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Low regularity integrators for semilinear parabolic equations with maximum bound principles 具有最大界原理的半线性抛物方程的低正则积分器
3区 数学
BIT Numerical Mathematics Pub Date : 2023-01-27 DOI: 10.1007/s10543-023-00946-2
Cao-Kha Doan, Thi-Thao-Phuong Hoang, Lili Ju, Katharina Schratz
{"title":"Low regularity integrators for semilinear parabolic equations with maximum bound principles","authors":"Cao-Kha Doan, Thi-Thao-Phuong Hoang, Lili Ju, Katharina Schratz","doi":"10.1007/s10543-023-00946-2","DOIUrl":"https://doi.org/10.1007/s10543-023-00946-2","url":null,"abstract":"This paper is concerned with conditionally structure-preserving, low regularity time integration methods for a class of semilinear parabolic equations of Allen–Cahn type. Important properties of such equations include maximum bound principle (MBP) and energy dissipation law; for the former, that means the absolute value of the solution is pointwisely bounded for all the time by some constant imposed by appropriate initial and boundary conditions. The model equation is first discretized in space by the central finite difference, then by iteratively using Duhamel’s formula, first- and second-order low regularity integrators (LRIs) are constructed for time discretization of the semi-discrete system. The proposed LRI schemes are proved to preserve the MBP and the energy stability in the discrete sense. Furthermore, their temporal error estimates are also successfully derived under a low regularity requirement that the exact solution of the semi-discrete problem is only assumed to be continuous in time. Numerical results show that the proposed LRI schemes are more accurate and have better convergence rates than classic exponential time differencing schemes, especially when the interfacial parameter approaches zero.","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135744571","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}
引用次数: 1
Perturbation bounds for stable gyroscopic systems 稳定陀螺系统的摄动界
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-01-25 DOI: 10.1007/s10543-023-00943-5
I. Ivičić, Suzana Miodragović
{"title":"Perturbation bounds for stable gyroscopic systems","authors":"I. Ivičić, Suzana Miodragović","doi":"10.1007/s10543-023-00943-5","DOIUrl":"https://doi.org/10.1007/s10543-023-00943-5","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51984128","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}
引用次数: 0
Low-rank Parareal: a low-rank parallel-in-time integrator. 低秩并行积分器:一个低秩并行积分器。
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-01-01 DOI: 10.1007/s10543-023-00953-3
Benjamin Carrel, Martin J Gander, Bart Vandereycken
{"title":"Low-rank Parareal: a low-rank parallel-in-time integrator.","authors":"Benjamin Carrel,&nbsp;Martin J Gander,&nbsp;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":null,"pages":null},"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}
引用次数: 7
Correction to: a dimension expanded preconditioning technique for saddle point problems 修正:鞍点问题的一维扩展预处理技术
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2022-11-02 DOI: 10.1007/s10543-022-00940-0
W. Luo, Xianming Gu, B. Carpentieri
{"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":null,"pages":null},"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}
引用次数: 0
Decomposition and conformal mapping techniques for the quadrature of nearly singular integrals 近似奇异积分求积的分解和保角映射技术
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2022-10-18 DOI: 10.1007/s10543-023-00984-w
William Mitchell, Abbie Natkin, Paige Robertson, Marika Sullivan, Xuechen Yu, Chenxin Zhu
{"title":"Decomposition and conformal mapping techniques for the quadrature of nearly singular integrals","authors":"William Mitchell, Abbie Natkin, Paige Robertson, Marika Sullivan, Xuechen Yu, Chenxin Zhu","doi":"10.1007/s10543-023-00984-w","DOIUrl":"https://doi.org/10.1007/s10543-023-00984-w","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47603562","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}
引用次数: 0
Fully discrete heterogeneous multiscale method for parabolic problems with multiple spatial and temporal scales 求解多时空尺度抛物型问题的完全离散非均匀多尺度方法
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2022-10-10 DOI: 10.1007/s10543-023-00973-z
D. Eckhardt, B. Verfürth
{"title":"Fully discrete heterogeneous multiscale method for parabolic problems with multiple spatial and temporal scales","authors":"D. Eckhardt, B. Verfürth","doi":"10.1007/s10543-023-00973-z","DOIUrl":"https://doi.org/10.1007/s10543-023-00973-z","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47374673","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}
引用次数: 0
An efficient adaptive multigrid method for the elasticity eigenvalue problem 弹性特征值问题的一种高效自适应多重网格方法
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2022-09-21 DOI: 10.1007/s10543-022-00939-7
Fei Xu, Qiumei Huang, Manting Xie
{"title":"An efficient adaptive multigrid method for the elasticity eigenvalue problem","authors":"Fei Xu, Qiumei Huang, Manting Xie","doi":"10.1007/s10543-022-00939-7","DOIUrl":"https://doi.org/10.1007/s10543-022-00939-7","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46151544","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}
引用次数: 0
A dimension expanded preconditioning technique for saddle point problems 鞍点问题的维数扩展预处理技术
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2022-09-14 DOI: 10.1007/s10543-022-00938-8
W. Luo, Xianming Gu, B. Carpentieri
{"title":"A dimension expanded preconditioning technique for saddle point problems","authors":"W. Luo, Xianming Gu, B. Carpentieri","doi":"10.1007/s10543-022-00938-8","DOIUrl":"https://doi.org/10.1007/s10543-022-00938-8","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42730614","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}
引用次数: 1
A hierarchically low-rank optimal transport dissimilarity measure for structured data 结构化数据的分层低秩最优传输相异性度量
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2022-09-08 DOI: 10.1007/s10543-022-00937-9
M. Motamed
{"title":"A hierarchically low-rank optimal transport dissimilarity measure for structured data","authors":"M. Motamed","doi":"10.1007/s10543-022-00937-9","DOIUrl":"https://doi.org/10.1007/s10543-022-00937-9","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42839191","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}
引用次数: 0
Low-rank tensor structure preservation in fractional operators by means of exponential sums 用指数和方法保存分数算子中的低秩张量结构
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2022-08-10 DOI: 10.1007/s10543-023-00974-y
Angelo A. Casulli, L. Robol
{"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":null,"pages":null},"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}
引用次数: 0
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