Numerical Methods for Partial Differential Equations最新文献_第2页

Error estimates of exponential wave integrators for the Dirac equation in the massless and nonrelativistic regime 无质量和非相对论状态下狄拉克方程指数波积分器的误差估计

IF 2.1 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2024-08-09 DOI: 10.1002/num.23128

Ying Ma, Lizhen Chen

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Determining a time‐varying potential in time‐fractional diffusion from observation at a single point 通过单点观测确定时间分形扩散中的时变势能

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2024-08-06 DOI: 10.1002/num.23136

Siyu Cen, Kwancheol Shin, Zhi Zhou

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On the optimality of voronoi‐based column selection 基于 voronoi 的列选择的最优性

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2024-08-06 DOI: 10.1002/num.23137

Maria Emelianenko, Guy B. Oldaker

{"title":"On the optimality of voronoi‐based column selection","authors":"Maria Emelianenko, Guy B. Oldaker","doi":"10.1002/num.23137","DOIUrl":"https://doi.org/10.1002/num.23137","url":null,"abstract":"While there exists a rich array of matrix column subset selection problem (CSSP) algorithms for use with interpolative and CUR‐type decompositions, their use can often become prohibitive as the size of the input matrix increases. In an effort to address these issues, in earlier work we developed a general framework that pairs a column‐partitioning routine with a column‐selection algorithm. Two of the four algorithms presented in that work paired the Centroidal Voronoi Orthogonal Decomposition (CVOD; Centroidal Voronoi Tessellation Based Proper Orthogonal Decomposition Analysis, 2003, 137–150) and an adaptive variant (adaptCVOD) with the Discrete Empirical Interpolation Method (DEIM; SIAM J. Sci. Computer. 38 (2016), no. 3, A1454–A1482). In this work, we extend this framework and pair the CVOD‐type algorithms with any CSSP algorithm that returns linearly independent columns. Our results include detailed error bounds for the solutions provided by these paired algorithms, as well as expressions that explicitly characterize how the quality of the selected column partition affects the resulting CSSP solution. In addition to examples involving matrix approximation, we test several of our partition‐based constructions on tasks commonly encountered in model order reduction (MOR).","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Semiexplicit K‐symplectic‐like methods with energy conservation for noncanonical Hamiltonian systems 非正则哈密顿系统能量守恒的半显式 K-交映法

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2024-08-05 DOI: 10.1002/num.23138

Beibei Zhu, Ran Gu

{"title":"Semiexplicit K‐symplectic‐like methods with energy conservation for noncanonical Hamiltonian systems","authors":"Beibei Zhu, Ran Gu","doi":"10.1002/num.23138","DOIUrl":"https://doi.org/10.1002/num.23138","url":null,"abstract":"For the nonseparable noncanonical Hamiltonian systems, we propose efficient K‐symplectic‐like methods which are semiexplicit and energy‐preserving. By introducing two copies of the phase space and constructing an augmented Hamiltonian, we can separate the noncanonical Hamiltonian system into two explicitly integrable parts. Subsequently, explicit K‐symplectic methods can be constructed by using the splitting and composing method. To enforce constraints on the two copies of the phase space, we provide two transformations with energy conservation property. This enables us to obtain semiexplicit K‐symplectic‐like methods that preserve energy. Two algorithms are provided to implement the semiexplicit K‐symplectic‐like methods with energy conservation and their convergence has been proved. Numerical results on two noncanonical Hamiltonian systems demonstrate that the energy errors of our proposed methods remain bounded within machine precision over long time without exhibiting energy drift. Furthermore, the proposed methods exhibit superior computational efficiency compared to the canonicalized symplectic methods of the same order.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

High‐order in‐cell discontinuous reconstruction path‐conservative methods for nonconservative hyperbolic systems–DR.MOOD method 非守恒双曲系统的高阶单元内不连续重构路径守恒方法--DR.MOOD 方法

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2024-08-02 DOI: 10.1002/num.23133

Ernesto Pimentel‐García, Manuel J. Castro, Christophe Chalons, Carlos Parés

引用次数: 0

Uniform and optimal error estimates of a nested Picard integrator for the nonlinear Schrödinger equation with wave operator 带波算子的非线性薛定谔方程嵌套皮卡尔积分器的均匀和最优误差估计

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2024-08-02 DOI: 10.1002/num.23135

Yongyong Cai, Yue Feng, Yichen Guo, Zhiguo Xu

引用次数: 0

Partitioning method for the finite element approximation of a 3D fluid‐2D plate interaction system 三维流体-二维板相互作用系统有限元近似的分区法

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2024-08-01 DOI: 10.1002/num.23132

Pelin G. Geredeli, Hemanta Kunwar, Hyesuk Lee

{"title":"Partitioning method for the finite element approximation of a 3D fluid‐2D plate interaction system","authors":"Pelin G. Geredeli, Hemanta Kunwar, Hyesuk Lee","doi":"10.1002/num.23132","DOIUrl":"https://doi.org/10.1002/num.23132","url":null,"abstract":"We consider the finite element approximation of a coupled fluid‐structure interaction (FSI) system, which comprises a three‐dimensional (3D) Stokes flow and a two‐dimensional (2D) fourth‐order Euler–Bernoulli or Kirchhoff plate. The interaction of these parabolic and hyperbolic partial differential equations (PDE) occurs at the boundary interface which is assumed to be fixed. The vertical displacement of the plate dynamics evolves on the flat portion of the boundary where the coupling conditions are implemented via the matching velocities of the plate and fluid flow, as well as the Dirichlet boundary trace of the pressure. This pressure term also acts as a coupling agent, since it appears as a forcing term on the flat, elastic plate domain. Our main focus in this work is to generate some numerical results concerning the approximate solutions to the FSI model. For this, we propose a numerical algorithm that sequentially solves the fluid and plate subsystems through an effective decoupling approach. Numerical results of test problems are presented to illustrate the performance of the proposed method.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141884918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 type of multigrid method for semilinear elliptic problems based on symmetric interior penalty discontinuous Galerkin method 基于对称内部惩罚非连续伽勒金方法的一种半线性椭圆问题多网格方法

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2024-08-01 DOI: 10.1002/num.23130

Fan Chen, Ming Cui, Chenguang Zhou

引用次数: 0

Optimal control of variably distributed‐order time‐fractional diffusion equation: Analysis and computation 可变分布阶时间分数扩散方程的优化控制：分析与计算

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2024-08-01 DOI: 10.1002/num.23134

Xiangcheng Zheng, Huan Liu, Hong Wang, Xu Guo

引用次数: 0

Numerical solution of convected wave equation in free field using artificial boundary method 用人工边界法数值求解自由场中的对流波方程

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2024-07-29 DOI: 10.1002/num.23131

Xin Wang, Jihong Wang, Yana Di, Jiwei Zhang

{"title":"Numerical solution of convected wave equation in free field using artificial boundary method","authors":"Xin Wang, Jihong Wang, Yana Di, Jiwei Zhang","doi":"10.1002/num.23131","DOIUrl":"https://doi.org/10.1002/num.23131","url":null,"abstract":"In this article, we propose two procedures focusing on the computation of the time‐dependent convected wave equation in a free field with a uniform background flow. Both procedures are based on a framework, expended from Du et al. (SIAM J. Sci. Comput. 40 (2018), A1430–A1445.), of constructing the Dirichlet‐to‐Dirichlet (DtD)‐type discrete absorbing boundary conditions (ABCs). The first procedure is dedicated to reducing the infinite problem into a finite problem by a direct application of the framework on the finite difference discretization of the convected wave equation. However, the presence of convection terms makes the stability analysis hard to implement, which motivates us to develop the second procedure. First, the convected wave equation is transformed into a standard wave equation by using the Prandtl‐Glauert‐Lorentz transformation. After that, we obtain the DtD‐type ABC by using the above framework, and on this basis, derive an equivalent Dirichlet‐to‐Neumann‐type ABCs, which makes stability and convergence analysis easy to be obtained by the classical energy method. The effectiveness and comparison of these two procedures are investigated through numerical experiments.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141863952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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