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Stabilised finite element method for Stokes problem with nonlinear slip condition 具有非线性滑移条件的斯托克斯问题的稳定有限元法
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2024-06-13 DOI: 10.1007/s10543-024-01025-w
T. Gustafsson, J. Videman
{"title":"Stabilised finite element method for Stokes problem with nonlinear slip condition","authors":"T. Gustafsson, J. Videman","doi":"10.1007/s10543-024-01025-w","DOIUrl":"https://doi.org/10.1007/s10543-024-01025-w","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141348645","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
On a quality measure for interval inclusions 关于区间夹杂的质量度量
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2024-05-13 DOI: 10.1007/s10543-024-01020-1
Siegfried M. Rump, Takeshi Ogita
{"title":"On a quality measure for interval inclusions","authors":"Siegfried M. Rump, Takeshi Ogita","doi":"10.1007/s10543-024-01020-1","DOIUrl":"https://doi.org/10.1007/s10543-024-01020-1","url":null,"abstract":"<p>Verification methods compute intervals which contain the solution of a given problem with mathematical rigour. In order to compare the quality of intervals some measure is desirable. We identify some anticipated properties and propose a method avoiding drawbacks of previous definitions.</p>","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140928636","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 local defect-correction method for the non-selfadjoint Steklov eigenvalue problems 非自洽斯特克洛夫特征值问题的多级局部缺陷校正方法
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2024-04-09 DOI: 10.1007/s10543-024-01022-z
Fei Xu, Bingyi Wang, Manting Xie
{"title":"Multilevel local defect-correction method for the non-selfadjoint Steklov eigenvalue problems","authors":"Fei Xu, Bingyi Wang, Manting Xie","doi":"10.1007/s10543-024-01022-z","DOIUrl":"https://doi.org/10.1007/s10543-024-01022-z","url":null,"abstract":"<p>In this paper, we design a multilevel local defect-correction method to solve the non-selfadjoint Steklov eigenvalue problems. Since the computation work needed for solving the non-selfadjoint Steklov eigenvalue problems increases exponentially as the scale of the problems increase, the main idea of our algorithm is to avoid solving large-scale equations especially large-scale Steklov eigenvalue problems directly. Firstly, we transform the non-selfadjoint Steklov eigenvalue problem into some symmetric boundary value problems defined in a multilevel finite element space sequence, and some small-scale non-selfadjoint Steklov eigenvalue problems defined in a low-dimensional auxiliary subspace. Next, the local defect-correction method is used to solve the symmetric boundary value problems, then the difficulty of solving these symmetric boundary value problems is further reduced by decomposing these large-scale problems into a series of small-scale subproblems. Overall, our algorithm can obtain the optimal error estimates with linear computational complexity, and the conclusions are proved by strict theoretical analysis which are different from the developed conclusions for equations with the Dirichlet boundary conditions.</p>","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140564915","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
Dynamical low-rank approximation of the Vlasov–Poisson equation with piecewise linear spatial boundary 具有片状线性空间边界的弗拉索夫-泊松方程的动态低阶近似
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2024-04-07 DOI: 10.1007/s10543-024-01019-8
{"title":"Dynamical low-rank approximation of the Vlasov–Poisson equation with piecewise linear spatial boundary","authors":"","doi":"10.1007/s10543-024-01019-8","DOIUrl":"https://doi.org/10.1007/s10543-024-01019-8","url":null,"abstract":"<h3>Abstract</h3> <p>Dynamical low-rank approximation (DLRA) for the numerical simulation of Vlasov–Poisson equations is based on separation of space and velocity variables, as proposed in several recent works. The standard approach for the time integration in the DLRA model uses a splitting of the tangent space projector for the low-rank manifold according to the separated variables. It can also be modified to allow for rank-adaptivity. A less studied aspect is the incorporation of boundary conditions in the DLRA model. In this work, a variational formulation of the projector splitting is proposed which allows to handle inflow boundary conditions on spatial domains with piecewise linear boundary. Numerical experiments demonstrate the principle feasibility of this approach.</p>","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140564916","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
Semi-explicit integration of second order for weakly coupled poroelasticity 弱耦合孔弹性的二阶半显式积分
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2024-04-07 DOI: 10.1007/s10543-024-01021-0
{"title":"Semi-explicit integration of second order for weakly coupled poroelasticity","authors":"","doi":"10.1007/s10543-024-01021-0","DOIUrl":"https://doi.org/10.1007/s10543-024-01021-0","url":null,"abstract":"<h3>Abstract</h3> <p>We introduce a semi-explicit time-stepping scheme of second order for linear poroelasticity satisfying a weak coupling condition. Here, semi-explicit means that the system, which needs to be solved in each step, decouples and hence improves the computational efficiency. The construction and the convergence proof are based on the connection to a differential equation with two time delays, namely one and two times the step size. Numerical experiments confirm the theoretical results and indicate the applicability to higher-order schemes.</p>","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140564840","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
Learning the flux and diffusion function for degenerate convection-diffusion equations using different types of observations 利用不同类型的观测结果学习退化对流扩散方程的通量和扩散函数
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2024-03-30 DOI: 10.1007/s10543-024-01018-9
Qing Li, S. Evje
{"title":"Learning the flux and diffusion function for degenerate convection-diffusion equations using different types of observations","authors":"Qing Li, S. Evje","doi":"10.1007/s10543-024-01018-9","DOIUrl":"https://doi.org/10.1007/s10543-024-01018-9","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140364115","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
Accurate Horner methods in real and complex floating-point arithmetic 实数和复数浮点运算中的精确霍纳方法
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2024-03-27 DOI: 10.1007/s10543-024-01017-w
Thomas R. Cameron, Stef Graillat
{"title":"Accurate Horner methods in real and complex floating-point arithmetic","authors":"Thomas R. Cameron, Stef Graillat","doi":"10.1007/s10543-024-01017-w","DOIUrl":"https://doi.org/10.1007/s10543-024-01017-w","url":null,"abstract":"<p>In this article, we derive accurate Horner methods in real and complex floating-point arithmetic. In particular, we show that these methods are as accurate as if computed in <i>k</i>-fold precision and then rounded into the working precision. When <i>k</i> is two, our methods are comparable or faster than the existing compensated Horner routines. When compared to multi-precision software, such as MPFR and MPC, our methods are significantly faster, up to <i>k</i> equal to eight, that is, up to 489 bits in the significand.</p>","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140312952","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
Highly localized RBF Lagrange functions for finite difference methods on spheres 球面有限差分法的高度局部化 RBF 拉格朗日函数
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2024-03-15 DOI: 10.1007/s10543-024-01016-x
W. Erb, T. Hangelbroek, F. J. Narcowich, C. Rieger, J. D. Ward
{"title":"Highly localized RBF Lagrange functions for finite difference methods on spheres","authors":"W. Erb, T. Hangelbroek, F. J. Narcowich, C. Rieger, J. D. Ward","doi":"10.1007/s10543-024-01016-x","DOIUrl":"https://doi.org/10.1007/s10543-024-01016-x","url":null,"abstract":"<p>The aim of this paper is to show how rapidly decaying RBF Lagrange functions on the sphere can be used to create a numerically feasible, stable finite difference method based on radial basis functions (an RBF-FD-like method). For certain classes of PDEs this approach leads to rigorous convergence estimates for stencils which grow moderately with increasing discretization fineness.</p>","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156271","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
Bounded perturbations resilient iterative methods for linear systems and least squares problems: operator-based approaches, analysis, and performance evaluation 线性系统和最小二乘问题的有界扰动弹性迭代法：基于算子的方法、分析和性能评估
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2024-03-05 DOI: 10.1007/s10543-024-01015-y
Mokhtar Abbasi, Touraj Nikazad
{"title":"Bounded perturbations resilient iterative methods for linear systems and least squares problems: operator-based approaches, analysis, and performance evaluation","authors":"Mokhtar Abbasi, Touraj Nikazad","doi":"10.1007/s10543-024-01015-y","DOIUrl":"https://doi.org/10.1007/s10543-024-01015-y","url":null,"abstract":"<p>We examine some bounded perturbations resilient iterative methods for addressing (constrained) consistent linear systems of equations and (constrained) least squares problems. We introduce multiple frameworks rooted in the operator of the Landweber iteration, adapting the operators to facilitate the minimization of absolute errors or residuals. We demonstrate that our operator-based methods exhibit comparable speed to powerful methods like CGLS, and we establish that the computational cost of our methods is nearly equal to that of CGLS. Furthermore, our methods possess the capability to handle constraints (e.g. non-negativity) and control the semi-convergence phenomenon. In addition, we provide convergence analysis of the methods when the current iterations are perturbed by summable vectors. This allows us to utilize these iterative methods for the superiorization methodology. We showcase their performance using examples drawn from tomographic imaging and compare them with CGLS, superiorized conjugate gradient (S-CG), and the non-negative flexible CGLS (NN-FCGLS) methods.</p>","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140034982","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
The variable two-step BDF method for parabolic equations 抛物方程的可变两步 BDF 法
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2024-03-01 DOI: 10.1007/s10543-024-01007-y
Georgios Akrivis, Minghua Chen, Jianxing Han, Fan Yu, Zhimin Zhang
{"title":"The variable two-step BDF method for parabolic equations","authors":"Georgios Akrivis, Minghua Chen, Jianxing Han, Fan Yu, Zhimin Zhang","doi":"10.1007/s10543-024-01007-y","DOIUrl":"https://doi.org/10.1007/s10543-024-01007-y","url":null,"abstract":"<p>The two-step backward difference formula (BDF) method on variable grids for parabolic equations with self-adjoint elliptic part is considered. Standard stability estimates for adjacent time-step ratios <span>(r_j:=k_j/k_{j-1}leqslant 1.8685)</span> and 1.9104, respectively, have been proved by Becker (BIT 38:644–662, 1998) and Emmrich (J Appl Math Comput 19:33–55, 2005) by the energy technique with a single multiplier. Even slightly improving the ratio is cumbersome. In this paper, we present a novel technique to examine the positive definiteness of banded matrices that are neither Toeplitz nor weakly diagonally dominant; this result can be viewed as a variant of the Grenander–Szegő theorem. Then, utilizing the energy technique with two multipliers, we establish stability for adjacent time-step ratios up to 1.9398.\u0000</p>","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140017990","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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