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Resolving entropy growth from iterative methods 用迭代法求解熵增长
3区 数学
BIT Numerical Mathematics Pub Date : 2023-09-15 DOI: 10.1007/s10543-023-00992-w
Viktor Linders, Hendrik Ranocha, Philipp Birken
{"title":"Resolving entropy growth from iterative methods","authors":"Viktor Linders, Hendrik Ranocha, Philipp Birken","doi":"10.1007/s10543-023-00992-w","DOIUrl":"https://doi.org/10.1007/s10543-023-00992-w","url":null,"abstract":"Abstract We consider entropy conservative and dissipative discretizations of nonlinear conservation laws with implicit time discretizations and investigate the influence of iterative methods used to solve the arising nonlinear equations. We show that Newton’s method can turn an entropy dissipative scheme into an anti-dissipative one, even when the iteration error is smaller than the time integration error. We explore several remedies, of which the most performant is a relaxation technique, originally designed to fix entropy errors in time integration methods. Thus, relaxation works well in consort with iterative solvers, provided that the iteration errors are on the order of the time integration method. To corroborate our findings, we consider Burgers’ equation and nonlinear dispersive wave equations. We find that entropy conservation results in more accurate numerical solutions than non-conservative schemes, even when the tolerance is an order of magnitude larger.","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135436731","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: 2
Parallel line identification for line-implicit-solvers 直线隐式求解器的平行线辨识
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-09-09 DOI: 10.1007/s10543-023-00977-9
Arne Rempke
{"title":"Parallel line identification for line-implicit-solvers","authors":"Arne Rempke","doi":"10.1007/s10543-023-00977-9","DOIUrl":"https://doi.org/10.1007/s10543-023-00977-9","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44485019","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
Stability and convergence of the variable-step time filtered backward Euler scheme for parabolic equations 抛物型方程变步长时间滤波后向欧拉格式的稳定性和收敛性
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-07-03 DOI: 10.1007/s10543-023-00982-y
Hong-lin Liao, T. Tang, Tao Zhou
{"title":"Stability and convergence of the variable-step time filtered backward Euler scheme for parabolic equations","authors":"Hong-lin Liao, T. Tang, Tao Zhou","doi":"10.1007/s10543-023-00982-y","DOIUrl":"https://doi.org/10.1007/s10543-023-00982-y","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43668320","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
Multilevel Monte Carlo using approximate distributions of the CIR process 多层蒙特卡罗使用近似分布的CIR过程
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-06-01 DOI: 10.1007/s10543-023-00980-0
C. Zheng
{"title":"Multilevel Monte Carlo using approximate distributions of the CIR process","authors":"C. Zheng","doi":"10.1007/s10543-023-00980-0","DOIUrl":"https://doi.org/10.1007/s10543-023-00980-0","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48347427","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
Asymptotically exact a posteriori error estimates for the BDM finite element approximation of mixed Laplace eigenvalue problems 混合拉普拉斯特征值问题的BDM有限元逼近的渐近精确后验误差估计
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-05-22 DOI: 10.1007/s10543-023-00976-w
P. Lederer
{"title":"Asymptotically exact a posteriori error estimates for the BDM finite element approximation of mixed Laplace eigenvalue problems","authors":"P. Lederer","doi":"10.1007/s10543-023-00976-w","DOIUrl":"https://doi.org/10.1007/s10543-023-00976-w","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48323469","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
Computation of the unit in the first place (ufp) and the unit in the last place (ulp) in precision-p base $$beta $$ 以precision-p为基数计算第一个单位(ufp)和最后一个单位(ulp) $$beta $$
3区 数学
BIT Numerical Mathematics Pub Date : 2023-04-29 DOI: 10.1007/s10543-023-00970-2
Siegfried M. Rump
{"title":"Computation of the unit in the first place (ufp) and the unit in the last place (ulp) in precision-p base $$beta $$","authors":"Siegfried M. Rump","doi":"10.1007/s10543-023-00970-2","DOIUrl":"https://doi.org/10.1007/s10543-023-00970-2","url":null,"abstract":"Abstract There are simple algorithms to compute the predecessor, successor, unit in the first place, unit in the last place etc. in binary arithmetic. In this note equally simple algorithms for computing the unit in the first place and the unit in the last place in precision- p base- $$beta $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>β</mml:mi> </mml:math> arithmetic with $$p geqslant 1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>⩾</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> and with $$beta geqslant 2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>β</mml:mi> <mml:mo>⩾</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> are presented. The algorithms work in the underflow range, and numbers close to overflow are treated by scaling. The algorithms use only the basic operations with directed rounding. If the successor (or predecessor) of a floating-point number is available, an algorithm in rounding to nearest is presented as well.","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135802277","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
Construction of Rosenbrock–Wanner method Rodas5P and numerical benchmarks within the Julia Differential Equations package 构建Rosenbrock-Wanner方法Rodas5P和Julia微分方程包内的数值基准
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-04-17 DOI: 10.1007/s10543-023-00967-x
G. Steinebach
{"title":"Construction of Rosenbrock–Wanner method Rodas5P and numerical benchmarks within the Julia Differential Equations package","authors":"G. Steinebach","doi":"10.1007/s10543-023-00967-x","DOIUrl":"https://doi.org/10.1007/s10543-023-00967-x","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41772404","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: 3
On numerical methods for the semi-nonrelativistic limit system of the nonlinear Dirac equation 非线性狄拉克方程半非相对论性极限系统的数值方法
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-04-13 DOI: 10.1007/s10543-023-00971-1
T. Jahnke, Michael Kirn
{"title":"On numerical methods for the semi-nonrelativistic limit system of the nonlinear Dirac equation","authors":"T. Jahnke, Michael Kirn","doi":"10.1007/s10543-023-00971-1","DOIUrl":"https://doi.org/10.1007/s10543-023-00971-1","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43185375","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
Proximal gradient algorithm for nonconvex low tubal rank tensor recovery 非凸低阶张量恢复的近端梯度算法
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-04-04 DOI: 10.1007/s10543-023-00964-0
Yanhui Liu, Xueying Zeng, Weiguo Wang
{"title":"Proximal gradient algorithm for nonconvex low tubal rank tensor recovery","authors":"Yanhui Liu, Xueying Zeng, Weiguo Wang","doi":"10.1007/s10543-023-00964-0","DOIUrl":"https://doi.org/10.1007/s10543-023-00964-0","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44004635","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
Product integration rules by the constrained mock-Chebyshev least squares operator 约束mock Chebyshev最小二乘算子的乘积积分规则
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-04-03 DOI: 10.1007/s10543-023-00968-w
F. Dell’Accio, Domenico Mezzanotte, Federico Nudo, D. Occorsio
{"title":"Product integration rules by the constrained mock-Chebyshev least squares operator","authors":"F. Dell’Accio, Domenico Mezzanotte, Federico Nudo, D. Occorsio","doi":"10.1007/s10543-023-00968-w","DOIUrl":"https://doi.org/10.1007/s10543-023-00968-w","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43029450","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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