SIAM Journal on Numerical Analysis最新文献_第10页

Structure Preserving Primal Dual Methods for Gradient Flows with Nonlinear Mobility Transport Distances 非线性流动传输距离梯度流的结构保持原点二元法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-02-05 DOI: 10.1137/23m1562068

José A. Carrillo, Li Wang, Chaozhen Wei

引用次数: 0

Numerical Methods and Analysis of Computing Quasiperiodic Systems 计算准周期系统的数值方法与分析

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-02-01 DOI: 10.1137/22m1524783

Kai Jiang, Shifeng Li, Pingwen Zhang

{"title":"Numerical Methods and Analysis of Computing Quasiperiodic Systems","authors":"Kai Jiang, Shifeng Li, Pingwen Zhang","doi":"10.1137/22m1524783","DOIUrl":"https://doi.org/10.1137/22m1524783","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 1, Page 353-375, February 2024. Abstract. Quasiperiodic systems are important space-filling ordered structures, without decay and translational invariance. How to solve quasiperiodic systems accurately and efficiently is a great challenge. A useful approach, the projection method (PM) [J. Comput. Phys., 256 (2014), pp. 428–440], has been proposed to compute quasiperiodic systems. Various studies have demonstrated that the PM is an accurate and efficient method to solve quasiperiodic systems. However, there is a lack of theoretical analysis of the PM. In this paper, we present a rigorous convergence analysis of the PM by establishing a mathematical framework of quasiperiodic functions and their high-dimensional periodic functions. We also give a theoretical analysis of the quasiperiodic spectral method (QSM) based on this framework. Results demonstrate that the PM and QSM both have exponential decay, and the QSM (PM) is a generalization of the periodic Fourier spectral (pseudospectral) method. Then, we analyze the computational complexity of the PM and QSM in calculating quasiperiodic systems. The PM can use a fast Fourier transform, while the QSM cannot. Moreover, we investigate the accuracy and efficiency of the PM, QSM, and periodic approximation method in solving the linear time-dependent quasiperiodic Schrödinger equation.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"8 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139660060","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

Numerical Integration of Schrödinger Maps via the Hasimoto Transform 通过 Hasimoto 变换对薛定谔图进行数值积分

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-01-31 DOI: 10.1137/22m1531555

Valeria Banica, Georg Maierhofer, Katharina Schratz

{"title":"Numerical Integration of Schrödinger Maps via the Hasimoto Transform","authors":"Valeria Banica, Georg Maierhofer, Katharina Schratz","doi":"10.1137/22m1531555","DOIUrl":"https://doi.org/10.1137/22m1531555","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 1, Page 322-352, February 2024. Abstract. We introduce a numerical approach to computing the Schrödinger map (SM) based on the Hasimoto transform which relates the SM flow to a cubic nonlinear Schrödinger (NLS) equation. In exploiting this nonlinear transform we are able to introduce the first fully explicit unconditionally stable symmetric integrators for the SM equation. Our approach consists of two parts: an integration of the NLS equation followed by the numerical evaluation of the Hasimoto transform. Motivated by the desire to study rough solutions to the SM equation, we also introduce a new symmetric low-regularity integrator for the NLS equation. This is combined with our novel fast low-regularity Hasimoto (FLowRH) transform, based on a tailored analysis of the resonance structures in the Magnus expansion and a fast realization based on block-Toeplitz partitions, to yield an efficient low-regularity integrator for the SM equation. This scheme in particular allows us to obtain approximations to the SM in a more general regime (i.e., under lower-regularity assumptions) than previously proposed methods. The favorable properties of our methods are exhibited both in theoretical convergence analysis and in numerical experiments.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"121 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139655653","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 Adaptive Spectral Method for Oscillatory Second-Order Linear ODEs with Frequency-Independent Cost 与频率相关成本的振荡二阶线性 ODE 的自适应谱方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-01-29 DOI: 10.1137/23m1546609

Fruzsina J. Agocs, Alex H. Barnett

{"title":"An Adaptive Spectral Method for Oscillatory Second-Order Linear ODEs with Frequency-Independent Cost","authors":"Fruzsina J. Agocs, Alex H. Barnett","doi":"10.1137/23m1546609","DOIUrl":"https://doi.org/10.1137/23m1546609","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 1, Page 295-321, February 2024. Abstract. We introduce an efficient numerical method for second-order linear ODEs whose solution may vary between highly oscillatory and slowly changing over the solution interval. In oscillatory regions the solution is generated via a nonoscillatory phase function that obeys the nonlinear Riccati equation. We propose a defect correction iteration that gives an asymptotic series for such a phase function; this is numerically approximated on a Chebyshev grid with a small number of nodes. For analytic coefficients we prove that each iteration, up to a certain maximum number, reduces the residual by a factor of order of the local frequency. The algorithm adapts both the stepsize and the choice of method, switching to a conventional spectral collocation method away from oscillatory regions. In numerical experiments we find that our proposal outperforms other state-of-the-art oscillatory solvers, most significantly at low to intermediate frequencies and at low tolerances, where it may use up to [math] times fewer function evaluations. Even in high-frequency regimes, our implementation is on average 10 times faster than other specialized solvers.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"343 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139573530","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 Tangential and Penalty-Free Finite Element Method for the Surface Stokes Problem 表面斯托克斯问题的切向和无惩罚有限元方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-01-25 DOI: 10.1137/23m1583995

Alan Demlow, Michael Neilan

{"title":"A Tangential and Penalty-Free Finite Element Method for the Surface Stokes Problem","authors":"Alan Demlow, Michael Neilan","doi":"10.1137/23m1583995","DOIUrl":"https://doi.org/10.1137/23m1583995","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 1, Page 248-272, February 2024. Abstract. Surface Stokes and Navier–Stokes equations are used to model fluid flow on surfaces. They have attracted significant recent attention in the numerical analysis literature because approximation of their solutions poses significant challenges not encountered in the Euclidean context. One challenge comes from the need to simultaneously enforce tangentiality and [math] conformity (continuity) of discrete vector fields used to approximate solutions in the velocity-pressure formulation. Existing methods in the literature all enforce one of these two constraints weakly either by penalization or by use of Lagrange multipliers. Missing so far is a robust and systematic construction of surface Stokes finite element spaces which employ nodal degrees of freedom, including MINI, Taylor–Hood, Scott–Vogelius, and other composite elements which can lead to divergence-conforming or pressure-robust discretizations. In this paper we construct surface MINI spaces whose velocity fields are tangential. They are not [math]-conforming, but do lie in [math] and do not require penalization to achieve optimal convergence rates. We prove stability and optimal-order energy-norm convergence of the method and demonstrate optimal-order convergence of the velocity field in [math] via numerical experiments. The core advance in the paper is the construction of nodal degrees of freedom for the velocity field. This technique also may be used to construct surface counterparts to many other standard Euclidean Stokes spaces, and we accordingly present numerical experiments indicating optimal-order convergence of nonconforming tangential surface Taylor–Hood [math] elements.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"155 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139551046","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 Positive and Moment-Preserving Fourier Spectral Method 正向和保时傅立叶谱方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-01-25 DOI: 10.1137/23m1563918

Zhenning Cai, Bo Lin, Meixia Lin

引用次数: 0

Higher-Order Monte Carlo through Cubic Stratification 通过立方分层实现高阶蒙特卡洛

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-01-24 DOI: 10.1137/22m1532287

Nicolas Chopin, Mathieu Gerber

引用次数: 0

Space-Time Virtual Elements for the Heat Equation 热方程的时空虚拟元素

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-01-18 DOI: 10.1137/22m154140x

Sergio Gomez, Lorenzo Mascotto, Andrea Moiola, Ilaria Perugia

引用次数: 0

A Lagrange–Galerkin Scheme for First Order Mean Field Game Systems 一阶均值场博弈系统的拉格朗日-加勒金方案

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-01-16 DOI: 10.1137/23m1561762

Elisabetta Carlini, Francisco J. Silva, Ahmad Zorkot

引用次数: 0

Analysis and Numerical Approximation of Stationary Second-Order Mean Field Game Partial Differential Inclusions 静态二阶均值场博弈偏微分方程的分析与数值逼近

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2024-01-12 DOI: 10.1137/22m1519274

Yohance A. P. Osborne, Iain Smears

{"title":"Analysis and Numerical Approximation of Stationary Second-Order Mean Field Game Partial Differential Inclusions","authors":"Yohance A. P. Osborne, Iain Smears","doi":"10.1137/22m1519274","DOIUrl":"https://doi.org/10.1137/22m1519274","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 1, Page 138-166, February 2024. Abstract. The formulation of mean field games (MFG) typically requires continuous differentiability of the Hamiltonian in order to determine the advective term in the Kolmogorov–Fokker–Planck equation for the density of players. However, in many cases of practical interest, the underlying optimal control problem may exhibit bang-bang controls, which typically lead to nondifferentiable Hamiltonians. We develop the analysis and numerical analysis of stationary MFG for the general case of convex, Lipschitz, but possibly nondifferentiable Hamiltonians. In particular, we propose a generalization of the MFG system as a partial differential inclusion (PDI) based on interpreting the derivative of the Hamiltonian in terms of subdifferentials of convex functions. We establish the existence of a weak solution to the MFG PDI system, and we further prove uniqueness under a similar monotonicity condition to the one considered by Lasry and Lions. We then propose a monotone finite element discretization of the problem, and we prove strong [math]-norm convergence of the approximations of the value function and strong [math]-norm convergence of the approximations of the density function. We illustrate the performance of the numerical method in numerical experiments featuring nonsmooth solutions.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"40 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139435461","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