Computers & Mathematics with Applications最新文献_第2页

Robust iterative spectral algorithms for smooth solutions of time-fractional nonlinear diffusion problems and convergence analysis 时间分数非线性扩散问题平稳解的稳健迭代谱算法及收敛性分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-29 DOI: 10.1016/j.camwa.2024.10.015

Muhammad Usman , Muhammad Hamid , Dianchen Lu , Zhengdi Zhang , Wojciech Sumelka

{"title":"Robust iterative spectral algorithms for smooth solutions of time-fractional nonlinear diffusion problems and convergence analysis","authors":"Muhammad Usman , Muhammad Hamid , Dianchen Lu , Zhengdi Zhang , Wojciech Sumelka","doi":"10.1016/j.camwa.2024.10.015","DOIUrl":"10.1016/j.camwa.2024.10.015","url":null,"abstract":"<div><div>Nonlinear time-fractional diffusion problems, a significant class of parabolic-type problems, appear in various diffusion phenomena that seem extensively in nature. Such physical problems arise in numerous fields, such as phase transition, filtration, biochemistry, and dynamics of biological groups. Because of its massive involvement, its accurate solutions have become a challenging task among researchers. In this framework, this article proposed two operational-based robust iterative spectral schemes for accurate solutions of the nonlinear time-fractional diffusion problems. Temporal and spatial variables are approximated using Vieta-Lucas polynomials, and derivative operators are approximated using novel operational matrices. The approximated solution, novel operational matrices, and uniform collection points convert the problem into a system of nonlinear equations. Here, two robust methods, namely Picard's iterative and Newton's, are incorporated to tackle a nonlinear system of equations. Some problems are considered in authenticating the present methods' accuracy, credibility, and reliability. An inclusive comparative study demonstrates that the proposed computational schemes are effective, accurate, and well-matched to find the numerical solutions to the problems mentioned above. The proposed methods improve the accuracy of numerical solutions from 27 % to 100 % when <span><math><mrow><mi>M</mi><mo>></mo><mn>2</mn></mrow></math></span> as compared to the existing results. The suggested methods' convergence, error bound, and stability are investigated theoretically and numerically.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142538691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Generalised adaptive cross approximation for convolution quadrature based boundary element formulation 基于卷积正交边界元素公式的广义自适应交叉逼近

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-28 DOI: 10.1016/j.camwa.2024.10.025

A.M. Haider , S. Rjasanow , M. Schanz

引用次数: 0

Innovative discretizations of PDEs: Towards an accurate representation of the reality PDEs 的创新离散化：实现对现实的准确呈现

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-28 DOI: 10.1016/j.camwa.2024.10.013

Fleurianne Bertrand, Daniele Boffi, Alexander Düster, Jean-Luc Guermond, Norbert Heuer, Jichun Li, Waldemar Rachowicz

引用次数: 0

A-priori and a-posteriori error estimates for discontinuous Galerkin method of the Maxwell eigenvalue problem 麦克斯韦特征值问题非连续伽勒金方法的先验和后验误差估计

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-24 DOI: 10.1016/j.camwa.2024.10.026

Jun Zhang , Zijiang Luo , Jiayu Han , Hu Chen

引用次数: 0

Fully parallel and pipelined sparse direct solver for large symmetric indefinite finite element problems 大型对称不定期有限元问题的全并行流水线稀疏直接求解器

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-24 DOI: 10.1016/j.camwa.2024.10.017

Yujie Wang , Shengquan Wang , Yong Cai , Guidong Wang , Guangyao Li

{"title":"Fully parallel and pipelined sparse direct solver for large symmetric indefinite finite element problems","authors":"Yujie Wang , Shengquan Wang , Yong Cai , Guidong Wang , Guangyao Li","doi":"10.1016/j.camwa.2024.10.017","DOIUrl":"10.1016/j.camwa.2024.10.017","url":null,"abstract":"<div><div>Sparse linear system solving is a primary computational cost in large-scale finite element analysis, and improving its performance is a key technological challenge in this field. Real-world engineering problems involve diverse materials, elements, and connectivity relationships, making it difficult for iterative methods to handle their global stiffness matrices. Direct methods, owing to their robustness, emerge as the preferred choice. In this paper, a novel block-based supernodal LDL<sup>T</sup> numerical factorization method is introduced. The computational process is disassembled into distinct tasks, and the dependency relationships between these tasks are expressed via a directed acyclic graph to guide the calculation sequence. Based on this approach, a global task pool and local task stack are established to store task queues, enhancing data reuse and multicore collaboration efficiency. Additionally, an effective task dispatch and work-stealing mechanism is implemented to prevent performance degradation caused by load imbalances. Numerical experiments, including a publicly available matrix test set and real-world engineering finite element problems, are conducted to compare the parallel performances of the Pardiso, MUMPS, and proposed solver. The results illustrate that the proposed solver performs significantly better than the other solvers when handling various types of sparse matrices and diverse architectures of multicore processors.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A least-squares Fourier frame method for nonlocal diffusion models on arbitrary domains 任意域上非局部扩散模型的最小二乘傅立叶框架法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-24 DOI: 10.1016/j.camwa.2024.10.024

Mengxia Shen , Haiyong Wang

{"title":"A least-squares Fourier frame method for nonlocal diffusion models on arbitrary domains","authors":"Mengxia Shen , Haiyong Wang","doi":"10.1016/j.camwa.2024.10.024","DOIUrl":"10.1016/j.camwa.2024.10.024","url":null,"abstract":"<div><div>We introduce a least-squares Fourier frame method for solving nonlocal diffusion models with Dirichlet volume constraint on arbitrary domains. The mathematical structure of a frame rather than a basis allows using a discrete least-squares approximation on irregular domains and imposing non-periodic boundary conditions. The method has inherited the one-dimensional integral expression of Fourier symbols of the nonlocal diffusion operator from Fourier spectral methods for any <em>d</em> spatial dimensions. High precision of its solution can be achieved via a direct solver such as pivoted QR decomposition even though the corresponding system is extremely ill-conditioned, due to the redundancy in the frame. The extension of AZ algorithm improves the complexity of solving the rectangular linear system to <span><math><mi>O</mi><mo>(</mo><mi>N</mi><msup><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⁡</mo><mi>N</mi><mo>)</mo></math></span> for 1<em>d</em> problems and <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⁡</mo><mi>N</mi><mo>)</mo></math></span> for 2<em>d</em> problems, compared with <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> of the direct solvers, where <em>N</em> is the number of degrees of freedom. We present ample numerical experiments to show the flexibility, fast convergence and asymptotical compatibility of the proposed method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A local projection stabilised HHO method for the Oseen problem 奥森问题的局部投影稳定 HHO 方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-24 DOI: 10.1016/j.camwa.2024.10.030

Gouranga Mallik , Rahul Biswas , Thirupathi Gudi

引用次数: 0

Special Issue: Advanced COmputational Methods in ENgineering (ACOMEN 2022) 特刊：高级工程计算方法（ACOMEN 2022）

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-23 DOI: 10.1016/j.camwa.2024.10.012

Maarten Arnst, Christophe Geuzaine, Ludovic Noels, Jean-Philippe Ponthot

引用次数: 0

Accurate and parallel simulation of the anisotropic dendrite crystal growth by Lagrangian data assimilation with directional operator splitting 通过拉格朗日数据同化与方向算子拆分对各向异性树枝状晶体生长进行精确并行模拟

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-22 DOI: 10.1016/j.camwa.2024.10.020

Fenglian Zheng , Yan Wang , Xufeng Xiao

{"title":"Accurate and parallel simulation of the anisotropic dendrite crystal growth by Lagrangian data assimilation with directional operator splitting","authors":"Fenglian Zheng , Yan Wang , Xufeng Xiao","doi":"10.1016/j.camwa.2024.10.020","DOIUrl":"10.1016/j.camwa.2024.10.020","url":null,"abstract":"<div><div>Dendritic crystal growth is a prevalent natural phenomenon that generates a crystalline structure resembling a tree during a phase transition. In practical computations, inaccuracies in model parameters and initial conditions can introduce observation errors, even leading to inaccurate results. To enhance the precision and efficiency of the numerical simulation, the data assimilation method with parallel simulation are considered in this study. Firstly, based on the phase-field dendritic crystal growth model, a Lagrangian data assimilation method, which adds Lagrange multiplier terms into the phase-field partial differential equations (PDEs), is presented to integrate the observed data of physical information to modify the numerical solution, thereby improving simulation accuracy. Secondly, to achieve efficient data assimilation, a parallel directional operator splitting method is presented to solve the modified data assimilation PDEs. Thirdly, in the section of numerical experiments, we investigate the validity of the method and assess the impact of various factors such as the Lagrange multiplier parameter, spatio-temporal sampling rate and parameter perturbation ratio on the effectiveness of data assimilation. The evaluation is conducted for two distinct problem categories: initial observation errors and model parameter errors. Experimental results demonstrate that our method can effectively assimilate experimental observations in simulations, thereby enhancing more accurate dendritic crystal growth processes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Three-dimensional peridynamic modeling of damage and penetration in composite plates exposed to localized explosive blasts 复合材料板在局部爆炸冲击波作用下的损伤和穿透的三维围动力学建模

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-22 DOI: 10.1016/j.camwa.2024.10.022

D.A. Abdoh

{"title":"Three-dimensional peridynamic modeling of damage and penetration in composite plates exposed to localized explosive blasts","authors":"D.A. Abdoh","doi":"10.1016/j.camwa.2024.10.022","DOIUrl":"10.1016/j.camwa.2024.10.022","url":null,"abstract":"<div><div>Localized failures in composites can lead to catastrophic consequences in some vehicles and systems, such as airplanes and submarines. The paper presents a new three-dimensional (3D) peridynamic model to explore the localized explosive effects on composite plates. The study utilizes the peridynamic method to simulate fractures and deformations in composite plates when exposed to localized explosive blasts. Accurate prediction of composites' performance during explosive blast events is crucial in the design process to avoid the deadly effects of their failures. This study highlights the following novelties: (1) We present, for the first time, a novel 3D mesh-free model to simulate the fracture and damage behavior of composite plates when exposed to explosive blasts; (2) The adopted numerical modeling technique enables highly efficient simulations of fractures and failures in composites when compared with other mesh-based numerical models; (3) We introduce a new mathematical framework to reflect the explosive pressure loads through different composite layers; (4) The study provides an accessible and efficient tool for engineers and researchers to enhance the design of composites in several industries instead relying on limited-access commercial software packages. In addition to the previous novelties, the paper presents a new parametric study that investigates the performance of several composite plates, such as titanium-aramid and aluminum-aramid composites, in explosive blast scenarios. Moreover, the roles of explosive mass and plate thickness in the failure mechanisms of composites are examined.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0