan Gu, Ji Lin, Chia -Ming Fan
Summary: Accurate and efficient analysis of the coupled electroelastic behavior of piezoelectric structures is challenging. The method of fundamental solutions (MFS) has emerged as a popular meshless boundary collocation method, but it is computationally expensive. In this paper, a localized version of the MFS (LMFS) is proposed for electroelastic analysis of 2D piezoelectric structures. The LMFS produces banded and sparse coefficient matrices, making it attractive for large-scale simulations.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2023)
Article
Engineering, Multidisciplinary
Yanan Xing, Lina Song, Chia-Ming Fan
Summary: In this paper, a generalized finite difference method is proposed for solving elasticity interface problems, which can transform the problem into coupled non-interface subproblems and handle complex geometrical interfaces well. The method also effectively deals with interface conditions with derivatives by using linear summation of nearby nodal values. Numerical examples demonstrate the accuracy and stability of the proposed method, showing that the H-1 error converges at a similar rate to the L-2 error and the size of jumps in interface conditions has minimal impact on stability.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Mathematics, Applied
Zengtao Chen, Fajie Wang
Summary: This paper presents a simple formula to determine the number of supporting nodes in the localized method of fundamental solutions (LMFS), which can determine a reasonable number of supporting nodes based on node spacing. Numerical experiments validated the effectiveness of the proposed methodology, providing a quantitative parameter selection strategy for the LMFS method.
Article
Mechanics
Piaopiao Peng, Heng Cheng, Yumin Cheng
Summary: This study presents a fast meshless method, the hybrid reproducing kernel particle method (HRKPM), for solving three-dimensional (3D) elasticity problems. The equilibrium equations of 3D elasticity are divided into three groups, each containing two equilibrium equations. By coupling the discrete equations for solving two arbitrary groups of equations, the complete solution of 3D elasticity can be obtained. The numerical results show that the HRKPM performs better than RKPM in solution efficiency.
INTERNATIONAL JOURNAL OF APPLIED MECHANICS
(2023)
Article
Mathematics, Applied
J. M. Granados, C. A. Bustamante, W. F. Florez
Summary: The meshless Method of Approximate Particular Solutions (MAPS) is used to solve natural, forced, and mixed convection heat transfer problems by approximating temperature and velocity with particular solutions of Poisson and Stokes equations. A relaxation strategy is implemented to couple momentum and energy equations and avoid convergence issues. The numerical scheme is able to accurately solve heat convection problems with various boundary conditions and geometries.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Computer Science, Interdisciplinary Applications
Junli Zhang, Chenchen Yang, Hui Zheng, Chia-Ming Fan, Ming-Fu Fu
Summary: In this paper, the newly-developed localized method of fundamental solutions (LMFS) is extended to analyze multidimensional boundary value problems governed by inhomogeneous partial differential equations (PDEs). The combination of the RC-MRM and the LMFS can directly analyze inhomogeneous governing equation and avoid troublesome caused by the two-steps schemes. The proposed scheme demonstrates high accuracy and efficiency based on numerical examples and systematic investigations.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Mathematics, Applied
Chein-Shan Liu, Fajie Wang, Yan Gu
APPLIED MATHEMATICS LETTERS
(2018)
Article
Mathematics, Applied
Yan Gu, Xiaoqiao He, Wen Chen, Chuanzeng Zhang
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2018)
Article
Mathematics, Applied
Yao-Ming Zhang, Fang-Ling Sun, Wen-Zhen Qu, Yan Gu, Der-Liang Young
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2018)
Article
Computer Science, Interdisciplinary Applications
Wenzhen Qu, Changjun Zheng, Yaoming Zhang, Yan Gu, Fajie Wang
COMPUTERS & STRUCTURES
(2018)
Article
Engineering, Mechanical
Yan Gu, Chuanzeng Zhang, Wenzhen Qu, Jieyu Ding
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2018)
Article
Computer Science, Interdisciplinary Applications
Wenzhen Qu, Wen Chen, Zhuojia Fu, Yan Gu
MATHEMATICS AND COMPUTERS IN SIMULATION
(2018)
Article
Engineering, Multidisciplinary
Wenzhen Qu, Yan Gu, Yaoming Zhang, Chia-Ming Fan, Chuanzeng Zhang
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2019)
Article
Mathematics, Applied
Chein-Shan Liu, Fajie Wang, Yan Gu
APPLIED MATHEMATICS LETTERS
(2019)
Article
Engineering, Multidisciplinary
Jun Lei, Yanjie Xu, Yan Gu, Chia-Ming Fan
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2019)
Article
Computer Science, Interdisciplinary Applications
Yan Gu, Wenzhen Qu, Wen Chen, Lina Song, Chuanzeng Zhang
JOURNAL OF COMPUTATIONAL PHYSICS
(2019)
Article
Computer Science, Hardware & Architecture
Guy E. Blelloch, Yan Gu, Julian Shun, Yihan Sun
JOURNAL OF THE ACM
(2020)
Article
Computer Science, Information Systems
Shangdi Yu, Yiqiu Wang, Yan Gu, Laxman Dhulipala, Julian Shun
Summary: This paper introduces the ParChain framework for designing parallel hierarchical agglomerative clustering algorithms, which achieve better speed and memory utilization compared to existing algorithms. Key optimizations such as range query and caching significantly contribute to the efficiency of the algorithms.
PROCEEDINGS OF THE VLDB ENDOWMENT
(2021)
Proceedings Paper
Computer Science, Information Systems
Yiqiu Wang, Shangdi Yu, Yan Gu, Julian Shun
Summary: This paper presents new parallel algorithms for generating Euclidean minimum spanning trees and spatial clustering hierarchies, which are theoretically efficient and outperform existing serial and parallel algorithms in terms of both work and space. The algorithms introduce a new notion of well-separation and memory optimization, leading to significant improvements in performance on large real-world and synthetic data sets.
SIGMOD '21: PROCEEDINGS OF THE 2021 INTERNATIONAL CONFERENCE ON MANAGEMENT OF DATA
(2021)
Proceedings Paper
Computer Science, Information Systems
Yiqiu Wang, Yan Gu, Julian Shun
SIGMOD'20: PROCEEDINGS OF THE 2020 ACM SIGMOD INTERNATIONAL CONFERENCE ON MANAGEMENT OF DATA
(2020)
Article
Mathematics, Applied
Manh Tuan Hoang, Matthias Ehrhardt
Summary: In this paper, a simple approach for solving stiff problems is proposed. Through nonlinear approximation and rigorous mathematical analysis, a class of explicit second-order one-step methods with L-stability and second-order convergence are constructed. The proposed methods generalize and improve existing nonstandard explicit integration schemes, and can be extended to higher-order explicit one-step methods.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Jian Liu, Zengqin Zhao
Summary: In this article, we investigate p(x)-biharmonic equations involving Leray-Lions type operators and Hardy potentials. Some new theorems regarding the existence of generalized solutions are reestablished for such equations when the Leray-Lions type operator and the nonlinearity satisfy suitable hypotheses in variable exponent Lebesgue spaces.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Chengcheng Cheng, Rong Yuan
Summary: This paper investigates the spreading dynamics of a nonlocal diffusion KPP model with free boundaries in time almost periodic media. By applying the novel positive time almost periodic function and satisfying the threshold condition for the kernel function, the unique asymptotic spreading speed of the free boundary problem is accurately expressed.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Xia Wang, Xin Meng, Libin Rong
Summary: In this study, a multiscale model incorporating the modes of infection and types of immune responses of HCV is developed. The basic and immune reproduction numbers are derived and five equilibria are identified. The global asymptotic stability of the equilibria is established using Lyapunov functions, highlighting the significant impact of the reproduction numbers on the overall stability of the model.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Junpu Li, Lan Zhang, Shouyu Cai, Na Li
Summary: This research proposes a regularized singular boundary method for quickly calculating the singularity of the special Green's function at origin. By utilizing the special Green's function and the origin intensity factor technique, an explicit intensity factor suitable for three-dimensional ocean dynamics is derived. The method does not involve singular integrals, resulting in improved computational efficiency and accuracy.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Ying Dong, Shuai Zhang, Yichen Zhang
Summary: This paper investigates a 2D chemotaxis-consumption system with rotation and no-flux-Dirichlet boundary conditions. It proves that under certain conditions on the rotation angle, the corresponding initial-boundary value problem has a classical solution that blows up at a finite time.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Shuhan Yao, Qi Hong, Yuezheng Gong
Summary: In this article, an extended quadratic auxiliary variable method is introduced for a droplet liquid film model. The method shows good numerical solvability and accuracy.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Tong Wang, Binxiang Dai
Summary: This paper investigates the spreading speed and traveling wave of an impulsive reaction-diffusion model with non-monotone birth function and age structure, which models the evolution of annually synchronized emergence of adult population with maturation. The result extends the work recently established in Bai, Lou, and Zhao (J. Nonlinear Sci. 2022). Numerical simulations are conducted to illustrate the findings.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Dinghao Zhu, Xiaodong Zhu
Summary: This paper constructs the soliton solutions of the KdV equation with non-zero background using the Riemann-Hilbert approach. The irregular Riemann-Hilbert problem is first constructed by direct and inverse scattering transform, and then regularized by introducing a novel transformation. The residue theorem is applied to derive the multi-soliton solutions at the simple poles of the Riemann-Hilbert problem. In particular, the interaction dynamics of the two-soliton solution are illustrated by considering their evolutions at different time.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Danhua He, Liguang Xu
Summary: This paper investigates the stability of conformable fractional delay differential systems with impulses. By establishing a conformable fractional Halanay inequality, the paper provides sufficient criteria for the conformable exponential stability of the systems.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Fei Sun, Xiaoli Li, Hongxing Rui
Summary: This paper presents a high-order numerical scheme for solving the compressible wormhole propagation problem. The scheme utilizes the fourth-order implicit Runge-Kutta method and the block-centered finite difference method, along with high-order interpolation technique and cut-off approach to achieve high-order and bound-preserving.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Zhijie Du, Huoyuan Duan
Summary: This study analyzes a direct discretization method for computing the eigenvalues of the Maxwell eigenproblem. It utilizes a specific finite element space and the classical variational formulation, and proves the convergence of the obtained finite element solutions.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Hongliang Li, Pingbing Ming
Summary: This paper proposes an asymptotic-preserving finite element method for solving a fourth order singular perturbation problem, which preserves the asymptotic transition of the underlying partial differential equation. The NZT element is analyzed as a representative, and a linear convergence rate is proved for the solution with sharp boundary layer. Numerical examples in two and three dimensions are consistent with the theoretical prediction.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Shuyang Xue, Yongli Song
Summary: This paper investigates the spatiotemporal dynamics of the memory-based diffusion equation driven by memory delay and nonlocal interaction. The nonlocal interaction, characterized by the given Green function, leads to inhomogeneous steady states with any modes. The joint effect of nonlocal interaction and memory delay can result in spatially inhomogeneous Hopf bifurcation and Turing-Hopf bifurcation.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Baoquan Zhou, Ningzhong Shi
Summary: This paper develops a stochastic SEIS epidemic model perturbed by Black-Karasinski process and investigates the impact of random fluctuations on disease outbreak. The results show that random fluctuations facilitate disease outbreak, and a sufficient condition for disease persistence is established.
APPLIED MATHEMATICS LETTERS
(2024)
