Article
Engineering, Multidisciplinary
Zakieh Avazzadeh, Omid Nikan, Anh Tuan Nguyen, Van Tien Nguyen
Summary: This paper presents an efficient stabilized meshless technique with a hybrid kernel to simulate the fractional Rayleigh-Stokes problem for an edge in a viscoelastic fluid. The proposed method approximates the unknown solution through two phases: temporal discretization and space discretization. The localized approach considers neighboring collocation nodes to avoid ill-conditioning in matrix systems, and the convergence and stability properties are discussed theoretically and confirmed numerically.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Computer Science, Interdisciplinary Applications
O. Nikan, A. Golbabai, J. A. Tenreiro Machado, T. Nikazad
Summary: This paper addresses the solution of the Rayleigh-Stokes problem for an edge in a generalized Oldroyd-B fluid using fractional derivatives and the radial basis function-generated finite difference (RBF-FD) method. The stability and convergence analysis of the proposed method are discussed, showing the feasibility and efficiency of the new approach on irregular domains. Additionally, the main idea of considering the distribution of data nodes within the local support domain to maintain a constant number of nodes is emphasized.
ENGINEERING WITH COMPUTERS
(2021)
Article
Mathematics, Applied
Siamak Banei, Kamal Shanazari
Summary: This study introduces a new numerical solution based on a meshless method for solving the two-dimensional forward-backward heat equation, utilizing domain decomposition and adaptive node techniques. The research proves the stability and convergence of the time discrete scheme, also presenting numerical experiments to demonstrate the performance of the collocation scheme.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Haixiang Zhang, Xuehua Yang, Da Xu
Summary: This study introduces a linearized orthogonal spline collocation method for solving the initial-boundary-value problem of semilinear subdiffusion equations with nonsmooth solutions. It provides a sharp error estimate in the L(2) norm without any restrictions on temporal and spatial mesh sizes, and includes the typical singularity of the solution near time t = 0. Numerical experiments validate the analytical results.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics
Xiao Wang, Juan Wang, Xin Wang, Chujun Yu
Summary: In this paper, a pseudo-spectral collocation method based on Fourier basis functions is proposed for the numerical solutions of 2D and 3D inhomogeneous elliptic boundary value problems. The method improves the numerical accuracy by using additional reconstruction techniques and the use of Fourier basis functions allows for faster computations.
Article
Mathematics, Applied
Shengdong Zhao, Yan Gu
Summary: This paper discusses the use of the localized Fourier collocation method (LFCM) for solving high-order partial differential equations (PDEs). The method divides the computational domain into overlapping subdomains and uses Fourier series expansion and moving-least square approximation to construct local systems of linear equations. The method yields a sparse and banded stiffness matrix, making it suitable for large-scale engineering simulations. Numerical experiments on fourth-order PDEs in two and three dimensions demonstrate the accuracy and efficiency of the method.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Applied
G. Garmanjani, S. Banei, K. Shanazari, Y. Azari
Summary: This paper proposes a truly meshless method based on the partition of unity method (PUM) for solving the two-dimensional forward-backward heat equations numerically. A novel method is proposed based on the domain decomposition scheme and RBF-PUM technique. The physical domain is divided into two subdomains, each defining a forward or a backward subproblem. The subproblems are solved using a radial basis function meshfree method based on partition of unity for spatial dimension and a finite difference scheme for the time derivative. The stability and convergence of the time discrete scheme are also proved. Numerical experiments are conducted to demonstrate the performance of the proposed method.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Mitja Jancic, Jure Slak, Gregor Kosec
Summary: Local meshless methods using RBFs augmented with monomials are popular for solving PDEs on scattered node sets in a dimension-independent way, but come at a higher cost in execution time. The study analyzes the ability of these methods on Poisson problems with mixed boundary conditions in different dimensions, demonstrating theoretical convergence orders and examining the trade-off between accuracy and execution time. Optimal order regimes for target accuracy ranges are identified and generalization guidelines are presented.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Engineering, Multidisciplinary
Yan Zeng, Yong Duan, Bi-Sen Liu
Summary: This paper presents a method for solving parabolic equations using the time-Parareal coupled unsymmetric collocation meshless method, demonstrating its ability to handle irregular geometries. Numerical experiments show convergence properties and the superiority of time parallelism.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Review
Computer Science, Interdisciplinary Applications
Pratik Suchde, Thibault Jacquemin, Oleg Davydov
Summary: Meshfree methods are increasingly popular for numerical simulation due to their avoidance of generating a mesh on the computational domain. However, many meshfree literature still uses mesh nodes for discretization. Efficient meshfree methods for generating point clouds are not well-known among the meshfree communities, leading to recent redevelopment of existing algorithms. This paper provides a brief overview of point cloud generation methods for domains and surfaces, discussing their features and challenges, especially in the context of industry-relevant complex geometries.
ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING
(2023)
Article
Mathematics, Applied
Qing Li, Huanzhen Chen, Hong Wang
Summary: In this article, a proper orthogonal decomposition-compact difference scheme (POD-CDS) is proposed for the displacement-stress form of a simply supported plate vibration model. It is proven that the POD-CDS can maintain the same spatial and temporal convergence rates and unconditional stability as the compact difference solution, while significantly improving computing efficiency. Stability and convergence analysis for the corresponding compact difference scheme is also conducted. Numerical experiments verify the theoretical findings and demonstrate that the POD-CDS is nearly 10-30 times faster than the compact difference scheme.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Peter Giesl, Carlos Argaez, Sigurdur Hafstein, Holger Wendland
Summary: By discretizing a certain type of continuous minimization problems with differential inequality constraints, the theory developed can compute complete Lyapunov functions for nonlinear dynamical systems. The resulting discretized problems are solved using efficient solution algorithms, and their solutions converge strongly in appropriate Sobolev spaces. This method proposes a new approach to compute complete Lyapunov functions as solutions of quadratic minimization problems, without requiring information about the chain-recurrent set.
MATHEMATICS OF COMPUTATION
(2021)
Article
Engineering, Multidisciplinary
Menglian Li, Omid Nikan, Wenlin Qiu, Da Xu
Summary: This paper presents a numerical technique for approximating the two-dimensional Burgers equation. The method involves two stages for approximating the unknown solution, discretizing the time derivative using the backward Euler method and approximating the spatial direction using a local radial basis function partition of unity (LRBF-PU) method. This technique offers advantages in reducing computational cost and obtaining a well linear system compared to global collocation techniques.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Multidisciplinary Sciences
O. Nikan, Z. Avazzadeh, J. A. Tenreiro Machado
Summary: This paper presents a local hybrid kernel meshless method to solve the modified time fractional diffusion problem. By optimizing the temporal discretization and spatial derivatives discretization, the method accurately models dynamic phenomena and improves computational efficiency.
JOURNAL OF ADVANCED RESEARCH
(2021)
Article
Mathematics, Interdisciplinary Applications
Ravshan Ashurov, Oqila Mukhiddinova, Sabir Umarov
Summary: This paper studies a nonlocal boundary value problem for the fractional version of the Rayleigh-Stokes equation, a well-known equation in fluid dynamics. The aim is to determine the values of the parameter beta that differentiate the two types of behavior of the semi-backward problem. The results show that the problem is well-posed if beta >= 1 or beta < 0, while the existence of a solution for beta in the range (0, 1) depends on the eigenvalues of the elliptic part of the equation and may require an additional condition on the orthogonality of the right-hand side and the boundary function to the eigenfunctions of the corresponding elliptic operator.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Mostafa Abbaszadeh, Mohammad Ivan Azis, Mehdi Dehghan, Reza Mohammadi-Arani
Summary: This paper proposes a new meshless numerical procedure, namely the gradient smoothing method (GSM), for simulating the pollutant transition equation in urban street canyons. The time derivative is approximated using the finite difference scheme, while the space derivative is discretized using the gradient smoothing method. Additionally, the proper orthogonal decomposition (POD) approach is employed to reduce CPU time. Several real-world examples are solved to verify the efficiency of the developed numerical procedure.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Biology
Niusha Narimani, Mehdi Dehghan
Summary: This paper numerically studies the therapies of prostate cancer in a two-dimensional space. The proposed model describes the tumor growth driven by a nutrient and the effects of cytotoxic chemotherapy and antiangiogenic therapy. The results obtained without using any adaptive algorithm show the response of the prostate tumor growth to different therapies.
COMPUTERS IN BIOLOGY AND MEDICINE
(2023)
Article
Engineering, Multidisciplinary
Mostafa Abbaszadeh, Yasmin Kalhor, Mehdi Dehghan, Marco Donatelli
Summary: The purpose of this research is to develop a numerical method for option pricing in jump-diffusion models. The proposed model consists of a backward partial integro-differential equation with diffusion and advection factors. Pseudo-spectral technique and cubic B-spline functions are used to solve the equation, and a second-order Strong Stability Preserved Runge-Kutta procedure is adopted. The efficiency and accuracy of the proposed method are demonstrated through various test cases.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Mahboubeh Najafi, Mehdi Dehghan
Summary: In this work, two-dimensional dendritic solidification is simulated using the meshless Diffuse Approximate Method (DAM). The Stefan problem is studied through the phase-field model, considering both isotropic and anisotropic materials for comparisons. The effects of changing some constants on the obtained patterns are investigated.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Computer Science, Interdisciplinary Applications
Hasan Zamani-Gharaghoshi, Mehdi Dehghan, Mostafa Abbaszadeh
Summary: This paper presents a local meshless collocation method for solving reaction-diffusion systems on surfaces. The proposed numerical procedure utilizes Pascal polynomial approximation and closest point method. This method is geometrically flexible and can be used to solve partial differential equations on unstructured point clouds. It only requires a set of arbitrarily scattered mesh-free points representing the underlying surface.
ENGINEERING WITH COMPUTERS
(2023)
Article
Mathematics, Applied
Majid Haghi, Mohammad Ilati, Mehdi Dehghan
Summary: In this paper, the cubic-quintic complex Ginzburg-Landau (CQCGL) equation is numerically studied in 1D, 2D, and 3D spaces. The equation is decomposed into three subproblems using the Strang splitting technique. Nonlinear ODEs are solved by the Runge-Kutta technique for the first and third problems, while a fourth-order RBF-generated Hermite finite difference (RBF-HFD) method is used for the second problem involving spatial derivatives. A temporal Richardson extrapolation technique is applied to improve the order of convergence in the time direction. Numerical results show that the proposed method improves the order of convergence and is accurate and efficient.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Alireza Hosseinian, Pouria Assari, Mehdi Dehghan
Summary: This paper presents a numerical method for solving nonlinear Volterra integral equations with delay arguments. The method uses the discrete collocation approach with thin plate splines as a type of radial basis functions. The method provides an effective and stable algorithm to estimate the solution, which can be easily implemented on a personal computer. The error analysis and convergence validation of the method are also provided.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Engineering, Multidisciplinary
Fatemeh Asadi-Mehregan, Pouria Assari, Mehdi Dehghan
Summary: This paper presents a computational algorithm for solving nonlinear systems of ordinary and partial differential equations resulting from HIV infection models. The method uses local radial basis functions as shape functions in the discrete collocation scheme, approximating the solution by a small set of nodes. The computational efficiency of the scheme is studied through several test examples.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Ali Ebrahimijahan, Mehdi Dehghan, Mostafa Abbaszadeh
Summary: In this study, the integrated radial basis functions-partition of unity (IRBF-PU) method is proposed for solving the coupled Schrodinger-Boussinesq equations in one-and two-dimensions. The IRBF-PU method is a local mesh-free method that offers flexibility and high accuracy for PDEs with smooth initial conditions. Numerical simulations demonstrate that the IRBF-PU method can effectively simulate solitary waves and preserve conservation laws. Furthermore, the obtained results are compared with other methods in the literature to validate the effectiveness and reliability of the proposed method.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Mostafa Abbaszadeh, AliReza Bagheri Salec, Alaa Salim Jebur
Summary: This paper investigates a time fractional distributed-order diffusion equation and analyzes its stability, convergence, and numerical accuracy.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Hasan Zamani-Gharaghoshi, Mehdi Dehghan, Mostafa Abbaszadeh
Summary: This article presents a numerical method for solving the surface Allen-Cahn model. The method is based on the generalized moving least-squares approximation and the closest point method. It does not depend on the structure of the underlying surface and only requires a set of arbitrarily distributed mesh-free points on the surface.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Computer Science, Interdisciplinary Applications
Mostafa Abbaszadeh, Mehdi Dehghan, Dunhui Xiao
Summary: This paper presents a new numerical formulation for simulating tumor growth. The proposed method utilizes the meshless Galerkin technique and a two-grid algorithm to improve accuracy and efficiency in obtaining simulation results.
ENGINEERING WITH COMPUTERS
(2023)
Article
Mathematics, Applied
Reza MohammadiArani, Mehdi Dehghan, Mostafa Abbaszadeh
Summary: Lattice Boltzmann method is a powerful solver for fluid flow, but it is challenging to use it to solve other partial differential equations. This paper challenges the LBM to solve the two-dimensional DKS equation by finding a suitable local equilibrium distribution function and proposes a modification for implementing boundary conditions in complex geometries.
APPLIED NUMERICAL MATHEMATICS
(2024)
Article
Mathematics, Applied
Mostafa Abbaszadeh, Alireza Bagheri Salec, Taghreed Abdul-Kareem Hatim Aal-Ezirej
Summary: In this paper, an improved Boussinesq model is studied. The existence, uniqueness, stability and convergence of the solution are analyzed through discretization and finite difference methods. The proposed scheme is validated through examples in 1D and 2D cases.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
Mostafa Abbaszadeh, AliReza Bagheri Salec, Shurooq Kamel Abd Al-Khafaji
Summary: This paper proposes a numerical method using spectral collocation and POD approach to solve systems of space fractional PDEs. The method achieves high accuracy and computational efficiency.
ENGINEERING COMPUTATIONS
(2023)
Article
Engineering, Multidisciplinary
Akshay J. Thomas, Mateusz Jaszczuk, Eduardo Barocio, Gourab Ghosh, Ilias Bilionis, R. Byron Pipes
Summary: We propose a physics-guided transfer learning approach to predict the thermal conductivity of additively manufactured short-fiber reinforced polymers using micro-structural characteristics obtained from tensile tests. A Bayesian framework is developed to transfer the thermal conductivity properties across different extrusion deposition additive manufacturing systems. The experimental results demonstrate the effectiveness and reliability of our method in accounting for epistemic and aleatory uncertainties.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Zhen Zhang, Zongren Zou, Ellen Kuhl, George Em Karniadakis
Summary: In this study, deep learning and artificial intelligence were used to discover a mathematical model for the progression of Alzheimer's disease. By analyzing longitudinal tau positron emission tomography data, a reaction-diffusion type partial differential equation for tau protein misfolding and spreading was discovered. The results showed different misfolding models for Alzheimer's and healthy control groups, indicating faster misfolding in Alzheimer's group. The study provides a foundation for early diagnosis and treatment of Alzheimer's disease and other misfolding-protein based neurodegenerative disorders using image-based technologies.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jonghyuk Baek, Jiun-Shyan Chen
Summary: This paper introduces an improved neural network-enhanced reproducing kernel particle method for modeling the localization of brittle fractures. By adding a neural network approximation to the background reproducing kernel approximation, the method allows for the automatic location and insertion of discontinuities in the function space, enhancing the modeling effectiveness. The proposed method uses an energy-based loss function for optimization and regularizes the approximation results through constraints on the spatial gradient of the parametric coordinates, ensuring convergence.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Bodhinanda Chandra, Ryota Hashimoto, Shinnosuke Matsumi, Ken Kamrin, Kenichi Soga
Summary: This paper proposes new and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). The proposed approach adopts a monolithic displacement-pressure formulation and integrates two stabilization strategies to ensure stability. The effectiveness of the proposed method is validated through benchmark cases and real-world scenarios involving violent free-surface fluid motion.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Chao Peng, Alessandro Tasora, Dario Fusai, Dario Mangoni
Summary: This article discusses the importance of the tangent stiffness matrix of constraints in multibody systems and provides a general formulation based on quaternion parametrization. The article also presents the analytical expression of the tangent stiffness matrix derived through linearization. Examples demonstrate the positive effect of this additional stiffness term on static and eigenvalue analyses.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Thibaut Vadcard, Fabrice Thouverez, Alain Batailly
Summary: This contribution presents a methodology for detecting isolated branches of periodic solutions to nonlinear mechanical equations. The method combines harmonic balance method-based solving procedure with the Melnikov energy principle. It is able to predict the location of isolated branches of solutions near families of autonomous periodic solutions. The relevance and accuracy of this methodology are demonstrated through academic and industrial applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Weisheng Zhang, Yue Wang, Sung-Kie Youn, Xu Guo
Summary: This study proposes a sketch-guided topology optimization approach based on machine learning, which incorporates computer sketches as constraint functions to improve the efficiency of computer-aided structural design models and meet the design intention and requirements of designers.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Leilei Chen, Zhongwang Wang, Haojie Lian, Yujing Ma, Zhuxuan Meng, Pei Li, Chensen Ding, Stephane P. A. Bordas
Summary: This paper presents a model order reduction method for electromagnetic boundary element analysis and extends it to computer-aided design integrated shape optimization of multi-frequency electromagnetic scattering problems. The proposed method utilizes a series expansion technique and the second-order Arnoldi procedure to reduce the order of original systems. It also employs the isogeometric boundary element method to ensure geometric exactness and avoid re-meshing during shape optimization. The Grey Wolf Optimization-Artificial Neural Network is used as a surrogate model for shape optimization, with radar cross section as the objective function.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
C. Pilloton, P. N. Sun, X. Zhang, A. Colagrossi
Summary: This paper investigates the smoothed particle hydrodynamics (SPH) simulations of violent sloshing flows and discusses the impact of volume conservation errors on the simulation results. Different techniques are used to directly measure the particles' volumes and stabilization terms are introduced to control the errors. Experimental comparisons demonstrate the effectiveness of the numerical techniques.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Ye Lu, Weidong Zhu
Summary: This work presents a novel global digital image correlation (DIC) method based on a convolution finite element (C-FE) approximation. The C-FE based DIC provides highly smooth and accurate displacement and strain results with the same element size as the usual finite element (FE) based DIC. The proposed method's formulation and implementation, as well as the controlling parameters, have been discussed in detail. The C-FE method outperformed the FE method in all tested examples, demonstrating its potential for highly smooth, accurate, and robust DIC analysis.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Mojtaba Ghasemi, Mohsen Zare, Amir Zahedi, Pavel Trojovsky, Laith Abualigah, Eva Trojovska
Summary: This paper introduces Lung performance-based optimization (LPO), a novel algorithm that draws inspiration from the efficient oxygen exchange in the lungs. Through experiments and comparisons with contemporary algorithms, LPO demonstrates its effectiveness in solving complex optimization problems and shows potential for a wide range of applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jingyu Hu, Yang Liu, Huixin Huang, Shutian Liu
Summary: In this study, a new topology optimization method is proposed for structures with embedded components, considering the tension/compression asymmetric interface stress constraint. The method optimizes the topology of the host structure and the layout of embedded components simultaneously, and a new interpolation model is developed to determine interface layers between the host structure and embedded components.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Qiang Liu, Wei Zhu, Xiyu Jia, Feng Ma, Jun Wen, Yixiong Wu, Kuangqi Chen, Zhenhai Zhang, Shuang Wang
Summary: In this study, a multiscale and nonlinear turbulence characteristic extraction model using a graph neural network was designed. This model can directly compute turbulence data without resorting to simplified formulas. Experimental results demonstrate that the model has high computational performance in turbulence calculation.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jacinto Ulloa, Geert Degrande, Jose E. Andrade, Stijn Francois
Summary: This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. The proper generalized decomposition (PGD) is leveraged to decompose the displacements into multiple time scales, separating the spatial and intra-cyclic dependence from the inter-cyclic variation, thereby reducing computational burden.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Utkarsh Utkarsh, Valentin Churavy, Yingbo Ma, Tim Besard, Prakitr Srisuma, Tim Gymnich, Adam R. Gerlach, Alan Edelman, George Barbastathis, Richard D. Braatz, Christopher Rackauckas
Summary: This article presents a high-performance vendor-agnostic method for massively parallel solving of ordinary and stochastic differential equations on GPUs. The method integrates with a popular differential equation solver library and achieves state-of-the-art performance compared to hand-optimized kernels.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
