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A parameterized block preconditioner for solving a class of complex symmetric linear systems 求解一类复对称线性系统的参数化块预调节器
IF 2.6 3区 数学
Advances in Computational Mathematics Pub Date : 2026-06-30 DOI: 10.1007/s10444-026-10326-3
Meng-Yao Li, Bo Wu
{"title":"A parameterized block preconditioner for solving a class of complex symmetric linear systems","authors":"Meng-Yao Li,&nbsp;Bo Wu","doi":"10.1007/s10444-026-10326-3","DOIUrl":"10.1007/s10444-026-10326-3","url":null,"abstract":"<div><p>This paper develops a new parameterized block (PB) preconditioner for solving the complex symmetric linear systems. We analyze the convergence behavior of the corresponding iteration scheme and derive the spectral properties of the preconditioned matrix. Numerical experiments are conducted to verify the effectiveness of the proposed method, demonstrating that the PB preconditioner significantly accelerates the convergence of the GMRES method when applied to complex symmetric linear systems.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148355663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Partial Floquet transformation and model order reduction of linear time-periodic systems 线性时间周期系统的部分Floquet变换与模型降阶
IF 2.6 3区 数学
Advances in Computational Mathematics Pub Date : 2026-06-26 DOI: 10.1007/s10444-026-10320-9
Sam Bender, Christopher Beattie
{"title":"Partial Floquet transformation and model order reduction of linear time-periodic systems","authors":"Sam Bender,&nbsp;Christopher Beattie","doi":"10.1007/s10444-026-10320-9","DOIUrl":"10.1007/s10444-026-10320-9","url":null,"abstract":"<div><p>Time-periodic dynamical systems occur commonly both in nature and as engineered systems. Large-scale linear time-periodic dynamical systems, for example, may arise through linearization of a nonlinear system about a given periodic solution (possibly as a consequence of a baseline periodic forcing) with subsequent spatial discretization. The potential need to simulate responses to a wide variety of input profiles (viewed as perturbations off a baseline periodic forcing) creates a potent incentive for effective model reduction strategies applicable to linear time-periodic (<span>ltp</span>) systems. Classical approaches that take into account the underlying time-periodic system structure often utilize the Floquet transform; however, computation of the Floquet transform is typically intractable for large-order systems. In this paper, we develop the notion of a <i>partial Floquet transformation</i> connected to selected invariant subspaces of a time-varying differential operator associated with the <span>ltp</span> system. We modify and repurpose the <i>Dominant Pole Algorithm</i> of Rommes to identify effective invariant subspaces useful for model reduction. We discuss the construction of associated partial Floquet transformations and time-varying reduction bases with which to produce effective reduced-order <span>ltp</span> models and illustrate the process on a simple time-periodic system.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-026-10320-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nested operator inference for adaptive data-driven learning of reduced-order models 用于自适应数据驱动的降阶模型学习的嵌套算子推理
IF 2.6 3区 数学
Advances in Computational Mathematics Pub Date : 2026-06-25 DOI: 10.1007/s10444-026-10322-7
Nicole Aretz, Karen Willcox
{"title":"Nested operator inference for adaptive data-driven learning of reduced-order models","authors":"Nicole Aretz,&nbsp;Karen Willcox","doi":"10.1007/s10444-026-10322-7","DOIUrl":"10.1007/s10444-026-10322-7","url":null,"abstract":"<div><p>This paper presents a data-driven, nested Operator Inference (OpInf) approach for learning physics-informed reduced-order models (ROMs) from snapshot data of high-dimensional dynamical systems. The approach exploits the inherent hierarchy within the reduced space to iteratively construct initial guesses for the OpInf learning problem that prioritize the interactions of the dominant modes. The initial guess computed for any target reduced dimension corresponds to a ROM with provably smaller or equal snapshot reconstruction error than with standard OpInf. Moreover, our nested OpInf algorithm can be warm-started from previously learned models, enabling versatile application scenarios involving dynamic basis and model form updates. We demonstrate the performance of our algorithm on a cubic heat conduction problem, with nested OpInf achieving a four times smaller error than standard OpInf at a comparable offline time. Further, we apply nested OpInf to a large-scale, parameterized model of the Greenland ice sheet where, despite model form approximation errors, it learns a ROM with, on average, 3 % error and computational speed-up factor above 19,000.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-026-10322-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Strong stability preserving two-derivative multistep Runge–Kutta methods 强稳定保二阶多步龙格-库塔方法
IF 2.6 3区 数学
Advances in Computational Mathematics Pub Date : 2026-06-17 DOI: 10.1007/s10444-026-10306-7
Xueyu Qin, Jian Yu, Teng Zhou, Chao Yan
{"title":"Strong stability preserving two-derivative multistep Runge–Kutta methods","authors":"Xueyu Qin,&nbsp;Jian Yu,&nbsp;Teng Zhou,&nbsp;Chao Yan","doi":"10.1007/s10444-026-10306-7","DOIUrl":"10.1007/s10444-026-10306-7","url":null,"abstract":"<div><p>We introduce the explicit strong stability preserving (SSP) two-derivative multistep Runge–Kutta (TDMSRK) methods. The order accuracy conditions and SSP theory for the TDMSRK methods are developed. By comparing the SSP coefficients of TDMSRK methods, Runge–Kutta schemes, two-derivative Runge–Kutta schemes, and general linear methods, it is indicated that the TDMSRK schemes have the largest effective SSP coefficient at the same order of accuracy. Some classical tests demonstrate the numerical stability of the TDMSRK methods on the Euler equation. Furthermore, the TDMSRK methods can achieve the expected order of accuracy and exhibit high computational efficiency in solving the Euler equation.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 weak Galerkin mixed finite element method for singularly perturbed biharmonic problems on a layer-adapted mesh in 2D 二维层自适应网格奇异摄动双调和问题的弱Galerkin混合有限元法
IF 2.6 3区 数学
Advances in Computational Mathematics Pub Date : 2026-06-16 DOI: 10.1007/s10444-026-10314-7
Aayushman Raina, Srinivasan Natesan, Şuayip Toprakseven
{"title":"A weak Galerkin mixed finite element method for singularly perturbed biharmonic problems on a layer-adapted mesh in 2D","authors":"Aayushman Raina,&nbsp;Srinivasan Natesan,&nbsp;Şuayip Toprakseven","doi":"10.1007/s10444-026-10314-7","DOIUrl":"10.1007/s10444-026-10314-7","url":null,"abstract":"<div><p>We present a mixed weak Galerkin finite element method (WG-FEM) for singularly perturbed biharmonic problems on the unit square domain with clamped boundary conditions. By introducing an auxiliary variable, the fourth-order equation is reformulated as a coupled second-order system. A layer-adapted Shishkin mesh is employed to efficiently capture boundary layers. We derive parameter-uniform error bounds in both the energy and balanced norms, proving convergence independent of the perturbation parameter. Numerical results are provided to confirm the theoretical analysis and to demonstrate the effectiveness of the mixed WG-FEM with layer-adapted meshes.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On convergence of residual-based extended Kaczmarz method for solving inconsistent linear systems 求解不一致线性系统的基于残差的扩展Kaczmarz方法的收敛性
IF 2.6 3区 数学
Advances in Computational Mathematics Pub Date : 2026-06-16 DOI: 10.1007/s10444-026-10321-8
Fang Chen, Chen-Xiao Gao
{"title":"On convergence of residual-based extended Kaczmarz method for solving inconsistent linear systems","authors":"Fang Chen,&nbsp;Chen-Xiao Gao","doi":"10.1007/s10444-026-10321-8","DOIUrl":"10.1007/s10444-026-10321-8","url":null,"abstract":"<div><p>The Kaczmarz-type methods, also called as the algebraic reconstruction techniques, have been studied and applied due to their high computational efficiency and good convergence property for solving very large systems of linear equations. Recently, the residual-based extended Kaczmarz method was proposed by Bao et al. [9] to solve the inconsistent linear systems. In theoretical framework, based on the condition that the <span>(i_{k-1})</span>-th element of the residual vector <span>(r_k)</span> in the <i>k</i>-th iteration step is equal to zero, the authors obtained the convergence theorem. However, this element is not always equal to zero, making the basic hypothesis of the convergence theorem be not satisfied, so that the convergence conclusion does not hold true. According to this meticulous observation, we give a correct and detailed analysis for the convergence property of the residual-based extended Kaczmarz method. As a result, we provide a corrected convergence theory for this iteration method. Also, we examine these results by a numerical example.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Mixed finite element methods for elliptic obstacle problems 椭圆型障碍问题的混合有限元方法
IF 2.1 3区 数学
Advances in Computational Mathematics Pub Date : 2026-06-09 DOI: 10.1007/s10444-026-10319-2
Thomas Führer, Francisco Fuica
{"title":"Mixed finite element methods for elliptic obstacle problems","authors":"Thomas Führer,&nbsp;Francisco Fuica","doi":"10.1007/s10444-026-10319-2","DOIUrl":"10.1007/s10444-026-10319-2","url":null,"abstract":"<div><p>Mixed variational formulations for the first-order system of the elastic membrane obstacle problem and the second-order system of the Kirchhoff–Love plate obstacle problem are proposed. The force exerted by the rigid obstacle is included as a new unknown. A priori and a posteriori error estimates are derived for both obstacle problems. The a posteriori error estimates are based on conforming postprocessed solutions. Numerical experiments conclude this work.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148236609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 symmetric (Q_1)-finite volume element scheme for anisotropic diffusion problems on unstructured convex quadrilateral meshes 非结构凸四边形网格上各向异性扩散问题的对称(Q_1) -有限体积元格式
IF 2.1 3区 数学
Advances in Computational Mathematics Pub Date : 2026-06-02 DOI: 10.1007/s10444-026-10318-3
Yanhui Zhou
{"title":"A symmetric (Q_1)-finite volume element scheme for anisotropic diffusion problems on unstructured convex quadrilateral meshes","authors":"Yanhui Zhou","doi":"10.1007/s10444-026-10318-3","DOIUrl":"10.1007/s10444-026-10318-3","url":null,"abstract":"<div><p>We study a symmetric <span>(Q_1)</span>-finite volume element scheme for anisotropic diffusion problems on unstructured convex quadrilateral meshes. This scheme was originally suggested in [39] where the diffusion coefficient is a scalar and the analysis was done for Poisson equations on a uniform rectangular mesh. In this paper, we prove the symmetry and positive definiteness of the global bilinear form, by which the well-posedness of the scheme is established on an arbitrary convex quadrilateral mesh with any mesh size and a full anisotropic diffusion tensor. Under a weak mesh assumption, which covers the structured convex quadrilateral mesh, we present a simply analysis (different from the standard cell analysis approach) for the proof of <span>(L^2)</span> coercivity of the symmetric scheme. Further, by Taylor expansion, the optimal <span>(L^2)</span> and <span>(H^1)</span> error estimates are verified on the bisection quadrilateral mesh with a full anisotropic diffusion tensor. Consequently, we improve the theoretical results in [39]. Finally, several numerical examples are provided to validate the theoretical findings.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Sparse grids vs. random points for high-dimensional polynomial approximation 稀疏网格与高维多项式近似的随机点
IF 2.1 3区 数学
Advances in Computational Mathematics Pub Date : 2026-06-02 DOI: 10.1007/s10444-026-10316-5
Jakob Eggl, Elias Mindlberger, Mario Ullrich
{"title":"Sparse grids vs. random points for high-dimensional polynomial approximation","authors":"Jakob Eggl,&nbsp;Elias Mindlberger,&nbsp;Mario Ullrich","doi":"10.1007/s10444-026-10316-5","DOIUrl":"10.1007/s10444-026-10316-5","url":null,"abstract":"<div><p>We study polynomial approximation on a <i>d</i>-cube, where <i>d</i> is large, and compare interpolation on sparse grids, aka Smolyak’s algorithm (SA), with a simple least squares method based on randomly generated points (LS) using standard benchmark functions. Our main motivation is the influential paper [4]. We repeat and extend their theoretical analysis and numerical experiments for SA and compare them to LS in dimensions up to 100. Our extensive experiments demonstrate that LS, even with only slight oversampling, consistently matches the accuracy of SA in low dimensions. In high dimensions, however, LS shows clear superiority.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-026-10316-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a deterministic block Kaczmarz-type method and its acceleration for the solution of large-scale linear systems 求解大型线性系统的确定性块kaczmarz型方法及其加速
IF 2.1 3区 数学
Advances in Computational Mathematics Pub Date : 2026-05-28 DOI: 10.1007/s10444-026-10317-4
Yong Liu, Jianjun Zhang
{"title":"On a deterministic block Kaczmarz-type method and its acceleration for the solution of large-scale linear systems","authors":"Yong Liu,&nbsp;Jianjun Zhang","doi":"10.1007/s10444-026-10317-4","DOIUrl":"10.1007/s10444-026-10317-4","url":null,"abstract":"<div><p>We propose a new deterministic block Kaczmarz-type method for solving large-scale consistent systems of linear equations. In the proposed method, the block of the subsystem of linear equations is determined by an easier to compute method, and it is pseudoinverse-free to solve the subsystem. To further accelerate the convergence rate of the proposed method, we present an accelerated version of this method using momentum. Linear convergence of the proposed method and its acceleration are proved. Numerical results show that the proposed method and its acceleration are effective and very fast for the test problems.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148173422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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