发布求助
文献互助 智能选刊 最新文献

SIAM Journal on Numerical Analysis最新文献

筛选
英文 中文
Pointwise Gradient Estimate of the Ritz Projection 里兹投影的点阵梯度估计
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2024-05-21 DOI: 10.1137/23m1571800
Lars Diening, Julian Rolfes, Abner J. Salgado
{"title":"Pointwise Gradient Estimate of the Ritz Projection","authors":"Lars Diening, Julian Rolfes, Abner J. Salgado","doi":"10.1137/23m1571800","DOIUrl":"https://doi.org/10.1137/23m1571800","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1212-1225, June 2024. <br/> Abstract. Let [math] be a convex polytope ([math]). The Ritz projection is the best approximation, in the [math]-norm, to a given function in a finite element space. When such finite element spaces are constructed on the basis of quasiuniform triangulations, we show a pointwise estimate on the Ritz projection. Namely, the gradient at any point in [math] is controlled by the Hardy–Littlewood maximal function of the gradient of the original function at the same point. From this estimate, the stability of the Ritz projection on a wide range of spaces that are of interest in the analysis of PDEs immediately follows. Among those are weighted spaces, Orlicz spaces, and Lorentz spaces.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"67 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141079251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Mean Dimension of Radial Basis Functions 径向基函数的平均维度
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2024-05-21 DOI: 10.1137/23m1614833
Christopher Hoyt, Art B. Owen
{"title":"Mean Dimension of Radial Basis Functions","authors":"Christopher Hoyt, Art B. Owen","doi":"10.1137/23m1614833","DOIUrl":"https://doi.org/10.1137/23m1614833","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1191-1211, June 2024. <br/> Abstract. We show that generalized multiquadric radial basis functions (RBFs) on [math] have a mean dimension that is [math] as [math] with an explicit bound for the implied constant, under moment conditions on their inputs. Under weaker moment conditions the mean dimension still approaches 1. As a consequence, these RBFs become essentially additive as their dimension increases. Gaussian RBFs by contrast can attain any mean dimension between 1 and [math]. We also find that a test integrand due to Keister that has been influential in quasi-Monte Carlo theory has a mean dimension that oscillates between approximately 1 and approximately 2 as the nominal dimension [math] increases.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"70 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141074216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Total Variation Error Bounds for the Accelerated Exponential Euler Scheme Approximation of Parabolic Semilinear SPDEs 加速指数欧拉方案逼近抛物线半线性 SPDE 的总变化误差边界
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2024-05-15 DOI: 10.1137/22m152596x
Charles-Edouard Bréhier
{"title":"Total Variation Error Bounds for the Accelerated Exponential Euler Scheme Approximation of Parabolic Semilinear SPDEs","authors":"Charles-Edouard Bréhier","doi":"10.1137/22m152596x","DOIUrl":"https://doi.org/10.1137/22m152596x","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1171-1190, June 2024. <br/> Abstract. We prove a new numerical approximation result for the solutions of semilinear parabolic stochastic partial differential equations, driven by additive space-time white noise in dimension 1. The temporal discretization is performed using an accelerated exponential Euler scheme, and we show that, under appropriate regularity conditions on the nonlinearity, the total variation distance between the distributions of the numerical approximation and of the exact solution at a given time converges to 0 when the time-step size vanishes, with order of convergence [math]. Equivalently, weak error estimates with order [math] are thus obtained for bounded measurable test functions. This is an original and major improvement compared with the performance of the standard linear implicit Euler scheme or exponential Euler methods, which do not converge in the sense of total variation when the time-step size vanishes. Equivalently weak error estimates for the standard schemes require twice differentiable test functions. The proof of the total variation error bounds for the accelerated exponential Euler scheme exploits some regularization property of the associated infinite-dimensional Kolmogorov equations.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"17 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141304419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Implicit and Fully Discrete Approximation of the Supercooled Stefan Problem in the Presence of Blow-Ups 存在炸裂的过冷斯特凡问题的隐含和完全离散近似法
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2024-05-09 DOI: 10.1137/22m1509722
Christa Cuchiero, Christoph Reisinger, Stefan Rigger
{"title":"Implicit and Fully Discrete Approximation of the Supercooled Stefan Problem in the Presence of Blow-Ups","authors":"Christa Cuchiero, Christoph Reisinger, Stefan Rigger","doi":"10.1137/22m1509722","DOIUrl":"https://doi.org/10.1137/22m1509722","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1145-1170, June 2024. <br/> Abstract.We consider two approximation schemes of the one-dimensional supercooled Stefan problem and prove their convergence, even in the presence of finite time blow-ups. All proofs are based on a probabilistic reformulation recently considered in the literature. The first scheme is a version of the time-stepping scheme studied by Kaushansky et al. [Ann. Appl. Probab., 33 (2023), pp. 274–298], but here the flux over the free boundary and its velocity are coupled implicitly. Moreover, we extend the analysis to more general driving processes than Brownian motion. The second scheme is a Donsker-type approximation, also interpretable as an implicit finite difference scheme, for which global convergence is shown under minor technical conditions. With stronger assumptions, which apply in cases without blow-ups, we obtain additionally a convergence rate arbitrarily close to 1/2. Our numerical results suggest that this rate also holds for less regular solutions, in contrast to explicit schemes, and allow a sharper resolution of the discontinuous free boundary in the blow-up regime.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"33 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140902996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Asymptotic Compatibility of a Class of Numerical Schemes for a Nonlocal Traffic Flow Model 一类非本地交通流模型数值方案的渐进兼容性
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2024-05-07 DOI: 10.1137/23m154488x
Kuang Huang, Qiang Du
{"title":"Asymptotic Compatibility of a Class of Numerical Schemes for a Nonlocal Traffic Flow Model","authors":"Kuang Huang, Qiang Du","doi":"10.1137/23m154488x","DOIUrl":"https://doi.org/10.1137/23m154488x","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1119-1144, June 2024. <br/> Abstract. This paper considers numerical discretization of a nonlocal conservation law modeling vehicular traffic flows involving nonlocal intervehicle interactions. The nonlocal model involves an integral over the range measured by a horizon parameter and it recovers the local Lighthill–Richards–Whitham model as the nonlocal horizon parameter goes to zero. Good numerical schemes for simulating these parameterized nonlocal traffic flow models should be robust with respect to the change of the model parameters but this has not been systematically investigated in the literature. We fill this gap through a careful study of a class of finite volume numerical schemes with suitable discretizations of the nonlocal integral, which include several schemes proposed in the literature and their variants. Our main contributions are to demonstrate the asymptotically compatibility of the schemes, which includes both the uniform convergence of the numerical solutions to the unique solution of nonlocal continuum model for a given positive horizon parameter and the convergence to the unique entropy solution of the local model as the mesh size and the nonlocal horizon parameter go to zero simultaneously. It is shown that with the asymptotically compatibility, the schemes can provide robust numerical computation under the changes of the nonlocal horizon parameter.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Asymptotic Preserving Discontinuous Galerkin Method for a Linear Boltzmann Semiconductor Model 线性玻尔兹曼半导体模型的渐近保留非连续伽勒金方法
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2024-05-06 DOI: 10.1137/22m1485784
Victor P. DeCaria, Cory D. Hauck, Stefan R. Schnake
{"title":"An Asymptotic Preserving Discontinuous Galerkin Method for a Linear Boltzmann Semiconductor Model","authors":"Victor P. DeCaria, Cory D. Hauck, Stefan R. Schnake","doi":"10.1137/22m1485784","DOIUrl":"https://doi.org/10.1137/22m1485784","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1067-1097, June 2024. <br/> Abstract. A key property of the linear Boltzmann semiconductor model is that as the collision frequency tends to infinity, the phase space density [math] converges to an isotropic function [math], called the drift-diffusion limit, where [math] is a Maxwellian and the physical density [math] satisfies a second-order parabolic PDE known as the drift-diffusion equation. Numerical approximations that mirror this property are said to be asymptotic preserving. In this paper we build a discontinuous Galerkin method to the semiconductor model, and we show this scheme is both uniformly stable in [math], where 1/[math] is the scale of the collision frequency, and asymptotic preserving. In particular, we discuss what properties the discrete Maxwellian must satisfy in order for the schemes to converge in [math] to an accurate [math]-approximation of the drift-diffusion limit. Discrete versions of the drift-diffusion equation and error estimates in several norms with respect to [math] and the spacial resolution are also included.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"26 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140845605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Kernel Interpolation of High Dimensional Scattered Data 高维分散数据的核插值
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2024-05-06 DOI: 10.1137/22m1519948
Shao-Bo Lin, Xiangyu Chang, Xingping Sun
{"title":"Kernel Interpolation of High Dimensional Scattered Data","authors":"Shao-Bo Lin, Xiangyu Chang, Xingping Sun","doi":"10.1137/22m1519948","DOIUrl":"https://doi.org/10.1137/22m1519948","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1098-1118, June 2024. <br/> Abstract. Data sites selected from modeling high-dimensional problems often appear scattered in nonpaternalistic ways. Except for sporadic-clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These features defy any theoretical treatment that requires local or global quasi-uniformity of distribution of data sites. Incorporating a recently-developed application of integral operator theory in machine learning, we propose and study in the current article a new framework to analyze kernel interpolation of high-dimensional data, which features bounding stochastic approximation error by the spectrum of the underlying kernel matrix. Both theoretical analysis and numerical simulations show that spectra of kernel matrices are reliable and stable barometers for gauging the performance of kernel-interpolation methods for high-dimensional data.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"15 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140845651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Novel Mixed Spectral Method and Error Estimates for Maxwell Transmission Eigenvalue Problems 麦克斯韦传输特征值问题的新型混合谱法和误差估计值
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2024-05-03 DOI: 10.1137/23m1544830
Jing An, Waixiang Cao, Zhimin Zhang
{"title":"A Novel Mixed Spectral Method and Error Estimates for Maxwell Transmission Eigenvalue Problems","authors":"Jing An, Waixiang Cao, Zhimin Zhang","doi":"10.1137/23m1544830","DOIUrl":"https://doi.org/10.1137/23m1544830","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1039-1066, June 2024. <br/> Abstract. In this paper, a novel mixed spectral-Galerkin method is proposed and studied for a Maxwell transmission eigenvalue problem in a spherical domain. The method utilizes vector spherical harmonics to achieve dimension reduction. By introducing an auxiliary vector function, the original problem is rewritten as an equivalent fourth-order coupled linear eigensystem, which is further decomposed into a sequence of one-dimensional fourth-order decoupled transverse-electric (TE) and transverse-magnetic (TM) modes. Based on compact embedding theory and the spectral approximation property of compact operators, error estimates for both eigenvalue and eigenfunction approximations are established for the TE mode. For the TM mode, an efficient essential polar condition and a high-order polynomial approximation method are designed to cope with the singularity and complexity caused by the coupled boundary conditions. Numerical experiments are presented to demonstrate the efficiency and robustness of our algorithm.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"42 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140821576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Gain Coefficients for Scrambled Halton Points 哈尔顿干扰点的增益系数
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2024-05-02 DOI: 10.1137/23m1601882
Art B. Owen, Zexin Pan
{"title":"Gain Coefficients for Scrambled Halton Points","authors":"Art B. Owen, Zexin Pan","doi":"10.1137/23m1601882","DOIUrl":"https://doi.org/10.1137/23m1601882","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1021-1038, June 2024. <br/>Abstract. Randomized quasi-Monte Carlo, via certain scramblings of digital nets, produces unbiased estimates of [math] with a variance that is [math] for any [math]. It also satisfies some nonasymptotic bounds where the variance is no larger than some [math] times the ordinary Monte Carlo variance. For scrambled Sobol’ points, this quantity [math] grows exponentially in [math]. For scrambled Faure points, [math] in any dimension, but those points are awkward to use for large [math]. This paper shows that certain scramblings of Halton sequences have gains below an explicit bound that is [math] but not [math] for any [math] as [math]. For [math], the upper bound on the gain coefficient is never larger than [math].","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"380 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140821140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Two-Level Block Preconditioned Jacobi–Davidson Method for Multiple and Clustered Eigenvalues of Elliptic Operators 椭圆算子多特征值和聚类特征值的两级块预处理雅各比-戴维森方法
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2024-04-22 DOI: 10.1137/23m1580711
Qigang Liang, Wei Wang, Xuejun Xu
{"title":"A Two-Level Block Preconditioned Jacobi–Davidson Method for Multiple and Clustered Eigenvalues of Elliptic Operators","authors":"Qigang Liang, Wei Wang, Xuejun Xu","doi":"10.1137/23m1580711","DOIUrl":"https://doi.org/10.1137/23m1580711","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 998-1019, April 2024. <br/> Abstract. In this paper, we propose a two-level block preconditioned Jacobi–Davidson (BPJD) method for efficiently solving discrete eigenvalue problems resulting from finite element approximations of [math]th ([math]) order symmetric elliptic eigenvalue problems. Our method works effectively to compute the first several eigenpairs, including both multiple and clustered eigenvalues with corresponding eigenfunctions, particularly. The method is highly parallelizable by constructing a new and efficient preconditioner using an overlapping domain decomposition (DD). It only requires computing a couple of small scale parallel subproblems and a quite small scale eigenvalue problem per iteration. Our theoretical analysis reveals that the convergence rate of the method is bounded by [math], where [math] is the diameter of subdomains and [math] is the overlapping size among subdomains. The constant [math] is independent of the mesh size [math] and the internal gaps among the target eigenvalues, demonstrating that our method is optimal and cluster robust. Meanwhile, the [math]-dependent constant [math] decreases monotonically to 1, as [math], which means that more subdomains lead to the better convergence rate. Numerical results supporting our theory are given.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"38 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140632364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
首页 上一页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信