{"title":"用于特征值计算的自适应平面波方法的收敛性和复杂性","authors":"Xiaoying Dai,Yan Pan,Bin Yang, Aihui Zhou","doi":"10.4208/aamm.oa-2023-0099","DOIUrl":null,"url":null,"abstract":"In this paper, we study the adaptive planewave discretization for a cluster\nof eigenvalues of second-order elliptic partial differential equations. We first design\nan a posteriori error estimator and prove both the upper and lower bounds. Based on\nthe a posteriori error estimator, we propose an adaptive planewave method. We then\nprove that the adaptive planewave approximations have the linear convergence rate\nand quasi-optimal complexity","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations\",\"authors\":\"Xiaoying Dai,Yan Pan,Bin Yang, Aihui Zhou\",\"doi\":\"10.4208/aamm.oa-2023-0099\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study the adaptive planewave discretization for a cluster\\nof eigenvalues of second-order elliptic partial differential equations. We first design\\nan a posteriori error estimator and prove both the upper and lower bounds. Based on\\nthe a posteriori error estimator, we propose an adaptive planewave method. We then\\nprove that the adaptive planewave approximations have the linear convergence rate\\nand quasi-optimal complexity\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.4208/aamm.oa-2023-0099\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.4208/aamm.oa-2023-0099","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations
In this paper, we study the adaptive planewave discretization for a cluster
of eigenvalues of second-order elliptic partial differential equations. We first design
an a posteriori error estimator and prove both the upper and lower bounds. Based on
the a posteriori error estimator, we propose an adaptive planewave method. We then
prove that the adaptive planewave approximations have the linear convergence rate
and quasi-optimal complexity
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.