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

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. <br/> 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. <br/> 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

Legendre Approximation-Based Stability Test for Distributed Delay Systems 基于Legendre近似的分布式延迟系统稳定性检验

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-04-08 DOI: 10.1137/23m1610859

Alejandro Castaño, Mathieu Bajodek, Sabine Mondié

引用次数: 0

Mesh-Preserving and Energy-Stable Parametric FEM for Geometric Flows of Surfaces 曲面几何流动的保网格和能量稳定参数有限元

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-03-27 DOI: 10.1137/24m1671542

Beiping Duan

引用次数: 0

Multiscale Hybrid-Mixed Methods for the Stokes and Brinkman Equations—A Priori Analysis Stokes和Brinkman方程的多尺度混合-混合方法-先验分析

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-03-12 DOI: 10.1137/24m1649368

Rodolfo Araya, Christopher Harder, Abner H. Poza, Frédéric Valentin

{"title":"Multiscale Hybrid-Mixed Methods for the Stokes and Brinkman Equations—A Priori Analysis","authors":"Rodolfo Araya, Christopher Harder, Abner H. Poza, Frédéric Valentin","doi":"10.1137/24m1649368","DOIUrl":"https://doi.org/10.1137/24m1649368","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 588-618, April 2025. <br/> Abstract. The multiscale hybrid-mixed (MHM) method for the Stokes operator was formally introduced in [R. Araya et al., Comput. Methods Appl. Mech. Engrg., 324, pp. 29–53, 2017] and numerically validated. The method has face degrees of freedom associated with multiscale basis functions computed from local Neumann problems driven by discontinuous polynomial spaces on skeletal meshes. The two-level MHM version approximates the multiscale basis using a stabilized finite element method. This work proposes the first numerical analysis for the one- and two-level MHM method applied to the Stokes/Brinkman equations within a new abstract framework relating MHM methods to discrete primal hybrid formulations. As a result, we generalize the two-level MHM method to include general second-level solvers and continuous polynomial interpolation on faces and establish abstract conditions to have those methods well-posed and optimally convergent on natural norms. We apply the abstract setting to analyze the MHM methods using stabilized and stable finite element methods as second-level solvers with (dis)continuous interpolation on faces. Also, we find that the discrete velocity and pressure variables preserve the balance of forces and conservation of mass at the element level. Numerical benchmarks assess theoretical results.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"16 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143618495","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

Irrational-Window-Filter Projection Method and Application to Quasiperiodic Schrödinger Eigenproblems 无理性窗滤波投影法及其在拟周期Schrödinger特征问题中的应用

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-03-11 DOI: 10.1137/24m1666197

Kai Jiang, Xueyang Li, Yao Ma, Juan Zhang, Pingwen Zhang, Qi Zhou

引用次数: 0

Piecewise Linear Interpolation of Noise in Finite Element Approximations of Parabolic SPDEs 抛物型spde有限元逼近中噪声的分段线性插值

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-03-10 DOI: 10.1137/23m1574117

Gabriel J. Lord, Andreas Petersson

{"title":"Piecewise Linear Interpolation of Noise in Finite Element Approximations of Parabolic SPDEs","authors":"Gabriel J. Lord, Andreas Petersson","doi":"10.1137/23m1574117","DOIUrl":"https://doi.org/10.1137/23m1574117","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 542-563, April 2025. <br/> Abstract. Efficient simulation of stochastic partial differential equations (SPDEs) on general domains requires noise discretization. This paper employs piecewise linear interpolation of noise in a fully discrete finite element approximation of a semilinear stochastic reaction-advection-diffusion equation on a convex polyhedral domain. The Gaussian noise is white in time, spatially correlated, and modeled as a standard cylindrical Wiener process on a reproducing kernel Hilbert space. This paper provides the first rigorous analysis of the resulting noise discretization error for a general spatial covariance kernel. The kernel is assumed to be defined on a larger regular domain, allowing for sampling by the circulant embedding method. The error bound under mild kernel assumptions requires nontrivial techniques like Hilbert–Schmidt bounds on products of finite element interpolants, entropy numbers of fractional Sobolev space embeddings, and an error bound for interpolants in fractional Sobolev norms. Examples with kernels encountered in applications are illustrated in numerical simulations using the FEniCS finite element software. Key findings include the following: noise interpolation does not introduce additional errors for Matérn kernels in [math]; there exist kernels that yield dominant interpolation errors; and generating noise on a coarser mesh does not always compromise accuracy.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"68 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143582914","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

Higher-Order Far-Field Boundary Conditions for Crystalline Defects 晶体缺陷的高阶远场边界条件

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-03-06 DOI: 10.1137/24m165836x

Julian Braun, Christoph Ortner, Yangshuai Wang, Lei Zhang

引用次数: 0