SIAM Journal on Numerical Analysis最新文献_第3页

Distributional Finite Element curl div Complexes and Application to Quad Curl Problems 分布有限元旋度复形及其在四旋度问题中的应用

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-05-14 DOI: 10.1137/23m1617400

Long Chen, Xuehai Huang, Chao Zhang

引用次数: 0

Spectral ACMS: A Robust Localized Approximated Component Mode Synthesis Method 谱ACMS：一种鲁棒局部逼近分量模态综合方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-05-12 DOI: 10.1137/24m1665362

Alexandre L. Madureira, Marcus Sarkis

{"title":"Spectral ACMS: A Robust Localized Approximated Component Mode Synthesis Method","authors":"Alexandre L. Madureira, Marcus Sarkis","doi":"10.1137/24m1665362","DOIUrl":"https://doi.org/10.1137/24m1665362","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1055-1077, June 2025. Abstract. We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous [math] coefficients. The methods are of Galerkin type and follow the Variational Multiscale and Localized Orthogonal Decomposition (LOD) approaches in the sense that it decouples spaces into multiscale and fine subspaces. In a first method, the multiscale basis functions are obtained by mapping coarse basis functions, based on corners used on primal iterative substructuring methods, to functions of global minimal energy. This approach delivers quasi-optimal a priori error energy approximation with respect to the mesh size, but it is not robust with respect to high-contrast coefficients. In a second method, edge modes based on local generalized eigenvalue problems are added to the corner modes. As a result, optimal a priori error energy estimate is achieved which is mesh and contrast independent. The methods converge at optimal rate even if the solution has minimum regularity, belonging only to the Sobolev space [math].","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"21 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143933581","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

Density Estimation for Elliptic PDE with Random Input by Preintegration and Quasi-Monte Carlo Methods 随机输入椭圆偏微分方程的预积分和拟蒙特卡罗估计

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-05-07 DOI: 10.1137/24m1640070

Alexander D. Gilbert, Frances Y. Kuo, Abirami Srikumar

{"title":"Density Estimation for Elliptic PDE with Random Input by Preintegration and Quasi-Monte Carlo Methods","authors":"Alexander D. Gilbert, Frances Y. Kuo, Abirami Srikumar","doi":"10.1137/24m1640070","DOIUrl":"https://doi.org/10.1137/24m1640070","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 3, Page 1025-1054, June 2025. Abstract. In this paper, we apply quasi-Monte Carlo (QMC) methods with an initial preintegration step to estimate cumulative distribution functions and probability density functions in uncertainty quantification (UQ). The distribution and density functions correspond to a quantity of interest involving the solution to an elliptic partial differential equation (PDE) with a lognormally distributed coefficient and a normally distributed source term. There is extensive previous work on using QMC to compute expected values in UQ, which have proven very successful in tackling a range of different PDE problems. However, the use of QMC for density estimation applied to UQ problems will be explored here for the first time. Density estimation presents a more difficult challenge compared to computing the expected value due to discontinuities present in the integral formulations of both the distribution and density. Our strategy is to use preintegration to eliminate the discontinuity by integrating out a carefully selected random parameter, so that QMC can be used to approximate the remaining integral. First, we establish regularity results for the PDE quantity of interest that are required for smoothing by preintegration to be effective. We then show that an [math]-point lattice rule can be constructed for the integrands corresponding to the distribution and density, such that after preintegration the QMC error is of order [math] for arbitrarily small [math]. This is the same rate achieved for computing the expected value of the quantity of interest. Numerical results are presented to reaffirm our theory.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"48 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143916087","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 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