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Convergence of trigonometric and finite-difference discretization schemes for FFT-based computational micromechanics 基于fft的计算细观力学的三角和有限差分离散格式的收敛性
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-02-01 DOI: 10.1007/s10543-023-00950-6
Changqing Ye, Eric T. Chung
{"title":"Convergence of trigonometric and finite-difference discretization schemes for FFT-based computational micromechanics","authors":"Changqing Ye, Eric T. Chung","doi":"10.1007/s10543-023-00950-6","DOIUrl":"https://doi.org/10.1007/s10543-023-00950-6","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"25 1","pages":"1-26"},"PeriodicalIF":1.5,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81566853","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: 5
Quadrature processes for efficient calculation of the Clausen functions 有效计算克劳森函数的正交过程
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-02-01 DOI: 10.1007/s10543-023-00944-4
Zora Lj. Golubović, G. Milovanović
{"title":"Quadrature processes for efficient calculation of the Clausen functions","authors":"Zora Lj. Golubović, G. Milovanović","doi":"10.1007/s10543-023-00944-4","DOIUrl":"https://doi.org/10.1007/s10543-023-00944-4","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"63 1","pages":"1-20"},"PeriodicalIF":1.5,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46417221","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
Rank-adaptive dynamical low-rank integrators for first-order and second-order matrix differential equations 一阶和二阶矩阵微分方程的秩自适应动态低秩积分器
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-01-31 DOI: 10.1007/s10543-023-00942-6
M. Hochbruck, M. Neher, Stefan Schrammer
{"title":"Rank-adaptive dynamical low-rank integrators for first-order and second-order matrix differential equations","authors":"M. Hochbruck, M. Neher, Stefan Schrammer","doi":"10.1007/s10543-023-00942-6","DOIUrl":"https://doi.org/10.1007/s10543-023-00942-6","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"63 1","pages":"1-24"},"PeriodicalIF":1.5,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49540924","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: 7
Analysis of algebraic flux correction schemes for semi-discrete advection problems 半离散平流问题的代数通量修正格式分析
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-01-30 DOI: 10.1007/s10543-023-00957-z
H. Hajduk, Andreas Rupp
{"title":"Analysis of algebraic flux correction schemes for semi-discrete advection problems","authors":"H. Hajduk, Andreas Rupp","doi":"10.1007/s10543-023-00957-z","DOIUrl":"https://doi.org/10.1007/s10543-023-00957-z","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"63 1","pages":"1-29"},"PeriodicalIF":1.5,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41677486","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 fractional Adams–Simpson-type method for nonlinear fractional ordinary differential equations with non-smooth data 具有非光滑数据的非线性分数阶常微分方程的分数阶adams - simpson型方法
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-01-30 DOI: 10.1007/s10543-023-00952-4
Yuan-Ming Wang, Bo Xie
{"title":"A fractional Adams–Simpson-type method for nonlinear fractional ordinary differential equations with non-smooth data","authors":"Yuan-Ming Wang, Bo Xie","doi":"10.1007/s10543-023-00952-4","DOIUrl":"https://doi.org/10.1007/s10543-023-00952-4","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"63 1","pages":"1-40"},"PeriodicalIF":1.5,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48005117","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
Dynamical low-rank integrators for second-order matrix differential equations 二阶矩阵微分方程的动态低阶积分器
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-01-30 DOI: 10.1007/s10543-023-00941-7
M. Hochbruck, M. Neher, Stefan Schrammer
{"title":"Dynamical low-rank integrators for second-order matrix differential equations","authors":"M. Hochbruck, M. Neher, Stefan Schrammer","doi":"10.1007/s10543-023-00941-7","DOIUrl":"https://doi.org/10.1007/s10543-023-00941-7","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"63 1","pages":"1-21"},"PeriodicalIF":1.5,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45897755","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: 4
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":"41 1","pages":"0"},"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":"63 1","pages":"1-16"},"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":"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}
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":"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}
引用次数: 0
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