Benjamin Carrel, Martin J Gander, Bart Vandereycken
{"title":"Low-rank Parareal: a low-rank parallel-in-time integrator.","authors":"Benjamin Carrel, Martin J Gander, Bart Vandereycken","doi":"10.1007/s10543-023-00953-3","DOIUrl":"https://doi.org/10.1007/s10543-023-00953-3","url":null,"abstract":"<p><p>In this work, the Parareal algorithm is applied to evolution problems that admit good low-rank approximations and for which the dynamical low-rank approximation (DLRA) can be used as time stepper. Many discrete integrators for DLRA have recently been proposed, based on splitting the projected vector field or by applying projected Runge-Kutta methods. The cost and accuracy of these methods are mostly governed by the rank chosen for the approximation. These properties are used in a new method, called low-rank Parareal, in order to obtain a time-parallel DLRA solver for evolution problems. The algorithm is analyzed on affine linear problems and the results are illustrated numerically.</p>","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"63 1","pages":"13"},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9899195/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9244043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Correction to: a dimension expanded preconditioning technique for saddle point problems","authors":"W. Luo, Xianming Gu, B. Carpentieri","doi":"10.1007/s10543-022-00940-0","DOIUrl":"https://doi.org/10.1007/s10543-022-00940-0","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"62 1","pages":"2035 - 2035"},"PeriodicalIF":1.5,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44690786","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}
{"title":"Low-rank tensor structure preservation in fractional operators by means of exponential sums","authors":"Angelo A. Casulli, L. Robol","doi":"10.1007/s10543-023-00974-y","DOIUrl":"https://doi.org/10.1007/s10543-023-00974-y","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"63 1","pages":"1-26"},"PeriodicalIF":1.5,"publicationDate":"2022-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43579189","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}