SIAM Journal on Numerical Analysis最新文献

A New Class of Splitting Methods That Preserve Ergodicity and Exponential Integrability for the Stochastic Langevin Equation 一类新的保持随机朗格万方程遍历性和指数可积性的分裂方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-04-28 DOI: 10.1137/24m1687686

Chuchu Chen, Tonghe Dang, Jialin Hong, Fengshan Zhang

{"title":"A New Class of Splitting Methods That Preserve Ergodicity and Exponential Integrability for the Stochastic Langevin Equation","authors":"Chuchu Chen, Tonghe Dang, Jialin Hong, Fengshan Zhang","doi":"10.1137/24m1687686","DOIUrl":"https://doi.org/10.1137/24m1687686","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 1000-1024, April 2025. Abstract. In this paper, we propose a new class of splitting methods to solve the stochastic Langevin equation, which can simultaneously preserve the ergodicity and exponential integrability of the original equation. The central idea is to extract a stochastic subsystem that possesses the strict dissipation from the original equation, which is inspired by the inheritance of the Lyapunov structure for obtaining the ergodicity. We prove that the exponential moment of the numerical solution is bounded, thus validating the exponential integrability of the proposed methods. Further, we show that under moderate verifiable conditions, the methods have the first-order convergence in both strong and weak senses, and we present several concrete splitting schemes based on the methods. The splitting strategy of methods can be readily extended to construct conformal symplectic methods and high-order methods that preserve both the ergodicity and the exponential integrability, as demonstrated in numerical experiments. Our numerical experiments also show that the proposed methods have good performance in the long-time simulation.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"31 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143884404","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

Reduced Krylov Basis Methods for Parametric Partial Differential Equations 参数偏微分方程的化简Krylov基方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-04-25 DOI: 10.1137/24m1661236

Yuwen Li, Ludmil T. Zikatanov, Cheng Zuo

{"title":"Reduced Krylov Basis Methods for Parametric Partial Differential Equations","authors":"Yuwen Li, Ludmil T. Zikatanov, Cheng Zuo","doi":"10.1137/24m1661236","DOIUrl":"https://doi.org/10.1137/24m1661236","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 976-999, April 2025. Abstract. This work is on a user-friendly reduced basis method for the solution of families of parametric partial differential equations by preconditioned Krylov subspace methods including the conjugate gradient method, generalized minimum residual method, and biconjugate gradient method. The proposed methods use a preconditioned Krylov subspace method for a high-fidelity discretization of one parameter instance to generate orthogonal basis vectors of the reduced basis subspace. Then large-scale discrete parameter-dependent problems are approximately solved in the low-dimensional Krylov subspace. We prove convergence estimates for the proposed method when the differential operator depends on two parameter coefficients and the preconditioner is the inverse of the operator at a fixed parameter. As is shown in numerical experiments, only a small number of Krylov subspace iterations are needed to simultaneously generate approximate solutions of a family of high-fidelity and large-scale parametrized systems in the reduced basis subspace. This reduces the computational cost by orders of magnitude, because (1) to construct the reduced basis vectors, we only solve one large-scale problem in the high-fidelity level; and (2) the family of problems restricted to the reduced basis subspace have much smaller sizes.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"44 1","pages":"976-999"},"PeriodicalIF":2.9,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143876070","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

Transient Dynamics under Structured Perturbations: Bridging Unstructured and Structured Pseudospectra 结构扰动下的瞬态动力学：桥接非结构和结构伪谱

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-04-22 DOI: 10.1137/24m1630876

Nicola Guglielmi, Christian Lubich

{"title":"Transient Dynamics under Structured Perturbations: Bridging Unstructured and Structured Pseudospectra","authors":"Nicola Guglielmi, Christian Lubich","doi":"10.1137/24m1630876","DOIUrl":"https://doi.org/10.1137/24m1630876","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 908-930, April 2025. Abstract. The structured [math]-stability radius is introduced as a quantity to assess the robustness of transient bounds of solutions to linear differential equations under structured perturbations of the matrix. This applies to general linear structures such as complex or real matrices with a given sparsity pattern or with restricted range and corange, or special classes such as Toeplitz matrices. The notion conceptually combines unstructured and structured pseudospectra in a joint pseudospectrum, allowing for the use of resolvent bounds as with unstructured pseudospectra and for structured perturbations as with structured pseudospectra. We propose and study an algorithm for computing the structured [math]-stability radius, which solves eigenvalue optimization problems via suitably discretized rank-1 matrix differential equations that originate from a gradient system. The proposed algorithm has essentially the same computational cost as the known rank-1 algorithms for computing unstructured and structured stability radii. Numerical experiments illustrate the behavior of the algorithm.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"138 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863066","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 Update of the Moment Equations for a Multi-Species, Homogeneous BGK Model 多物种齐次BGK模型矩方程的隐式更新

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-04-22 DOI: 10.1137/24m165421x

Evan Habbershaw, Cory D. Hauck, Steven M. Wise

引用次数: 0

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