SIAM Journal on Numerical Analysis最新文献_第2页

Interpolatory [math]-Optimality Conditions for Structured Linear Time-Invariant Systems 结构化线性定常系统的最优性条件

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-04-22 DOI: 10.1137/23m1610033

Petar Mlinarić, Peter Benner, Serkan Gugercin

引用次数: 0

A New Analysis of Empirical Interpolation Methods and Chebyshev Greedy Algorithms 经验插值方法与切比雪夫贪婪算法的新分析

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-04-22 DOI: 10.1137/24m1634230

Yuwen Li

引用次数: 0

Energy Stable and Maximum Bound Principle Preserving Schemes for the [math]-Tensor Flow of Liquid Crystals 液晶[数学]张量流的能量稳定和最大界原理保持方案

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-04-18 DOI: 10.1137/23m1598866

Dianming Hou, Xiaoli Li, Zhonghua Qiao, Nan Zheng

{"title":"Energy Stable and Maximum Bound Principle Preserving Schemes for the [math]-Tensor Flow of Liquid Crystals","authors":"Dianming Hou, Xiaoli Li, Zhonghua Qiao, Nan Zheng","doi":"10.1137/23m1598866","DOIUrl":"https://doi.org/10.1137/23m1598866","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 854-880, April 2025. Abstract. In this paper, we propose two efficient fully discrete schemes for [math]-tensor flow of liquid crystals by using the first- and second-order stabilized exponential scalar auxiliary variable (sESAV) approach in time and the finite difference method for spatial discretization. The modified discrete energy dissipation laws are unconditionally satisfied for both two constructed schemes. A particular feature is that, for two-dimensional (2D) and a kind of three-dimensional (3D) [math]-tensor flow, the unconditional maximum bound principle (MBP) preservation of the constructed first-order scheme is successfully established, and the proposed second-order scheme preserves the discrete MBP property with a mild restriction on the time-step sizes. Furthermore, we rigorously derive the corresponding error estimates for the fully discrete second-order schemes by using the built-in stability results. Finally, various numerical examples validating the theoretical results, such as the orientation of liquid crystal in 2D and 3D, are presented for the constructed schemes.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"17 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143847058","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

POD-ROM Methods: From a Finite Set of Snapshots to Continuous-in-Time Approximations po - rom方法：从有限快照集到连续时间逼近

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-04-11 DOI: 10.1137/24m1645681

Bosco García-Archilla, Volker John, Julia Novo

{"title":"POD-ROM Methods: From a Finite Set of Snapshots to Continuous-in-Time Approximations","authors":"Bosco García-Archilla, Volker John, Julia Novo","doi":"10.1137/24m1645681","DOIUrl":"https://doi.org/10.1137/24m1645681","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 800-826, April 2025. Abstract. This paper studies discretization of time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Most of the analysis in the literature has been performed on fully discrete methods using first order methods in time, typically the implicit Euler time integrator. Our aim is to show which kind of error bounds can be obtained using any time integrator, both in the full order model (FOM), applied to compute the snapshots, and in the POD-ROM method. To this end, we analyze in this paper the continuous-in-time case for both the FOM and POD-ROM methods, although the POD basis is obtained from snapshots taken at a discrete (i.e., not continuous) set of times. Two cases for the set of snapshots are considered: the case in which the snapshots are based on first order divided differences in time and the case in which they are based on temporal derivatives. Optimal pointwise-in-time error bounds between the FOM and the POD-ROM solutions are proved for the [math] norm of the error for a semilinear reaction-diffusion model problem. The dependency of the errors on the distance in time between two consecutive snapshots and on the tail of the POD eigenvalues is tracked. Our detailed analysis allows us to show that, in some situations, a small number of snapshots in a given time interval might be sufficient to accurately approximate the solution in the full interval. Numerical studies support the error analysis.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"118 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143823161","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

Locking-Free Hybrid High-Order Method for Linear Elasticity 线性弹性的无锁混合高阶方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-04-11 DOI: 10.1137/24m1650363

Carsten Carstensen, Ngoc Tien Tran

{"title":"Locking-Free Hybrid High-Order Method for Linear Elasticity","authors":"Carsten Carstensen, Ngoc Tien Tran","doi":"10.1137/24m1650363","DOIUrl":"https://doi.org/10.1137/24m1650363","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 827-853, April 2025. Abstract. The hybrid high-order (HHO) scheme has many successful applications including linear elasticity as the first step towards computational solid mechanics. The striking advantage is the simplicity among other higher-order nonconforming schemes and its geometric flexibility as a polytopal method on the expanse of a parameter-free refined stabilization. This paper utilizes just one reconstruction operator for the linear Green strain and therefore does not rely on a split in deviatoric and spherical behavior as in the classical HHO discretization. The a priori error analysis provides quasi-best approximation with [math]-independent equivalence constants. The reliable and (up to data oscillations) efficient a posteriori error estimates are stabilization-free and [math]-robust. The error analysis is carried out on simplicial meshes to allow conforming piecewise polynomial finite elements in the kernel of the stabilization terms. Numerical benchmarks provide empirical evidence for optimal convergence rates of the a posteriori error estimator in an associated adaptive mesh-refining algorithm also in the incompressible limit, where this paper provides corresponding assertions for the Stokes problem.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"45 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143823160","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 Hybrid Two-Level Weighted Schwarz Method for Helmholtz Equations Helmholtz方程的混合二能级加权Schwarz方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-04-10 DOI: 10.1137/24m1637994

Qiya Hu, Ziyi Li

{"title":"A Hybrid Two-Level Weighted Schwarz Method for Helmholtz Equations","authors":"Qiya Hu, Ziyi Li","doi":"10.1137/24m1637994","DOIUrl":"https://doi.org/10.1137/24m1637994","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 716-743, April 2025. Abstract. In this paper we are concerned with a weighted additive Schwarz method with local impedance boundary conditions for a family of Helmholtz problems in two or three dimensions. These problems are discretized by the finite element method with conforming nodal finite elements. We design and analyze an adaptive coarse space for this kind of weighted additive Schwarz method. This coarse space is constructed by some eigenfunctions of local generalized eigenvalue problems posed on the subspaces consisting of local discrete Helmholtz-harmonic functions from impedance boundary data on [math], where [math] is a considered subdomain. Such a generalized eigenvalue problem is defined by two different bilinear forms, [math] and [math], where [math] denotes a weight operator related to [math], and [math] with [math] being the wave number. We prove that a hybrid two-level weighted Schwarz preconditioner with the proposed coarse space possesses uniform convergence independent of the mesh size, the subdomain size, and the wave numbers under suitable assumptions. This result seems the first rigorous convergence result on two-level weighted Schwarz method with local impedance boundary conditions for Helmholtz equations. We also introduce an economical coarse space to avoid solving generalized eigenvalue problems. Numerical experiments confirm the theoretical results.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"108 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143814010","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

Dropout Ensemble Kalman Inversion for High Dimensional Inverse Problems 高维反问题的Dropout集成卡尔曼反演

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-04-10 DOI: 10.1137/23m159860x

Shuigen Liu, Sebastian Reich, Xin T. Tong

引用次数: 0

Unique Solvability and Error Analysis of a Scheme Using the Lagrange Multiplier Approach for Gradient Flows 梯度流拉格朗日乘子法格式的唯一可解性及误差分析

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-04-10 DOI: 10.1137/24m1659303

Qing Cheng, Jie Shen, Cheng Wang

{"title":"Unique Solvability and Error Analysis of a Scheme Using the Lagrange Multiplier Approach for Gradient Flows","authors":"Qing Cheng, Jie Shen, Cheng Wang","doi":"10.1137/24m1659303","DOIUrl":"https://doi.org/10.1137/24m1659303","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 772-799, April 2025. Abstract. The unique solvability and error analysis of a scheme using the original Lagrange multiplier approach proposed in [Q. Cheng, C. Liu, and J. Shen, Comput. Methods Appl. Mech. Engrg., 367 (2020), 13070] for gradient flows is studied in this paper. We identify a necessary and sufficient condition that must be satisfied for the nonlinear algebraic equation arising from the original Lagrange multiplier approach to admit a unique solution in the neighborhood of its exact solution. Then we find that the unique solvability of the original Lagrange multiplier approach depends on the aforementioned condition and may be valid over a finite time period. Afterward, we propose a modified Lagrange multiplier approach to ensure that the computation can continue even if the aforementioned condition was not satisfied. Using the Cahn–Hilliard equation as an example, we prove rigorously the unique solvability and establish optimal error estimates of a second-order Lagrange multiplier scheme assuming this condition and that the time step is sufficiently small. We also present numerical results to demonstrate that the modified Lagrange multiplier approach is much more robust and can use a much larger time step than the original Lagrange multiplier approach.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"34 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143814009","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

Perfectly Matched Layer Method for the Wave Scattering Problem by a Step-Like Surface 类阶梯表面波散射问题的完美匹配层法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-04-10 DOI: 10.1137/24m1654221

Wangtao Lu, Weiying Zheng, Xiaopeng Zhu

{"title":"Perfectly Matched Layer Method for the Wave Scattering Problem by a Step-Like Surface","authors":"Wangtao Lu, Weiying Zheng, Xiaopeng Zhu","doi":"10.1137/24m1654221","DOIUrl":"https://doi.org/10.1137/24m1654221","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 744-771, April 2025. Abstract. This paper is concerned with the convergence theory of a perfectly matched layer (PML) method for wave scattering problems in a half plane bounded by a step-like surface. When a plane wave impinges upon the surface, the scattered waves are composed of an outgoing radiative field and two known parts. The first part consists of two parallel reflected plane waves of different phases, which propagate in two different subregions separated by a half-line parallel to the wave direction. The second part stands for an outgoing corner-scattering field which is discontinuous and represented by a double-layer potential. A piecewise circular PML is defined by introducing two types of complex coordinates transformations in the two subregions, respectively. A PML variational problem is proposed to approximate the scattered waves. The exponential convergence of the PML solution is established by two results based on the technique of Cagniard–de Hoop transform. First, we show that the discontinuous corner-scattering field decays exponentially in the PML. Second, we show that the transparent boundary condition (TBC) defined by the PML is an exponentially small perturbation of the original TBC defined by the radiation condition. Numerical examples validate the theory and demonstrate the effectiveness of the proposed PML.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"39 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143814011","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

Spectral Correctness of the Simplicial Discontinuous Galerkin Approximation of the First-Order Form of Maxwell’s Equations with Discontinuous Coefficients 不连续系数麦克斯韦方程组一阶形式的简单不连续伽辽金近似的谱正确性

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-04-09 DOI: 10.1137/24m1638331

Alexandre Ern, Jean-Luc Guermond

引用次数: 0