CSIAM Transactions on Applied Mathematics最新文献_第6页

A Family of curl-curl Conforming Finite Elements on Tetrahedral Meshes 四面体网格上的一类旋-旋合有限元

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2020-06-01 DOI: 10.4208/csiam-am.2020-0023

Qian Zhang

引用次数: 10

Advantage and Disadvantage of Dispersal in Two-Species Competition Models 两种群竞争模型中分散的优缺点

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2020-06-01 DOI: 10.4208/csiam-am.2020-0002

M. Lou

引用次数: 2

Analysis of Coarse-Grained Lattice Models and Connections to Nonlocal Interactions 粗粒度格模型的分析及其与非局部相互作用的联系

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2020-06-01 DOI: 10.4208/csiam-am.2020-0009

Q. Du

引用次数: 1

A Derivative-Free Geometric Algorithm for Optimization on a Sphere 球面上的无导数几何优化算法

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2020-06-01 DOI: 10.4208/csiam-am.2020-0026

Yannan Chen

{"title":"A Derivative-Free Geometric Algorithm for Optimization on a Sphere","authors":"Yannan Chen","doi":"10.4208/csiam-am.2020-0026","DOIUrl":"https://doi.org/10.4208/csiam-am.2020-0026","url":null,"abstract":"Optimization on a unit sphere finds crucial applications in science and engineering. However, derivatives of the objective function may be difficult to compute or corrupted by noises, or even not available in many applications. Hence, we propose a Derivative-Free Geometric Algorithm (DFGA) which, to the best of our knowledge, is the first derivative-free algorithm that takes trust region framework and explores the spherical geometry to solve the optimization problem with a spherical constraint. Nice geometry of the spherical surface allows us to pursue the optimization at each iteration in a local tangent space of the sphere. Particularly, by applying Householder and Cayley transformations, DFGA builds a quadratic trust region model on the local tangent space such that the local optimization can essentially be treated as an unconstrained optimization. Under mild assumptions, we show that there exists a subsequence of the iterates generated by DFGA converging to a stationary point of this spherical optimization. Furthermore, under the Lojasiewicz property, we show that all the iterates generated by DFGA will converge with at least a linear or sublinear convergence rate. Our numerical experiments on solving the spherical location problems, subspace clustering and image segmentation problems resulted from hypergraph partitioning, indicate DFGA is very robust and efficient for solving optimization on a sphere without using derivatives.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":"142 ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41273197","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: 2

How to Define Dissipation-Preserving Energy for Time-Fractional Phase-Field Equations 如何定义时间分数相场方程的保耗散能量

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2020-06-01 DOI: 10.4208/csiam-am.2020-0024

Chaoyu Quan, T. Tang, Jiang Yang

引用次数: 34

Dynamical Analysis of Transmission Model of the Cattle Foot-and-Mouth Disease 牛口蹄疫传播模型的动力学分析

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2020-06-01 DOI: 10.4208/csiam-am.2020-0011

Feng Li

引用次数: 1

An Adaptive Block Bregman Proximal Gradient Method for Computing Stationary States of Multicomponent Phase-Field Crystal Model 多组分相场晶体模型稳态计算的自适应块Bregman近端梯度法

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2020-05-26 DOI: 10.4208/csiam-am.so-2021-0002

Chenglong Bao, Chang Chen, Kai Jiang

{"title":"An Adaptive Block Bregman Proximal Gradient Method for Computing Stationary States of Multicomponent Phase-Field Crystal Model","authors":"Chenglong Bao, Chang Chen, Kai Jiang","doi":"10.4208/csiam-am.so-2021-0002","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2021-0002","url":null,"abstract":"In this paper, we compute the stationary states of the multicomponent phase-field crystal model by formulating it as a block constrained minimization problem. The original infinite-dimensional non-convex minimization problem is approximated by a finite-dimensional constrained non-convex minimization problem after an appropriate spatial discretization. To efficiently solve the above optimization problem, we propose a so-called adaptive block Bregman proximal gradient (AB-BPG) algorithm that fully exploits the problem's block structure. The proposed method updates each order parameter alternatively, and the update order of blocks can be chosen in a deterministic or random manner. Besides, we choose the step size by developing a practical linear search approach such that the generated sequence either keeps energy dissipation or has a controllable subsequence with energy dissipation. The convergence property of the proposed method is established without the requirement of global Lipschitz continuity of the derivative of the bulk energy part by using the Bregman divergence. The numerical results on computing stationary ordered structures in binary, ternary, and quinary component coupled-mode Swift-Hohenberg models have shown a significant acceleration over many existing methods.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2020-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43983089","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

Detecting Suspected Epidemic Cases Using Trajectory Big Data 利用轨迹大数据检测疑似疫情

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2020-04-01 DOI: 10.4208/CSIAM-AM.2020-0006

Chuansai Zhou, Wen Yuan, Jun Wang, Hai-feng Xu, Yong Jiang, Xinmin Wang, Q. Wen, Pingwen Zhang

{"title":"Detecting Suspected Epidemic Cases Using Trajectory Big Data","authors":"Chuansai Zhou, Wen Yuan, Jun Wang, Hai-feng Xu, Yong Jiang, Xinmin Wang, Q. Wen, Pingwen Zhang","doi":"10.4208/CSIAM-AM.2020-0006","DOIUrl":"https://doi.org/10.4208/CSIAM-AM.2020-0006","url":null,"abstract":"Emerging infectious diseases are existential threats to human health and global stability. The recent outbreaks of the novel coronavirus COVID-19 have rapidly formed a global pandemic, causing hundreds of thousands of infections and huge economic loss. The WHO declares that more precise measures to track, detect and isolate infected people are among the most effective means to quickly contain the outbreak. Based on trajectory provided by the big data and the mean field theory, we establish an aggregated risk mean field that contains information of all risk-spreading particles by proposing a spatio-temporal model named HiRES risk map. It has dynamic fine spatial resolution and high computation efficiency enabling fast update. We then propose an objective individual epidemic risk scoring model named HiRES-p based on HiRES risk maps, and use it to develop statistical inference and machine learning methods for detecting suspected epidemic-infected individuals. We conduct numerical experiments by applying the proposed methods to study the early outbreak of COVID-19 in China. Results show that the HiRES risk map has strong ability in capturing global trend and local variability of the epidemic risk, thus can be applied to monitor epidemic risk at country, province, city and community levels, as well as at specific high-risk locations such as hospital and station. HiRES-p score seems to be an effective measurement of personal epidemic risk. The accuracy of both detecting methods are above 90% when the population infection rate is under 20%, which indicates great application potential in epidemic risk prevention and control practice.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49008756","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: 15

Optimality Conditions for Constrained Minimax Optimization 约束极大极小优化的最优性条件

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2020-04-01 DOI: 10.4208/csiam-am.2020-0014

Yuhong Dai, Liwei Zhang

引用次数: 18

An Efficient Threshold Dynamics Method for Topology Optimization for Fluids 流体拓扑优化的有效阈值动力学方法

IF 1.3

CSIAM Transactions on Applied Mathematics Pub Date : 2018-12-22 DOI: 10.4208/csiam-am.so-2021-0007

Huangxin Chen, Haitao Leng, Dong Wang, Xiaoping Wang

{"title":"An Efficient Threshold Dynamics Method for Topology Optimization for Fluids","authors":"Huangxin Chen, Haitao Leng, Dong Wang, Xiaoping Wang","doi":"10.4208/csiam-am.so-2021-0007","DOIUrl":"https://doi.org/10.4208/csiam-am.so-2021-0007","url":null,"abstract":"We propose an efficient threshold dynamics method for topology optimization for fluids modeled with the Stokes equation. The proposed algorithm is based on minimization of an objective energy function that consists of the dissipation power in the fluid and the perimeter approximated by nonlocal energy, subject to a fluid volume constraint and the incompressibility condition. We show that the minimization problem can be solved with an iterative scheme in which the Stokes equation is approximated by a Brinkman equation. The indicator functions of the fluid-solid regions are then updated according to simple convolutions followed by a thresholding step. We demonstrate mathematically that the iterative algorithm has the total energy decaying property. The proposed algorithm is simple and easy to implement. A simple adaptive time strategy is also used to accelerate the convergence of the iteration. Extensive numerical experiments in both two and three dimensions show that the proposed iteration algorithm converges in much fewer iterations and is more efficient than many existing methods. In addition, the numerical results show that the algorithm is very robust and insensitive to the initial guess and the parameters in the model.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2018-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44393055","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: 5