Journal of Computational and Applied Mathematics最新文献_第7页

A greedy MOR method for the tracking of eigensolutions to parametric elliptic PDEs 用于跟踪参数椭圆 PDEs 特征解的贪婪 MOR 方法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-17 DOI: 10.1016/j.cam.2024.116270

Moataz Alghamdi , Daniele Boffi , Francesca Bonizzoni

引用次数: 0

Error analysis of the explicit-invariant energy quadratization (EIEQ) numerical scheme for solving the Allen–Cahn equation 用于求解艾伦-卡恩方程的显式不变能量四分法（EIEQ）数值方案的误差分析

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-16 DOI: 10.1016/j.cam.2024.116224

Jun Zhang , Fangying Song , Xiaofeng Yang , Yu Zhang

引用次数: 0

Generalized Multiscale Finite Element Method for discrete network (graph) models 离散网络（图）模型的广义多尺度有限元法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-13 DOI: 10.1016/j.cam.2024.116275

Maria Vasilyeva

引用次数: 0

Unconditional error analysis of the linearized transformed L1 virtual element method for nonlinear coupled time-fractional Schrödinger equations 非线性耦合时分数薛定谔方程线性化变换 L1 虚拟元素法的无条件误差分析

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-13 DOI: 10.1016/j.cam.2024.116283

Yanping Chen , Jixiao Guo

{"title":"Unconditional error analysis of the linearized transformed L1 virtual element method for nonlinear coupled time-fractional Schrödinger equations","authors":"Yanping Chen , Jixiao Guo","doi":"10.1016/j.cam.2024.116283","DOIUrl":"10.1016/j.cam.2024.116283","url":null,"abstract":"<div><div>This paper constructs a linearized transformed <span><math><mrow><mi>L</mi><mn>1</mn></mrow></math></span> virtual element method for the generalized nonlinear coupled time-fractional Schrödinger equations. The solutions to such problems typically exhibit singular behavior at the beginning. To avoid this pitfall, we introduce an identical <span><math><mi>s</mi></math></span>-fractional differential system derived from a smoothing transformation of variables <span><math><mrow><mi>t</mi><mo>=</mo><msup><mrow><mi>s</mi></mrow><mrow><mn>1</mn><mo>/</mo><mi>α</mi></mrow></msup></mrow></math></span>, <span><math><mrow><mn>0</mn><mo><</mo><mi>α</mi><mo><</mo><mn>1</mn></mrow></math></span>. By utilizing the discrete complementary convolution kernels, we prove the boundedness and error estimates of the solution of time-discrete system. Moreover, the unconditionally optimal error bounds of the proposed fully discrete scheme are derived in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm without restriction on the grid ratio. Finally, numerical tests on a set of polygonal meshes are presented to verify the theoretical results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142312509","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 new space transformed finite element method for elliptic interface problems in Rn Rn 中椭圆界面问题的新空间变换有限元法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-12 DOI: 10.1016/j.cam.2024.116277

Raghunath Bandha, Rajen Kumar Sinha

{"title":"A new space transformed finite element method for elliptic interface problems in Rn","authors":"Raghunath Bandha, Rajen Kumar Sinha","doi":"10.1016/j.cam.2024.116277","DOIUrl":"10.1016/j.cam.2024.116277","url":null,"abstract":"<div><p>Interface problems, where distinct materials or physical domains meet, pose significant challenges in numerical simulations due to the discontinuities and sharp gradients across interfaces. Traditional finite element methods struggle to capture such behavior accurately. A new space transformed finite element method (ST-FEM) is developed for solving elliptic interface problems in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. A homeomorphic stretching transformation is introduced to obtain an equivalent problem in the transformed domain which can be solved easily, and the solution can be projected back to original domain by the inverse transformation. Compared with the existing methods, this new scheme has capability of handling discontinuities across the interface. The proposed approach has advantages in circumventing interface approximation properties and reducing the degree of freedom. We initially develop ST-FEM for elliptic problems and subsequently expand upon this concept to address elliptic interface problems. We prove optimal a priori error estimates in the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norms, and quasi-optimal error estimate for the maximum norm. Finally, numerical experiments demonstrate the superior accuracy and convergence properties of the ST-FEM when compared to the standard finite element method. The interface is assumed to be a <span><math><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></math></span>-sphere, nevertheless, our analysis can cover symmetric domains such as an ellipsoid or a cylinder.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142241453","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

Representation computation for the hypergeometric function of a Hermitian matrix argument 赫米矩阵参数的超几何函数的表示计算

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-12 DOI: 10.1016/j.cam.2024.116258

Duong Thanh Phong

引用次数: 0

A new proper orthogonal decomposition method with second difference quotients for the wave equation 波方程的新适当正交分解法与二次差商

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-12 DOI: 10.1016/j.cam.2024.116279

Andrew Janes, John R. Singler

{"title":"A new proper orthogonal decomposition method with second difference quotients for the wave equation","authors":"Andrew Janes, John R. Singler","doi":"10.1016/j.cam.2024.116279","DOIUrl":"10.1016/j.cam.2024.116279","url":null,"abstract":"<div><div>Recently, researchers have investigated the relationship between proper orthogonal decomposition (POD), difference quotients (DQs), and pointwise in time error bounds for POD reduced order models of partial differential equations. In a recent work (Eskew and Singler, Adv. Comput. Math., 49, 2023, no. 2, Paper No. 13), a new approach to POD with DQs was developed that is more computationally efficient than the standard DQ POD approach and it also retains the guaranteed pointwise in time error bounds of the standard method. In this work, we extend this new DQ POD approach to the case of second difference quotients (DDQs). Specifically, a new POD method utilizing DDQs and only one snapshot and one DQ is developed and used to prove ROM error bounds for the damped wave equation. This new approach eliminates data redundancy in the standard DDQ POD approach that uses all of the snapshots, DQs, and DDQs. We show that this new DDQ approach also has pointwise in time data error bounds similar to DQ POD and use it to prove pointwise and energy ROM error bounds. We provide numerical results for the POD ROM errors to demonstrate the theoretical results. We also explore an application of POD to simulate ROMs past the training interval for collecting the snapshot data for the standard POD approach and the DDQ POD method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142358924","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 multilevel finite element method for a generalized nonlinear Schrödinger equation 广义非线性薛定谔方程的新型多级有限元方法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-12 DOI: 10.1016/j.cam.2024.116280

Fei Xu , Yasai Guo , Manting Xie

{"title":"A novel multilevel finite element method for a generalized nonlinear Schrödinger equation","authors":"Fei Xu , Yasai Guo , Manting Xie","doi":"10.1016/j.cam.2024.116280","DOIUrl":"10.1016/j.cam.2024.116280","url":null,"abstract":"<div><p>In this article, we focus on an efficient multilevel finite element method to solve the time-dependent nonlinear Schrödinger equation which is one of the most important equations of mathematical physics. For the time derivative, we adopt implicit schemes including the backward Euler method and the Crank–Nicolson method. Based on these stable implicit schemes, the proposed method requires solving a nonlinear elliptic problem at each time step. For these nonlinear elliptic equations, a multilevel mesh sequence is constructed. At each mesh level, we first derive a rough approximation by correcting the approximation of the previous mesh level in a special correction subspace. The correction subspace is composed of a coarse finite element space and an additional approximate solution derived from the previous mesh level. Next, we only need to solve a linearized elliptic equation by inserting the rough approximation into the nonlinear term. Then, we derive an accurate approximate solution by performing the aforementioned solving process on the multilevel mesh sequence until we reach the final mesh level. Owing to the special construct of the correction subspace, we derive a multilevel finite element method to solve the nonlinear Schrödinger equation for the first time, and meanwhile we also derive an optimal error estimate with linear computational complexity. Additionally, unlike the existing multilevel methods for nonlinear problems, that typically require bounded second-order derivatives of the nonlinear terms, the nonlinear term in our study requires only one-order derivatives. Numerical results are provided to support our theoretical analysis and demonstrate the efficiency of the presented method.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142173521","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

Convergence analysis and applicability of a domain decomposition method with nonlocal interface boundary conditions 具有非局部界面边界条件的域分解方法的收敛性分析和适用性

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-12 DOI: 10.1016/j.cam.2024.116276

Hongru Li, Miltiadis V. Papalexandris

{"title":"Convergence analysis and applicability of a domain decomposition method with nonlocal interface boundary conditions","authors":"Hongru Li, Miltiadis V. Papalexandris","doi":"10.1016/j.cam.2024.116276","DOIUrl":"10.1016/j.cam.2024.116276","url":null,"abstract":"<div><p>In the past, the domain decomposition method was developed successfully for solving large-scale linear systems. However, the problems with significant nonlocal effect remain a major challenger for applying the method efficiently. In order to sort out the problem, a non-overlapping domain decomposition method with nonlocal interface boundary conditions was recently proposed and studied both theoretically and numerically. This paper is the report on the further development of the method, aiming to provide a comprehensive convergence analysis of the method, with supplementary numerical tests to support the theoretical result. The nonlocal effect of the problem is found to be reflected in both the governing equation and boundary conditions, and the effect of the latter was never taken into account, although playing a significant role in affecting the convergence. In addition, the paper extends the applicability of the analysis result drawn from the Poisson’s equation to more complicated problems by examining the symbols of the Steklov–Poincaré operators. The extended application includes a model equation arising from fluid dynamics and the high performance of the domain decomposition method in solving this equation is better elaborated.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142241450","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

Mixed finite element method for multi-layer elastic contact systems 多层弹性接触系统的混合有限元法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-12 DOI: 10.1016/j.cam.2024.116281

Zhizhuo Zhang , Mikaël Barboteu , Xiaobing Nie , Serge Dumont , Mahmoud Abdel-Aty , Jinde Cao

引用次数: 0