Computers & Mathematics with Applications最新文献

Proving the stability estimates of variational least-squares kernel-based methods

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-18 DOI: 10.1016/j.camwa.2024.12.008

Meng Chen, Leevan Ling, Dongfang Yun

{"title":"Proving the stability estimates of variational least-squares kernel-based methods","authors":"Meng Chen, Leevan Ling, Dongfang Yun","doi":"10.1016/j.camwa.2024.12.008","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.008","url":null,"abstract":"Motivated by the need for the rigorous analysis of the numerical stability of variational least-squares kernel-based methods for solving second-order elliptic partial differential equations, we provide previously lacking stability inequalities. This fills a significant theoretical gap in the previous work [Comput. Math. Appl. 103 (2021) 1-11], which provided error estimates based on a conjecture on the stability. With the stability estimate now rigorously proven, we complete the theoretical foundations and compare the convergence behavior to the proven rates. Furthermore, we establish another stability inequality involving weighted-discrete norms, and provide a theoretical proof demonstrating that the exact quadrature weights are not necessary for the weighted least-squares kernel-based collocation method to converge. Our novel theoretical insights are validated by numerical examples, which showcase the relative efficiency and accuracy of these methods on data sets with large mesh ratios. The results confirm our theoretical predictions regarding the performance of variational least-squares kernel-based method, least-squares kernel-based collocation method, and our new weighted least-squares kernel-based collocation method. Most importantly, our results demonstrate that all methods converge at the same rate, validating the convergence theory of weighted least-squares in our proven theories.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"258 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841377","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

Strong approximation of the time-fractional Cahn–Hilliard equation driven by a fractionally integrated additive noise

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-16 DOI: 10.1016/j.camwa.2024.12.007

Mariam Al-Maskari, Samir Karaa

{"title":"Strong approximation of the time-fractional Cahn–Hilliard equation driven by a fractionally integrated additive noise","authors":"Mariam Al-Maskari, Samir Karaa","doi":"10.1016/j.camwa.2024.12.007","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.007","url":null,"abstract":"In this article, we present a numerical scheme for solving a time-fractional stochastic Cahn–Hilliard equation driven by an additive fractionally integrated Gaussian noise. The model involves a Caputo fractional derivative in time of order <mml:math altimg=\"si1.svg\"><mml:mi>α</mml:mi><mml:mo>∈</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:math> and a fractional time-integral noise of order <mml:math altimg=\"si2.svg\"><mml:mi>γ</mml:mi><mml:mo>∈</mml:mo><mml:mo stretchy=\"false\">[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">]</mml:mo></mml:math>. Our numerical approach combines a piecewise linear finite element method in space with a convolution quadrature in time, designed to handle both time-fractional operators, along with the <mml:math altimg=\"si3.svg\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>-projection for the noise. We conduct a detailed analysis of both spatially semidiscrete and fully discrete schemes, deriving strong convergence rates through energy-based arguments. The solution's temporal Hölder continuity played a key role in the error analysis. Unlike the stochastic Allen–Cahn equation, the inclusion of the unbounded elliptic operator in front of the cubic nonlinearity in our model added complexity and challenges to the error analysis. To address these challenges, we introduce novel techniques and refined error estimates. We conclude with numerical examples that validate our theoretical findings.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"12 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841376","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

LRBF meshless methods for predicting soil moisture distribution in root zone

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-13 DOI: 10.1016/j.camwa.2024.11.028

Mohamed Boujoudar, Abdelaziz Beljadid, Ahmed Taik

{"title":"LRBF meshless methods for predicting soil moisture distribution in root zone","authors":"Mohamed Boujoudar, Abdelaziz Beljadid, Ahmed Taik","doi":"10.1016/j.camwa.2024.11.028","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.11.028","url":null,"abstract":"The main purpose of this study is to develop a numerical model of unsaturated flow in soils with plant root water uptake. The Richards equation and different sink term formulations are used in the numerical model to describe the distribution of soil moisture in the root zone. The Kirchhoff transformed Richards equation is used and the Gardner model is considered for capillary pressure. In the proposed numerical approach, we used localized radial basis function (LRBF) meshless techniques in space and the backward Euler scheme for temporal discretization to solve the system. The LRBF approach is an accurate and computationally efficient method that does not require mesh generation and is flexible in addressing high-dimensional problems. Furthermore, this method leads to a sparse matrix system, which avoids ill-conditioning issues. We implement the numerical model of infiltration and plant root water uptake for one, two, and three-dimensional soils. Numerical experiments are performed using nontrivial analytical solutions and available experimental data to validate the performance of the proposed numerical techniques. The results demonstrate the capability of the proposed numerical model to predict soil moisture dynamics in root zone.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"82 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841378","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

Effective nonlocal finite element formulation for free vibration analysis of S-FGM doubly curved nanoshells based on linear strain–displacement relations using TSDT

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-12 DOI: 10.1016/j.camwa.2024.11.021

Weeraphan Jiammeepreecha, Komkorn Chaidachatorn, Boonchai Phungpaingam, Karun Klaycham, Somchai Chucheepsakul

{"title":"Effective nonlocal finite element formulation for free vibration analysis of S-FGM doubly curved nanoshells based on linear strain–displacement relations using TSDT","authors":"Weeraphan Jiammeepreecha, Komkorn Chaidachatorn, Boonchai Phungpaingam, Karun Klaycham, Somchai Chucheepsakul","doi":"10.1016/j.camwa.2024.11.021","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.11.021","url":null,"abstract":"This paper presents an effective nonlocal finite element method (FEM) for investigating the free vibration behavior of sigmoid functionally graded material (S-FGM) nanoshells using nonlocal elasticity theory. The effective nonlocal parameters via third-order shear deformation theory (TSDT) are varied along the thickness of the nanoshells following the sigmoid function. In this study, two different sigmoid functions FGM (S1-FGM and S2-FGM) are considered for the ceramic volume fraction. For S1-FGM, the top and bottom surfaces are ceramic and metal, respectively, whereas the middle surface has the average properties of its constituent materials. In order to increase the stiffness of S1-FGM, ceramic and metal are used at the bottom and midplane surfaces, respectively, to form S2-FGM, which is used to investigate and compare with S1-FGM. The governing equation of the S-FGM nanoshells is formulated based on Hamilton's principle. The numerical results are obtained by finite element method (FEM) with a nine-node quadrilateral (Q9) Lagrangian element and are in close agreement with the published results. The numerical investigation indicates that the frequency parameter decreases with increasing nonlocal parameters. The frequency parameters of S1-FGM nanoshells decrease slowly when the sigmoid material index increases, whereas the frequency parameters of the S2-FGM shells increase quickly (0 ≤ <ce:italic>n</ce:italic> ≤ 1). then slowly as the sigmoid material index increases. Finally, the effects of the geometrical parameters of the S-FGM nanoshells accounting for the effective nonlocal parameters on the non-dimensional frequency parameter are investigated.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"30 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841383","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 high-precision numerical method based on spectral deferred correction for solving the time-fractional Allen-Cahn equation

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-12 DOI: 10.1016/j.camwa.2024.11.034

Jing Wang, Xuejuan Chen, Jinghua Chen

引用次数: 0

High-order gas-kinetic scheme with TENO class reconstruction for the Euler and Navier-Stokes equations

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-12 DOI: 10.1016/j.camwa.2024.12.002

Junlei Mu, Congshan Zhuo, Qingdian Zhang, Sha Liu, Chengwen Zhong

{"title":"High-order gas-kinetic scheme with TENO class reconstruction for the Euler and Navier-Stokes equations","authors":"Junlei Mu, Congshan Zhuo, Qingdian Zhang, Sha Liu, Chengwen Zhong","doi":"10.1016/j.camwa.2024.12.002","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.002","url":null,"abstract":"The high-order gas-kinetic scheme (HGKS) with WENO spatial reconstruction method has been extensively validated through numerous numerical experiments, demonstrating its superior accuracy, efficiency and robustness. In comparison to WENO class schemes, TENO class schemes exhibit significantly improved robustness, low numerical dissipation and sharp discontinuity capturing. This paper introduces two types of fifth-order HGKS utilizing TENO class schemes. One approach involves replacing the WENO scheme with the TENO scheme in the conventional WENO GKS. Both WENO and TENO schemes provide non-equilibrium state values at the cell interface. The slopes of the non-equilibrium state, as well as the values and slopes of the equilibrium state, are obtained through additional linear reconstruction. Another type of HGKS scheme named TENO GKS with adaptive order (TENO-A GKS), is similar to most multi-resolution HGKS schemes. Following a robust scale-separation procedure, a tailored ENO-like stencil selection strategy is proposed to ensure that high-order accuracy is maintained in smooth regions by selecting the candidate reconstruction from a large stencil, while enforcing the ENO property near discontinuities by adopting the candidate reconstruction from small smooth stencils. These TENO schemes include TENO schemes with adaptive accuracy order and adaptive dissipation control (TENO-AA) and TENO schemes with dual ENO-like stencil selection (TENO-D). The HGKS scheme based on TENO-A reconstruction takes advantage of the large stencil to provide point values and slopes of the non-equilibrium states. By dynamically merging the reconstructed non-equilibrium slopes, the need for extra reconstruction of the equilibrium states at the beginning of each time step can be avoided. The simple TENO-A GKS scheme exhibits better robustness compared to the conventional WENO GKS or TENO GKS.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"5 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841380","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

Dynamic analysis of the three-phase magneto-electro-elastic (MEE) structures with the overlapping triangular finite elements

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-12 DOI: 10.1016/j.camwa.2024.11.025

Cong Liu, Kaifu Li, Shaosong Min, Yingbin Chai

{"title":"Dynamic analysis of the three-phase magneto-electro-elastic (MEE) structures with the overlapping triangular finite elements","authors":"Cong Liu, Kaifu Li, Shaosong Min, Yingbin Chai","doi":"10.1016/j.camwa.2024.11.025","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.11.025","url":null,"abstract":"The conventional finite element method (FEM) usually fails to generate sufficiently fine numerical solutions in the analyses of Mageto-electro-elastic (MEE) structures in which three different types of physical fields are coupled together. To enhance the performance of the FEM in analyzing MEE structures, in this work a novel overlapping triangular finite element is introduced for dynamic analysis of MEE structures. In this new paradigm for finite element analysis, both local and global numerical approximations are used to construct the considered three-phase physical fields. The local numerical approximation is built by using the method of finite spheres (MFS) and the global numerical approximation is based on the traditional finite element interpolation. In the local numerical approximation, the polynomials or other specially-designed functions can be used as the nodal degrees of freedom. Free vibration and harmonic response analyses are carried out to show the abilities of the overlapping triangular elements in analyzing the three-phase MEE structures. It is demonstrated by the numerical solutions that the present overlapping triangular elements are much more effective to predict the dynamic behaviors of the MEE structures and more accurate solutions can be generated than the traditional FEM with the same mesh. Therefore, the present overlapping triangular elements embody great potential in analyzing various complicated MEE structures in practical engineering applications.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"48 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841382","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

Multi-resolution isogeometric analysis – efficient adaptivity utilizing the multi-patch structure

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-12 DOI: 10.1016/j.camwa.2024.12.005

Stefan Takacs, Stefan Tyoler

{"title":"Multi-resolution isogeometric analysis – efficient adaptivity utilizing the multi-patch structure","authors":"Stefan Takacs, Stefan Tyoler","doi":"10.1016/j.camwa.2024.12.005","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.005","url":null,"abstract":"Isogeometric Analysis (IgA) is a spline-based approach to the numerical solution of partial differential equations. The concept of IgA was designed to address two major issues. The first issue is the exact representation of domains generated from Computer-Aided Design (CAD) software. In practice, this can be realized only with multi-patch IgA, often in combination with trimming or similar techniques. The second issue is the realization of high-order discretizations (by increasing the spline degree) with a number of degrees of freedom comparable to low-order methods. High-order methods can deliver their full potential only if the solution to be approximated is sufficiently smooth; otherwise, adaptive methods are required. A zoo of local refinement strategies for splines has been developed in the last decades. Such approaches impede the utilization of recent advances that rely on tensor-product splines, e.g., matrix assembly and preconditioning. We propose a strategy for adaptive IgA that utilizes well-known approaches from the multi-patch IgA toolbox: using tensor-product splines locally, but allow for unstructured patch configurations globally. Our approach moderately increases the number of patches and utilizes different grid sizes for each patch. This allows reusing the existing code bases, recovers the convergence rates of other adaptive approaches, and increases the number of degrees of freedom only marginally. We provide an algorithm for the computation of a global basis and show that it works in any case. Additionally, we give approximation error estimates. Numerical experiments illustrate our results.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"23 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841381","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

Adaptive fast L1 − 2 scheme for solving time fractional parabolic problems

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-10 DOI: 10.1016/j.camwa.2024.12.003

Jiliang Cao, Wansheng Wang, Aiguo Xiao

{"title":"Adaptive fast L1 − 2 scheme for solving time fractional parabolic problems","authors":"Jiliang Cao, Wansheng Wang, Aiguo Xiao","doi":"10.1016/j.camwa.2024.12.003","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.003","url":null,"abstract":"In this paper, we study a posteriori error estimates of the fast <mml:math altimg=\"si1.svg\"><mml:mi>L</mml:mi><mml:mn>1</mml:mn><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">−</mml:mo><mml:mn>2</mml:mn></mml:math> scheme for time discretization of time fractional parabolic differential equations. To overcome the huge workload caused by the nonlocality of fractional derivative, a fast algorithm is applied to the construction of the <mml:math altimg=\"si1.svg\"><mml:mi>L</mml:mi><mml:mn>1</mml:mn><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">−</mml:mo><mml:mn>2</mml:mn></mml:math> scheme. Employing the numerical solution obtained by the fast <mml:math altimg=\"si1.svg\"><mml:mi>L</mml:mi><mml:mn>1</mml:mn><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">−</mml:mo><mml:mn>2</mml:mn></mml:math> scheme, a piecewise continuous function approximating the exact solution is constructed. Then, by exploring the error equations, a posteriori error estimates are obtained in different norms, which depend only on the discretization parameters and the data of the problems. Various numerical experiments for the fractional parabolic equations with smooth or nonsmooth exact solutions on different time meshes, including the frequently-used graded mesh, are carried out to verify and complement our theoretical results. Based on the obtained a posteriori error estimates, a time adaptive algorithm is proposed to reduce the computational cost substantially and provides efficient error control for the solution.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"21 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142804472","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

Fractional-order dependent Radial basis functions meshless methods for the integral fractional Laplacian

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-12-10 DOI: 10.1016/j.camwa.2024.11.027

Zhaopeng Hao, Zhiqiang Cai, Zhongqiang Zhang

引用次数: 0