SIAM Journal on Numerical Analysis最新文献_第10页

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

Gaussian Process Regression under Computational and Epistemic Misspecification 计算和认知错误规范下的高斯过程回归

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-03-05 DOI: 10.1137/23m1624749

Daniel Sanz-Alonso, Ruiyi Yang

引用次数: 0

On Polynomial Interpolation in the Monomial Basis 关于单项式基上的多项式插值

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-03-05 DOI: 10.1137/23m1623215

Zewen Shen, Kirill Serkh

引用次数: 0

Discretization of Total Variation in Optimization with Integrality Constraints 具有完整性约束的优化中总变分的离散化

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-02-25 DOI: 10.1137/24m164608x

Annika Schiemann, Paul Manns

{"title":"Discretization of Total Variation in Optimization with Integrality Constraints","authors":"Annika Schiemann, Paul Manns","doi":"10.1137/24m164608x","DOIUrl":"https://doi.org/10.1137/24m164608x","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 1, Page 437-460, February 2025. <br/> Abstract. We introduce discretizations of infinite-dimensional optimization problems with total variation regularization and integrality constraints on the optimization variables. We advance the discretization of the dual formulation of the total variation term with Raviart–Thomas functions, which is known from the literature for certain convex problems. Since we have an integrality constraint, the previous analysis from Caillaud and Chambolle [IMA J. Numer. Anal., 43 (2022), pp. 692–736] no longer holds. Even weaker [math]-convergence results no longer hold because the recovery sequences generally need to attain noninteger values to recover the total variation of the limit function. We solve this issue by introducing a discretization of the input functions on an embedded, finer mesh. A superlinear coupling of the mesh sizes implies an averaging on the coarser mesh of the Raviart–Thomas ansatz, which enables us to recover the total variation of integer-valued limit functions with integer-valued discretized input functions. Moreover, we are able to estimate the discretized total variation of the recovery sequence by the total variation of its limit and an error depending on the mesh size ratio. For the discretized optimization problems, we additionally add a constraint that vanishes in the limit and enforces compactness of the sequence of minimizers, which yields their convergence to a minimizer of the original problem. This constraint contains a degree of freedom whose admissible range is determined. Its choice may have a strong impact on the solutions in practice as we demonstrate with an example from imaging.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"18 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143495222","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

Corrigendum: Domain Decomposition Approaches for Mesh Generation via the Equidistribution Principle 勘误：通过均分原理生成网格的域分解方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-02-25 DOI: 10.1137/24m1693453

Martin J. Gander, Ronald D. Haynes, Felix Kwok

引用次数: 0

Rational Methods for Abstract, Linear, Nonhomogeneous Problems without Order Reduction 无阶约抽象、线性、非齐次问题的有理方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-02-24 DOI: 10.1137/24m165942x

Carlos Arranz-Simón, César Palencia

引用次数: 0

Long Time Stability and Numerical Stability of Implicit Schemes for Stochastic Heat Equations 随机热方程隐式格式的长时间稳定性和数值稳定性

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-02-18 DOI: 10.1137/24m1636691

Xiaochen Yang, Yaozhong Hu

引用次数: 0

Parameterized Wasserstein Hamiltonian Flow 参数化瓦瑟斯坦-哈密顿流

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-02-14 DOI: 10.1137/23m159281x

Hao Wu, Shu Liu, Xiaojing Ye, Haomin Zhou

{"title":"Parameterized Wasserstein Hamiltonian Flow","authors":"Hao Wu, Shu Liu, Xiaojing Ye, Haomin Zhou","doi":"10.1137/23m159281x","DOIUrl":"https://doi.org/10.1137/23m159281x","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 1, Page 360-395, February 2025. <br/> Abstract. In this work, we propose a numerical method to compute the Wasserstein Hamiltonian flow (WHF), which is a Hamiltonian system on the probability density manifold. Many well-known PDE systems can be reformulated as WHFs. We use the parameterized function as a push-forward map to characterize the solution of WHF, and convert the PDE to a finite-dimensional ODE system, which is a Hamiltonian system in the phase space of the parameter manifold. We establish theoretical error bounds for the continuous time approximation scheme in the Wasserstein metric. For the numerical implementation, neural networks are used as push-forward maps. We design an effective symplectic scheme to solve the derived Hamiltonian ODE system so that the method preserves some important quantities such as Hamiltonian. The computation is done by a fully deterministic symplectic integrator without any neural network training. Thus, our method does not involve direct optimization over network parameters and hence can avoid errors introduced by the stochastic gradient descent or similar methods, which are usually hard to quantify and measure in practice. The proposed algorithm is a sampling-based approach that scales well to higher dimensional problems. In addition, the method also provides an alternative connection between the Lagrangian and Eulerian perspectives of the original WHF through the parameterized ODE dynamics.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"10 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143417624","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