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Space-Time FEM-BEM Couplings for Parabolic Transmission Problems 抛物传输问题的时空FEM-BEM耦合
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2025-09-05 DOI: 10.1137/24m1695646
Thomas Führer, Gregor Gantner, Michael Karkulik
{"title":"Space-Time FEM-BEM Couplings for Parabolic Transmission Problems","authors":"Thomas Führer, Gregor Gantner, Michael Karkulik","doi":"10.1137/24m1695646","DOIUrl":"https://doi.org/10.1137/24m1695646","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 5, Page 1909-1932, October 2025. <br/> Abstract. We develop couplings of a recent space-time first-order system least-squares method for parabolic problems and space-time boundary element methods for the heat equation to numerically solve a parabolic transmission problem on the full space and a finite time interval. In particular, we demonstrate coercivity of the couplings under certain restrictions and validate our theoretical findings by numerical experiments.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003458","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 Analysis of the Parallel Orbital-Updating Approach for Eigenvalue Problems 特征值问题并行轨道更新方法的数值分析
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2025-08-22 DOI: 10.1137/24m1690084
Xiaoying Dai, Yan Li, Bin Yang, Aihui Zhou
{"title":"Numerical Analysis of the Parallel Orbital-Updating Approach for Eigenvalue Problems","authors":"Xiaoying Dai, Yan Li, Bin Yang, Aihui Zhou","doi":"10.1137/24m1690084","DOIUrl":"https://doi.org/10.1137/24m1690084","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 4, Page 1886-1908, August 2025. <br/> Abstract. The parallel orbital-updating approach is an orbital/eigenfunction iteration based approach for solving eigenvalue problems when many eigenpairs are required. It has been proven to be efficient, for instance, in electronic structure calculations. In this paper, based on the investigation of a quasi-orthogonality, we present the numerical analysis of the parallel orbital-updating approach for linear eigenvalue problems, including convergence and error estimates of the numerical approximations.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"15 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144900116","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 Unified Framework on the Original Energy Laws of Three Effective Classes of Runge–Kutta Methods for Phase Field Crystal Type Models 相场晶体型模型中三种有效类龙格-库塔方法原始能量定律的统一框架
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2025-08-20 DOI: 10.1137/24m1701770
Xuping Wang, Xuan Zhao, Hong-lin Liao
{"title":"A Unified Framework on the Original Energy Laws of Three Effective Classes of Runge–Kutta Methods for Phase Field Crystal Type Models","authors":"Xuping Wang, Xuan Zhao, Hong-lin Liao","doi":"10.1137/24m1701770","DOIUrl":"https://doi.org/10.1137/24m1701770","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 4, Page 1808-1832, August 2025. <br/> Abstract. The main theoretical obstacle to establishing the original energy dissipation laws of Runge–Kutta methods for phase field equations is verifying the maximum norm boundedness of the stage solutions without assuming global Lipschitz continuity of the nonlinear bulk. We present a unified theoretical framework for the energy stability of three effective classes of Runge–Kutta methods, including the additive implicit-explicit Runge–Kutta, explicit exponential Runge–Kutta, and corrected integrating factor Runge–Kutta methods, for the Swift–Hohenberg and phase field crystal models. By the standard discrete energy argument, it is proven that the three classes of Runge–Kutta methods preserve the original energy dissipation law if the associated differentiation matrices are positive definite. Our main tools include the differential form with the associated differentiation matrix, the discrete orthogonal convolution kernel, and the principle of mathematical induction. Many existing Runge–Kutta methods in the literature are revisited by evaluating the lower bound on the minimum eigenvalues of the associated differentiation matrices. Our theoretical approach paves a new way toward the internal nonlinear stability of Runge–Kutta methods for dissipative semilinear parabolic problems.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"15 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144900120","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 P-Version of Convolution Quadrature in Wave Propagation 波传播中卷积正交的p型
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2025-08-14 DOI: 10.1137/24m1642524
Alexander Rieder
{"title":"A P-Version of Convolution Quadrature in Wave Propagation","authors":"Alexander Rieder","doi":"10.1137/24m1642524","DOIUrl":"https://doi.org/10.1137/24m1642524","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 4, Page 1729-1756, August 2025. <br/> Abstract. We consider a novel way of discretizing wave scattering problems using the general formalism of convolution quadrature, but instead of reducing the time step size ([math]-method), we achieve accuracy by increasing the order of the method ([math]-method). We base this method on discontinuous Galerkin time stepping and use the Z-transform. We show that for a certain class of incident waves, the resulting schemes observe a (root)-exponential convergence rate with respect to the number of boundary integral operators that need to be applied. Numerical experiments confirm the finding.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"105 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144840295","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
Improved High-Index Saddle Dynamics for Finding Saddle Points and Solution Landscape 改进的高指数鞍动态寻找鞍点和解决方案景观
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2025-08-14 DOI: 10.1137/25m173212x
Hua Su, Haoran Wang, Lei Zhang, Jin Zhao, Xiangcheng Zheng
{"title":"Improved High-Index Saddle Dynamics for Finding Saddle Points and Solution Landscape","authors":"Hua Su, Haoran Wang, Lei Zhang, Jin Zhao, Xiangcheng Zheng","doi":"10.1137/25m173212x","DOIUrl":"https://doi.org/10.1137/25m173212x","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 4, Page 1757-1775, August 2025. <br/> Abstract. We present an improved high-index saddle dynamics (iHiSD) for finding saddle points and constructing solution landscapes, which is a crossover dynamics from gradient flow to traditional HiSD such that the Morse theory for gradient flow could be involved. We propose analysis for the reflection manifold in iHiSD and then prove its stable and nonlocal convergence from stationary points that may not be close to the target saddle point, which reduces the dependence of the convergence of HiSD on the initial value. We then present and analyze a discretized iHiSD for implementation. Furthermore, based on Morse theory, we prove that any two saddle points could be connected by a sequence of trajectories of iHiSD. Ideally, this implies that a solution landscape with a finite number of stationary points could be completely constructed by means of iHiSD, which partly answers the completeness issue of the solution landscape for the first time and indicates the necessity of integrating the gradient flow in HiSD. Different methods are compared by numerical experiments to substantiate the effectiveness of the iHiSD method.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144840296","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 Stochastic Preconditioned Douglas–Rachford Splitting Method for Saddle-Point Problems 鞍点问题的随机预条件Douglas-Rachford分裂方法
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2025-08-12 DOI: 10.1137/23m1622490
Yakun Dong, Kristian Bredies, Hongpeng Sun
{"title":"A Stochastic Preconditioned Douglas–Rachford Splitting Method for Saddle-Point Problems","authors":"Yakun Dong, Kristian Bredies, Hongpeng Sun","doi":"10.1137/23m1622490","DOIUrl":"https://doi.org/10.1137/23m1622490","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 4, Page 1691-1728, August 2025. <br/> Abstract. In this article, we propose and study a stochastic and relaxed preconditioned Douglas–Rachford splitting method to solve saddle-point problems that have separable dual variables. We prove the almost sure convergence of the iteration sequences in Hilbert spaces for a class of convex-concave and nonsmooth saddle-point problems. We also provide the sublinear convergence rate for the ergodic sequence concerning the expectation of the restricted primal-dual gap functions. Numerical experiments show the high efficiency of the proposed stochastic and relaxed preconditioned Douglas–Rachford splitting methods.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"15 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144819998","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
Quasi-Monte Carlo for Partial Differential Equations with Generalized Gaussian Input Uncertainty 广义高斯输入不确定性偏微分方程的拟蒙特卡罗算法
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2025-08-11 DOI: 10.1137/24m1708164
Philipp A. Guth, Vesa Kaarnioja
{"title":"Quasi-Monte Carlo for Partial Differential Equations with Generalized Gaussian Input Uncertainty","authors":"Philipp A. Guth, Vesa Kaarnioja","doi":"10.1137/24m1708164","DOIUrl":"https://doi.org/10.1137/24m1708164","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 4, Page 1666-1690, August 2025. <br/> Abstract. There has been a surge of interest in uncertainty quantification for parametric partial differential equations (PDEs) with Gevrey regular inputs. The Gevrey class contains functions that are infinitely smooth with a growth condition on the higher-order partial derivatives, but which are nonetheless not analytic in general. Recent studies by Chernov and Lê [Comput. Math. Appl., 164 (2024), pp. 116–130; SIAM J. Numer. Anal., 62 (2024), pp. 1874–1900] as well as Harbrecht, Schmidlin, and Schwab [Math. Models Methods Appl. Sci., 34 (2024), pp. 881–917] analyze the setting wherein the input random field is assumed to be uniformly bounded with respect to the uncertain parameters. In this paper, we relax this assumption and allow for parameter-dependent bounds. The parametric inputs are modeled as generalized Gaussian random variables, and we analyze the application of quasi-Monte Carlo (QMC) integration to assess the PDE response statistics using randomly shifted rank-1 lattice rules. In addition to the QMC error analysis, we also consider the dimension truncation and finite element errors in this setting.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"42 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144819942","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 Stabilized Nonconforming Finite Element Method for the Surface Biharmonic Problem 表面双调和问题的稳定非协调有限元法
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2025-08-06 DOI: 10.1137/24m1707936
Shuonan Wu, Hao Zhou
{"title":"A Stabilized Nonconforming Finite Element Method for the Surface Biharmonic Problem","authors":"Shuonan Wu, Hao Zhou","doi":"10.1137/24m1707936","DOIUrl":"https://doi.org/10.1137/24m1707936","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 4, Page 1642-1665, August 2025. <br/> Abstract. This paper presents a novel stabilized nonconforming finite element method for solving the surface biharmonic problem. The method extends the New-Zienkiewicz-type (NZT) element to polyhedral (approximated) surfaces by employing the Piola transform to establish the connection of vertex gradients across adjacent elements. Key features of the surface NZT finite element space include its [math]-relative conformity and weak [math] conformity, allowing for stabilization without the use of artificial parameters. Under the assumption that the exact solution and the dual problem possess only [math] regularity, we establish optimal error estimates in the energy norm and provide, for the first time, a comprehensive analysis yielding optimal second-order convergence in the broken [math] norm. Numerical experiments are provided to support the theoretical results and indicate that the stabilization term might be unnecessary.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"16 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144787661","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 Localized Orthogonal Decomposition Method for Heterogeneous Stokes Problems 非均质Stokes问题的局部正交分解方法
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2025-08-01 DOI: 10.1137/24m1704166
Moritz Hauck, Alexei Lozinski
{"title":"A Localized Orthogonal Decomposition Method for Heterogeneous Stokes Problems","authors":"Moritz Hauck, Alexei Lozinski","doi":"10.1137/24m1704166","DOIUrl":"https://doi.org/10.1137/24m1704166","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 4, Page 1617-1641, August 2025. <br/> Abstract. In this paper, we propose a multiscale method for heterogeneous Stokes problems. The method is based on the localized orthogonal decomposition (LOD) methodology and has approximation properties independent of the regularity of the coefficients. We apply the LOD to an appropriate reformulation of the Stokes problem, which allows us to construct exponentially decaying basis functions for the velocity approximation while using a piecewise constant pressure approximation. The exponential decay motivates a localization of the basis computation, which is essential for the practical realization of the method. We perform a rigorous a priori error analysis and prove optimal convergence rates for the velocity approximation and a postprocessed pressure approximation, provided that the supports of the basis functions are logarithmically increased with the desired accuracy. Numerical experiments support the theoretical results of this paper.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"69 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766090","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
Error Analysis of BDF 1–6 Time-Stepping Methods for the Transient Stokes Problem: Velocity and Pressure Estimates BDF - 6时间步进方法在瞬态斯托克斯问题中的误差分析：速度和压力估计
IF 2.9 2区 数学
SIAM Journal on Numerical Analysis Pub Date : 2025-07-24 DOI: 10.1137/23m1606800
Alessandro Contri, Balázs Kovács, André Massing
{"title":"Error Analysis of BDF 1–6 Time-Stepping Methods for the Transient Stokes Problem: Velocity and Pressure Estimates","authors":"Alessandro Contri, Balázs Kovács, André Massing","doi":"10.1137/23m1606800","DOIUrl":"https://doi.org/10.1137/23m1606800","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 4, Page 1586-1616, August 2025. <br/> Abstract. We present a new stability and error analysis of fully discrete approximation schemes for the transient Stokes equation. For the spatial discretization, we consider a wide class of Galerkin finite element methods which includes both inf-sup stable spaces and symmetric pressure stabilized formulations. We extend the results from Burman and Fernández [SIAM J. Numer. Anal., 47 (2009), pp. 409–439] and provide a unified theoretical analysis of backward difference formula methods of orders 1 to 6. The main novelty of our approach lies in deriving optimal-order stability and error estimates for both the velocity and the pressure using Dahlquist’s [math]-stability concept together with the multiplier technique introduced by Nevanlinna and Odeh and recently by Akrivis et al. [SIAM J. Numer. Anal., 59 (2021), pp. 2449–2472]. When combined with a method-dependent Ritz projection for the initial data, unconditional stability can be shown, while for arbitrary interpolation, pressure stability is subordinate to the fulfillment of a mild inverse CFL-type condition between space and time discretizations.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"119 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702055","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
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