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A New Locking-Free Virtual Element Method for Linear Elasticity Problems 线性弹性问题的一种新的无锁定虚拟单元方法
应用数学年刊:英文版 Pub Date : 2023-09-01 DOI: 10.4208/aam.oa-2023-0024
Jianguo Huang, Sen Lin and Yue Yu
{"title":"A New Locking-Free Virtual Element Method for Linear Elasticity Problems","authors":"Jianguo Huang, Sen Lin and Yue Yu","doi":"10.4208/aam.oa-2023-0024","DOIUrl":"https://doi.org/10.4208/aam.oa-2023-0024","url":null,"abstract":". This paper devises a new lowest-order conforming virtual element method (VEM) for planar linear elasticity with the pure displacement/traction boundary condition. The main trick is to view a generic polygon K as a new one (cid:101) K with additional vertices consisting of interior points on edges of K , so that the discrete admissible space is taken as the V 1 type virtual element space related to the partition { (cid:101) K } instead of { K } . The method is proved to converge with optimal convergence order both in H 1 and L 2 norms and uniformly with respect to the Lam´e constant λ . Numerical tests are presented to illustrate the good performance of the proposed VEM and confirm the theoretical results.","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44305830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Iterative Thresholding Method for the Heat Transfer Problem 热传递问题的迭代阈值法
应用数学年刊:英文版 Pub Date : 2023-09-01 DOI: 10.4208/aam.oa-2023-0017
Luyu Cen and Xiaoping Wang
{"title":"An Iterative Thresholding Method for the Heat Transfer Problem","authors":"Luyu Cen and Xiaoping Wang","doi":"10.4208/aam.oa-2023-0017","DOIUrl":"https://doi.org/10.4208/aam.oa-2023-0017","url":null,"abstract":". In this paper, we propose a simple energy decaying iterative thresh-olding algorithm to solve the heat transfer problem. The material domain is implicitly represented by its characteristic function, and the problem is formulated into a minimum-minimum problem. We prove that the energy is decreasing in each iteration. Numerical experiments for two types the heat transfer problems (volume to point and volume to sides) are performed to demonstrate the effectiveness of the proposed methods.","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47606132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Improved Analysis of PINNs: Alleviate the CoD for Compositional Solutions 改进的PINNs分析：减轻组合解决方案的CoD
应用数学年刊:英文版 Pub Date : 2023-09-01 DOI: 10.4208/aam.oa-2023-0021
Yuling Jiao, Xiliang Lu, Jerry Zhijian Yang, Cheng Yuan and Pingwen Zhang
{"title":"Improved Analysis of PINNs: Alleviate the CoD for Compositional Solutions","authors":"Yuling Jiao, Xiliang Lu, Jerry Zhijian Yang, Cheng Yuan and Pingwen Zhang","doi":"10.4208/aam.oa-2023-0021","DOIUrl":"https://doi.org/10.4208/aam.oa-2023-0021","url":null,"abstract":". In this paper, we present an improved analysis of the Physics In-formed Neural Networks (PINNs) method for solving second-order elliptic equations. By assuming an intrinsic sparse structure in the underlying solution, we provide a convergence rate analysis that can overcome the curse of dimensionality (CoD). Specifically, using some approximation theory in Sobolev space together with the multivariate Faa di Bruno formula, we first derive the approximation error for composition functions with a small degree of freedom in each compositional layer. Furthermore, by integrating several results on the statistical error of neural networks, we obtain a refined convergence rate analysis for PINNs in solving elliptic equations with compositional solutions. We also demonstrate the benefits of the intrinsic sparse structure with two simple numerical examples.","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47061352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fast High Order and Energy Dissipative Schemes with Variable Time Steps for Time-Fractional Molecular Beam Epitaxial Growth Model 时间分数分子束外延生长模型的快速高阶变时间步长消能格式
应用数学年刊:英文版 Pub Date : 2023-09-01 DOI: 10.4208/aam.oa-2023-0007
Dianming Hou, Zhonghua Qiaoand Tao Tang
{"title":"Fast High Order and Energy Dissipative Schemes with Variable Time Steps for Time-Fractional Molecular Beam Epitaxial Growth Model","authors":"Dianming Hou, Zhonghua Qiaoand Tao Tang","doi":"10.4208/aam.oa-2023-0007","DOIUrl":"https://doi.org/10.4208/aam.oa-2023-0007","url":null,"abstract":"","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43436056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Error Analysis of the Nonconforming $P_1$ Finite Element Method to the Sequential Regularization Formulation for Unsteady Navier-Stokes Equations 非定常Navier-Stokes方程序贯正则化公式的非定常P_1有限元法误差分析
应用数学年刊:英文版 Pub Date : 2023-09-01 DOI: 10.4208/aam.oa-2023-0016
Yanming Lai, Kewei Liang, Ping Lin, Xiliang Lu and Qimeng Quan
{"title":"Error Analysis of the Nonconforming $P_1$ Finite Element Method to the Sequential Regularization Formulation for Unsteady Navier-Stokes Equations","authors":"Yanming Lai, Kewei Liang, Ping Lin, Xiliang Lu and Qimeng Quan","doi":"10.4208/aam.oa-2023-0016","DOIUrl":"https://doi.org/10.4208/aam.oa-2023-0016","url":null,"abstract":"","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42301682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Linearized Adaptive Dynamic Diffusion Finite Element Method for Convection-Diffusion-Reaction Equations 对流扩散反应方程的线性自适应动态扩散有限元方法
应用数学年刊:英文版 Pub Date : 2023-09-01 DOI: 10.4208/aam.oa-2023-0018
Shaohong Du, Qianqian Hou and Xiaoping Xie
{"title":"A Linearized Adaptive Dynamic Diffusion Finite Element Method for Convection-Diffusion-Reaction Equations","authors":"Shaohong Du, Qianqian Hou and Xiaoping Xie","doi":"10.4208/aam.oa-2023-0018","DOIUrl":"https://doi.org/10.4208/aam.oa-2023-0018","url":null,"abstract":". In this paper, we consider a modified nonlinear dynamic diffusion (DD) method for convection-diffusion-reaction equations. This method is free of stabilization parameters and capable of precluding spurious oscillations. We develop a reliable and efficient residual-type a posteriori error estimator","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45816750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonisospectral Lotka--Volterra Systems as a Candidate Model for Food Chain 作为食物链候选模型的非等谱Lotka-Volterra系统
应用数学年刊:英文版 Pub Date : 2023-06-01 DOI: 10.4208/aam.oa-2023-0014
Xiaohui Hu
{"title":"Nonisospectral Lotka--Volterra Systems as a Candidate Model for Food Chain","authors":"Xiaohui Hu","doi":"10.4208/aam.oa-2023-0014","DOIUrl":"https://doi.org/10.4208/aam.oa-2023-0014","url":null,"abstract":". In this paper, we derive a generalized nonisospectral semi-infinite Lotka–Volterra equation, which possesses a determinant solution. We also give its a Lax pair expressed in terms of symmetric orthogonal polynomials. In addition, if the simplified case of the moment evolution relation is considered, that is, without the convolution term, we also give a generalized nonisospectral finite Lotka–Volterra equation with an explicit determinant solution. Finally, an application of the generalized nonisospectral continuous-time Lotka–Volterra equation in the food chain is investigated by numerical simulation. Our approach is mainly based on Hirota’s bilinear method and determinant techniques.","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42017586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonnegative Low Rank Matrix Completion by Riemannian Optimalization Methods 黎曼优化方法的非负低秩矩阵补全
应用数学年刊:英文版 Pub Date : 2023-06-01 DOI: 10.4208/aam.oa-2023-0010
Guang-Jing Song null, Michael K. Ng
{"title":"Nonnegative Low Rank Matrix Completion by Riemannian Optimalization Methods","authors":"Guang-Jing Song null, Michael K. Ng","doi":"10.4208/aam.oa-2023-0010","DOIUrl":"https://doi.org/10.4208/aam.oa-2023-0010","url":null,"abstract":"","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43304932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
$U$-Eigenvalues’ Inclusion Sets of Complex Tensors 复张量的$U$-特征值包含集
应用数学年刊:英文版 Pub Date : 2023-06-01 DOI: 10.4208/aam.oa-2023-0006
C. Null, H. Yao
{"title":"$U$-Eigenvalues’ Inclusion Sets of Complex Tensors","authors":"C. Null, H. Yao","doi":"10.4208/aam.oa-2023-0006","DOIUrl":"https://doi.org/10.4208/aam.oa-2023-0006","url":null,"abstract":"","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47474600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rough Heston Models with Variable Vol-of-Vol and Option Pricing 变容量Rough Heston模型与期权定价
应用数学年刊:英文版 Pub Date : 2023-06-01 DOI: 10.4208/aam.oa-2023-0009
Hui Liang, Jingtang Ma null, Zhengguang Shi
{"title":"Rough Heston Models with Variable Vol-of-Vol and Option Pricing","authors":"Hui Liang, Jingtang Ma null, Zhengguang Shi","doi":"10.4208/aam.oa-2023-0009","DOIUrl":"https://doi.org/10.4208/aam.oa-2023-0009","url":null,"abstract":". In this paper, a rough Heston model with variable volatility of volatility (vol-of-vol) is derived by modifying the generalized nonlinear Hawkes process and extending the scaling techniques. Then the nonlinear fractional Riccati equation for the characteristic function of the asset log-price is derived. The existence, uniqueness and regularity of the solution to the nonlinear fractional Riccati equation are proved and the equation is solved by the Adams methods. Finally the Fourier-cosine methods are combined with the Adams methods to price the options.","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44622738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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