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Numerical Mathematics-Theory Methods and Applications最新文献

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Absorbing Interface Conditions for the Simulation of Wave Propagation on NonUniform Meshes 模拟波浪在非均匀网格上传播的吸收界面条件
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0105
C. Li, Yuhui Liu, Fengru Wang, Jerry Zhijian Yang null, Cheng Yuan
{"title":"Absorbing Interface Conditions for the Simulation of Wave Propagation on NonUniform Meshes","authors":"C. Li, Yuhui Liu, Fengru Wang, Jerry Zhijian Yang null, Cheng Yuan","doi":"10.4208/nmtma.oa-2022-0105","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0105","url":null,"abstract":"We proposed absorbing interface conditions for the simulation of linear wave propagation on non-uniform meshes. Based on the superposition principle of second-order linear wave equations, we decompose the interface condition problem into two subproblems around the interface: for the first one the conventional artificial absorbing boundary conditions is applied, while for the second one, the local analytic solutions can be derived. The proposed interface conditions permit a two-way transmission of low-frequency waves across mesh interfaces which can be supported by both coarse and fine meshes, and perform a one-way absorption of high-frequency waves which can only be supported by fine meshes when they travel from fine mesh regions to coarse ones. Numerical examples are presented to illustrate the efficiency of the proposed absorbing interface conditions. AMS subject classifications: 35K10, 65N06","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48621800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Geometric Design of Letters in Times Roman Font via RBF Meshless Collocation Method 基于RBF无网格搭配法的Times Roman字体字母几何设计
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0189
Lionel Amuzu, C. S. Chen, Kwesi Acheampong and Huiqing Zhu
{"title":"Geometric Design of Letters in Times Roman Font via RBF Meshless Collocation Method","authors":"Lionel Amuzu, C. S. Chen, Kwesi Acheampong and Huiqing Zhu","doi":"10.4208/nmtma.oa-2022-0189","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0189","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43857846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 of Weak Galerkin Finite Element Method for Second Order Linear Wave Equation in Heterogeneous Media 非均匀介质中二阶线性波动方程的弱Galerkin有限元法的收敛性
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2021-0080
B. Deka, Papri Roy, Naresh Kumar null, R. Kumar
{"title":"Convergence of Weak Galerkin Finite Element Method for Second Order Linear Wave Equation in Heterogeneous Media","authors":"B. Deka, Papri Roy, Naresh Kumar null, R. Kumar","doi":"10.4208/nmtma.oa-2021-0080","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2021-0080","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43002509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Finding Symmetry Groups of Some Quadratic Programming Problems 一类二次规划问题的对称群的求法
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0092
{"title":"Finding Symmetry Groups of Some Quadratic Programming Problems","authors":"","doi":"10.4208/nmtma.oa-2022-0092","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0092","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49629676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Extended Two-Step Method for Inverse Eigenvalue Problems with Multiple Eigenvalues 多特征值反特征值问题的扩展两步法
4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2023-0002
Yue Wang and Weiping Shen
{"title":"An Extended Two-Step Method for Inverse Eigenvalue Problems with Multiple Eigenvalues","authors":"Yue Wang and Weiping Shen","doi":"10.4208/nmtma.oa-2023-0002","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2023-0002","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135195041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Green Function Method for Quantum Transport Based on the Generalized Fourier Transform 基于广义傅里叶变换的量子输运格林函数方法
4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0164
Haiyan Jiang, Xingming Gao, Yueguang Hu and Tiao Lu
{"title":"Green Function Method for Quantum Transport Based on the Generalized Fourier Transform","authors":"Haiyan Jiang, Xingming Gao, Yueguang Hu and Tiao Lu","doi":"10.4208/nmtma.oa-2022-0164","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0164","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135626591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model 全电子Kohn-Sham模型保结构梯度流法的收敛性分析
4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0195
Yedan Shen, Ting Wang, Jie Zhou and Guanghui Hu
{"title":"A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model","authors":"Yedan Shen, Ting Wang, Jie Zhou and Guanghui Hu","doi":"10.4208/nmtma.oa-2022-0195","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0195","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135046057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Adaptive Physics-Informed Neural Network with Two-Stage Learning Strategy to Solve Partial Differential Equations 求解偏微分方程的两阶段学习策略自适应物理知情神经网络
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0063
{"title":"An Adaptive Physics-Informed Neural Network with Two-Stage Learning Strategy to Solve Partial Differential Equations","authors":"","doi":"10.4208/nmtma.oa-2022-0063","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0063","url":null,"abstract":". Physics-Informed Neural Network (PINN) represents a new approach to solve Partial Differential Equations (PDEs). PINNs aim to solve PDEs by integrating governing equations and the initial/boundary conditions (I/BCs) into a loss function. However, the imbalance of the loss function caused by parameter settings usually makes it difficult for PINNs to converge, e.g. because they fall into local optima. In other words, the presence of balanced PDE loss, initial loss and boundary loss may be critical for the convergence. In addition, existing PINNs are not able to reveal the hidden errors caused by non-convergent boundaries and conduction errors caused by the PDE near the boundaries. Overall, these problems have made PINN-based methods of limited use on practical situations. In this paper, we propose a novel physics-informed neural network, i.e. an adaptive physics-informed neural network with a two-stage training process. Our algorithm adds spatio-temporal coefficient and PDE balance parameter to the loss function, and solve PDEs using a two-stage training process: pre-training and formal training. The pre-training step ensures the convergence of boundary loss, whereas the formal training process completes the solution of PDE","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48839344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 of a Quasi-Monte CarloBased Deep Learning Algorithm for Solving Partial Differential Equations 求解偏微分方程的拟蒙特卡罗深度学习算法的收敛性分析
4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0166
Fengjiang Fu and Xiaoqun Wang
{"title":"Convergence Analysis of a Quasi-Monte CarloBased Deep Learning Algorithm for Solving Partial Differential Equations","authors":"Fengjiang Fu and Xiaoqun Wang","doi":"10.4208/nmtma.oa-2022-0166","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0166","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135421680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Algebraic Multigrid-Based Physical Factorization Preconditioner for the Multi-Group Radiation Diffusion Equations in Three Dimensions 三维多群辐射扩散方程的代数多网格物理分解预条件
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0054
X. Yue, Zekai Zhang, Xiaowen Xu, Shuying Zhai null, S. Shu
{"title":"An Algebraic Multigrid-Based Physical Factorization Preconditioner for the Multi-Group Radiation Diffusion Equations in Three Dimensions","authors":"X. Yue, Zekai Zhang, Xiaowen Xu, Shuying Zhai null, S. Shu","doi":"10.4208/nmtma.oa-2022-0054","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0054","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47952344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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