Computers & Mathematics with Applications最新文献_第3页

Overlapping domain decomposition methods for finite volume discretizations 有限体积离散的重叠域分解方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-22 DOI: 10.1016/j.camwa.2024.10.018

Jinjin Zhang , Yanru Su , Xinfeng Gao , Xuemin Tu

引用次数: 0

An α-robust and new two-grid nonuniform L2-1σ FEM for nonlinear time-fractional diffusion equation 用于非线性时间分数扩散方程的α-稳健和新型双网格非均匀 L2-1σ 有限元模型

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-21 DOI: 10.1016/j.camwa.2024.10.023

Zhijun Tan

{"title":"An α-robust and new two-grid nonuniform L2-1σ FEM for nonlinear time-fractional diffusion equation","authors":"Zhijun Tan","doi":"10.1016/j.camwa.2024.10.023","DOIUrl":"10.1016/j.camwa.2024.10.023","url":null,"abstract":"<div><div>This paper constructs and analyzes an <em>α</em>-robust and new two-grid finite element method (FEM) with nonuniform L2-<span><math><msub><mrow><mn>1</mn></mrow><mrow><mi>σ</mi></mrow></msub></math></span> formula and its fast algorithms for nonlinear time-fractional diffusion equations. The method incorporates a nonuniform L2-<span><math><msub><mrow><mn>1</mn></mrow><mrow><mi>σ</mi></mrow></msub></math></span> formula to achieve temporal second-order accuracy and address the initial solution singularity. By employing a spatial two-grid FEM, computational costs are reduced. Utilizing the cut-off technique and an auxiliary function, the condition on the nonlinear term is lessened to meet the local Lipschitz requirement. We further devise the associated fast algorithms for two-grid nonuniform L2-<span><math><msub><mrow><mn>1</mn></mrow><mrow><mi>σ</mi></mrow></msub></math></span> FEM. To prevent roundoff errors, we introduce an innovative fast algorithm to precisely calculate the kernel coefficients. An <em>α</em>-robust analysis of the stability and optimal error estimates in terms of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm for the fully discrete scheme is presented. The derived error bound remains stable as the order of the fractional derivative <span><math><mi>α</mi><mo>→</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msup></math></span>. Furthermore, a new two-grid algorithm and its corresponding fast algorithm are proposed to decrease the computational expenses by eliminating redundancy in discrete convolutional summation. Numerical experiments support our theoretical results, confirming that two-grid FEMs offer greater efficiency in comparison to FEM.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529039","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

Structure deformation analysis of the deep excavation based on the local radial basis function collocation method 基于局部径向基函数配准法的深基坑结构变形分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-21 DOI: 10.1016/j.camwa.2024.10.014

Cheng Deng , Hui Zheng , Rongping Zhang , Liangyong Gong , Xiangcou Zheng

{"title":"Structure deformation analysis of the deep excavation based on the local radial basis function collocation method","authors":"Cheng Deng , Hui Zheng , Rongping Zhang , Liangyong Gong , Xiangcou Zheng","doi":"10.1016/j.camwa.2024.10.014","DOIUrl":"10.1016/j.camwa.2024.10.014","url":null,"abstract":"<div><div>This study introduces a local radial basis function collocation method (LRBFCM) to analyzing structural deformation in deep excavation within a two dimensional geotechnical model. To mitigate the size effect caused by a large length-to-width ratio, a technique known as the ‘direct method’ is employed. This method effectively reduces the influence of the shape parameter, thereby improving the accuracy of the partial derivative calculations in LRBFCM. The combination of LRBFCM with the direct method is applied to the deep excavation problem, which consists of both the soil and support structures. The soil is modeled using the Drucker-Prager (D-P) elastic-plastic model, while an elastic model is employed for the support structure. Elastic-plastic discretization is performed using incremental theory. The proposed approach is validated through four different examples, comparing the results with numerical solutions obtained from traditional finite element methods (FEM). This study advocates the use of the direct method to optimize the distribution of local influence nodes, particularly in cases involving large length-to-width ratios. The combination of LRBFCM with incremental theory is shown to be effective for addressing elastic-plastic problems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529037","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

IGG(χ): A new and simple implicit gradient scheme on unstructured meshes IGG(χ)：非结构网格上一种新的简单隐式梯度方案

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-21 DOI: 10.1016/j.camwa.2024.10.021

Vishnu Prakash K, Ganesh Natarajan

{"title":"IGG(χ): A new and simple implicit gradient scheme on unstructured meshes","authors":"Vishnu Prakash K, Ganesh Natarajan","doi":"10.1016/j.camwa.2024.10.021","DOIUrl":"10.1016/j.camwa.2024.10.021","url":null,"abstract":"<div><div>A new and simple implicit Green-Gauss gradient (IGG) scheme for unstructured meshes is proposed exploiting the ideas from the linearity-preserving U-MUSCL scheme to define values at cell faces. We construct an implicit one-parameter family of gradient schemes referred to as IGG(<em>χ</em>) where <em>χ</em> is a free-parameter. The computed gradients are at least first-order accurate on generic polygonal meshes and second-order accurate on uniform Cartesian meshes except when <span><math><mi>χ</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>3</mn></math></span> for which fourth-order accuracy can be realised. A theoretical analysis is carried out to understand the effect of the control parameter <em>χ</em> on accuracy and resolution of the gradients and numerical experiments on various mesh topologies confirm the theoretical findings. Finite volume simulations of the Poisson and Euler equations on Cartesian and unstructured meshes further highlight that the IGG(<em>χ</em>) is a versatile gradient scheme that gives second-order accurate solutions with the iterative convergence of the solver dependent on the choice of the <em>χ</em> parameter. The framework described in this study can also be employed to devise an implicit least-squares gradient scheme that applies equally well to unstructured finite volume and meshfree solvers.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529733","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

The fundamental solution element method based on irregular polygonal meshes 基于不规则多边形网格的基本解元法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-18 DOI: 10.1016/j.camwa.2024.10.011

Hua-Yu Liu, Xiao-Wei Gao, Jun Lv

引用次数: 0

Unveiling novel insights into Kirchhoff migration for a fast and effective object detection from experimental Fresnel dataset 揭示基尔霍夫迁移的新见解，从菲涅尔实验数据集中快速有效地检测物体

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-17 DOI: 10.1016/j.camwa.2024.10.019

Won-Kwang Park

引用次数: 0

Two-grid weak Galerkin finite element method for nonlinear parabolic equations 非线性抛物方程的双网格弱 Galerkin 有限元方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-17 DOI: 10.1016/j.camwa.2024.10.007

Jianghong Zhang , Fuzheng Gao , Jintao Cui

引用次数: 0

Solving incompressible Navier-Stokes equations: A nonlinear multiscale approach 求解不可压缩的纳维-斯托克斯方程：非线性多尺度方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-17 DOI: 10.1016/j.camwa.2024.10.009

Riedson Baptista , Isaac P. dos Santos , Lucia Catabriga

{"title":"Solving incompressible Navier-Stokes equations: A nonlinear multiscale approach","authors":"Riedson Baptista , Isaac P. dos Santos , Lucia Catabriga","doi":"10.1016/j.camwa.2024.10.009","DOIUrl":"10.1016/j.camwa.2024.10.009","url":null,"abstract":"<div><div>In this work, we present a nonlinear variational multiscale finite element method for solving both stationary and transient incompressible Navier-Stokes equations. The method is founded on a two-level decomposition of the approximation space, where a nonlinear artificial viscosity operator is exclusively added to the unresolved scales. It can be regarded as a self-adaptive method, since the amount of subgrid viscosity is automatically introduced according to the residual of the equation, in its strong form, associated with the resolved scales. Two variants for the subgrid viscosity are presented: one considering only the residual of the momentum equation and the other also incorporating the residual of the conservation of mass. To alleviate the computational cost typical of two-scale methods, the microscale space is defined through polynomial functions that vanish on the boundary of the elements, known as bubble functions. We compared the numerical and computational performance of the method with the results obtained by the Streamline-Upwind/Petrov-Galerkin (SUPG) formulation combined with the Pressure Stabilizing/Petrov-Galerkin (PSPG) method through a set of 2D reference problems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445941","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 novel explicit fast numerical scheme for the Cauchy problem for integro-differential equations with a difference kernel and its application 带差分核的整微分方程 Cauchy 问题的新型显式快速数值方案及其应用

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-17 DOI: 10.1016/j.camwa.2024.10.016

Anatoly A. Alikhanov , Mohammad Shahbazi Asl , Dongfang Li

{"title":"A novel explicit fast numerical scheme for the Cauchy problem for integro-differential equations with a difference kernel and its application","authors":"Anatoly A. Alikhanov , Mohammad Shahbazi Asl , Dongfang Li","doi":"10.1016/j.camwa.2024.10.016","DOIUrl":"10.1016/j.camwa.2024.10.016","url":null,"abstract":"<div><div>The present study focuses on designing a second-order novel explicit fast numerical scheme for the Cauchy problem incorporating memory associated with an evolutionary equation, where the integral term's kernel is a discrete difference operator. The Cauchy problem under consideration is related to a real finite-dimensional Hilbert space and includes a self-adjoint operator that is both positive and definite. We introduce a transformative technique for converting the Cauchy problem incorporating memory, into a local evolutionary system of equations by approximating the difference kernel using the sum of exponentials (SoE) approach. A second-order explicit scheme is then constructed to solve the local system. We thoroughly investigate the stability of this explicit scheme, and present the necessary conditions for the stability of the scheme. Moreover, we extended our investigation to encompass time-fractional diffusion-wave equations (TFDWEs) involving a fractional Caputo derivative with an order ranging between (1,2). Initially, we transform the main TFDWE model into a new model that incorporates the fractional Riemann-Liouville integral. Subsequently, we expand the applicability of our idea to develop an explicit fast numerical algorithm for approximating the model. The stability properties of this fast scheme for solving TFDWEs are assessed. Numerical simulations including a two-dimensional Cauchy problem as well as one-dimensional and two-dimensional TFDWE models are provided to validate the accuracy and experimental order of convergence of the schemes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445307","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

An efficient decoupled and dimension reduction scheme for quad-curl eigenvalue problem in balls and spherical shells 球和球壳四曲面特征值问题的高效解耦和降维方案

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-10-15 DOI: 10.1016/j.camwa.2024.10.010

Jiantao Jiang , Zhimin Zhang

{"title":"An efficient decoupled and dimension reduction scheme for quad-curl eigenvalue problem in balls and spherical shells","authors":"Jiantao Jiang , Zhimin Zhang","doi":"10.1016/j.camwa.2024.10.010","DOIUrl":"10.1016/j.camwa.2024.10.010","url":null,"abstract":"<div><div>In this paper, we propose a spectral-Galerkin approximation for the quad-curl eigenvalue problem within spherical geometries. Utilizing vector spherical harmonics in conjunction with the Laplace-Beltrami operator, we decompose the quad-curl eigenvalue problem into two distinct categories of fourth-order equations: corresponding to the transverse electric (TE) and transverse magnetic (TM) modes. A thorough analysis is provided for the TE mode. The TM mode, however, is characterized by a system of coupled fourth-order equations that are subject to a divergence-free condition. We develop two separate sets of vector basis functions tailored for the coupled system in both solid spheres and spherical shells. Moreover, we design a parameterized technique aimed at eliminating spurious eigenpairs. Numerical examples are presented to demonstrate the high precision achieved by the proposed method. We also include graphs to illustrate the localization of the eigenfunctions. Furthermore, we employ Bessel functions to analyze the quad-curl problem, revealing the intrinsic connection between the eigenvalues and the zeros of combinations of Bessel functions.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142437977","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