Advances in Computational Mathematics最新文献_第9页

Averaging property of wedge product and naturality in discrete exterior calculus 离散外部微积分中的楔积平均特性和自然性

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-31 DOI: 10.1007/s10444-024-10179-8

Mark D. Schubel, Daniel Berwick-Evans, Anil N. Hirani

引用次数: 0

Two-grid stabilized finite element methods with backtracking for the stationary Navier-Stokes equations 静态纳维-斯托克斯方程的双网格稳定有限元法与回溯法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-30 DOI: 10.1007/s10444-024-10180-1

Jing Han, Guangzhi Du

引用次数: 0

Analysis of the leapfrog-Verlet method applied to the Kuwabara-Kono force model in discrete element method simulations of granular materials 粒状材料离散元法模拟中库瓦巴拉-科诺力模型的跃迁-韦勒法应用分析

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-23 DOI: 10.1007/s10444-024-10162-3

Gabriel Nóbrega Bufolo, Yuri Dumaresq Sobral

引用次数: 0

Randomized greedy magic point selection schemes for nonlinear model reduction 用于非线性模型还原的随机贪婪魔法点选择方案

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-22 DOI: 10.1007/s10444-024-10172-1

Ralf Zimmermann, Kai Cheng

{"title":"Randomized greedy magic point selection schemes for nonlinear model reduction","authors":"Ralf Zimmermann, Kai Cheng","doi":"10.1007/s10444-024-10172-1","DOIUrl":"10.1007/s10444-024-10172-1","url":null,"abstract":"<div><p>An established way to tackle model nonlinearities in projection-based model reduction is via relying on partial information. This idea is shared by the methods of gappy proper orthogonal decomposition (POD), missing point estimation (MPE), masked projection, hyper reduction, and the (discrete) empirical interpolation method (DEIM). The selected indices of the partial information components are often referred to as “magic points.” The original contribution of the work at hand is a novel randomized greedy magic point selection. It is known that the greedy method is associated with minimizing the norm of an oblique projection operator, which, in turn, is associated with solving a sequence of rank-one SVD update problems. We propose simplification measures so that the resulting greedy point selection has the following main features: (1) The inherent rank-one SVD update problem is tackled in a way, such that its dimension does not grow with the number of selected magic points. (2) The approach is online efficient in the sense that the computational costs are independent from the dimension of the full-scale model. To the best of our knowledge, this is the first greedy magic point selection that features this property. We illustrate the findings by means of numerical examples. We find that the computational cost of the proposed method is orders of magnitude lower than that of its deterministic counterpart. Nevertheless, the prediction accuracy is just as good if not better. When compared to a state-of-the-art randomized method based on leverage scores, the randomized greedy method outperforms its competitor.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10172-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141737016","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

The (L_q)-weighted dual programming of the linear Chebyshev approximation and an interior-point method 线性切比雪夫近似的 $$L_q$$ 加权对偶编程和一种内点法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-22 DOI: 10.1007/s10444-024-10177-w

Yang Linyi, Zhang Lei-Hong, Zhang Ya-Nan

引用次数: 0

On Krylov subspace methods for skew-symmetric and shifted skew-symmetric linear systems 关于偏斜对称和移位偏斜对称线性系统的克雷洛夫子空间方法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-19 DOI: 10.1007/s10444-024-10178-9

Kui Du, Jia-Jun Fan, Xiao-Hui Sun, Fang Wang, Ya-Lan Zhang

{"title":"On Krylov subspace methods for skew-symmetric and shifted skew-symmetric linear systems","authors":"Kui Du, Jia-Jun Fan, Xiao-Hui Sun, Fang Wang, Ya-Lan Zhang","doi":"10.1007/s10444-024-10178-9","DOIUrl":"10.1007/s10444-024-10178-9","url":null,"abstract":"<div><p>Krylov subspace methods for solving linear systems of equations involving skew-symmetric matrices have gained recent attention. Numerical equivalences among Krylov subspace methods for nonsingular skew-symmetric linear systems have been given in Greif et al. [SIAM J. Matrix Anal. Appl., 37 (2016), pp. 1071–1087]. In this work, we extend the results of Greif et al. to singular skew-symmetric linear systems. In addition, we systematically study three Krylov subspace methods (called S<span>(^3)</span>CG, S<span>(^3)</span>MR, and S<span>(^3)</span>LQ) for solving shifted skew-symmetric linear systems. They all are based on Lanczos triangularization for skew-symmetric matrices and correspond to CG, MINRES, and SYMMLQ for solving symmetric linear systems, respectively. To the best of our knowledge, this is the first work that studies S<span>(^3)</span>LQ. We give some new theoretical results on S<span>(^3)</span>CG, S<span>(^3)</span>MR, and S<span>(^3)</span>LQ. We also provide relations among the three methods and those based on Golub–Kahan bidiagonalization and Saunders–Simon–Yip tridiagonalization. Numerical examples are given to illustrate our theoretical findings.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141725760","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

Adaptive choice of near-optimal expansion points for interpolation-based structure-preserving model reduction 自适应选择近优扩展点，实现基于插值的结构保持模型还原

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-19 DOI: 10.1007/s10444-024-10166-z

Quirin Aumann, Steffen W. R. Werner

{"title":"Adaptive choice of near-optimal expansion points for interpolation-based structure-preserving model reduction","authors":"Quirin Aumann, Steffen W. R. Werner","doi":"10.1007/s10444-024-10166-z","DOIUrl":"10.1007/s10444-024-10166-z","url":null,"abstract":"<div><p>Interpolation-based methods are well-established and effective approaches for the efficient generation of accurate reduced-order surrogate models. Common challenges for such methods are the automatic selection of good or even optimal interpolation points and the appropriate size of the reduced-order model. An approach that addresses the first problem for linear, unstructured systems is the iterative rational Krylov algorithm (IRKA), which computes optimal interpolation points through iterative updates by solving linear eigenvalue problems. However, in the case of preserving internal system structures, optimal interpolation points are unknown, and heuristics based on nonlinear eigenvalue problems result in numbers of potential interpolation points that typically exceed the reasonable size of reduced-order systems. In our work, we propose a projection-based iterative interpolation method inspired by IRKA for generally structured systems to adaptively compute near-optimal interpolation points as well as an appropriate size for the reduced-order system. Additionally, the iterative updates of the interpolation points can be chosen such that the reduced-order model provides an accurate approximation in specified frequency ranges of interest. For such applications, our new approach outperforms the established methods in terms of accuracy and computational effort. We show this in numerical examples with different structures.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10166-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141730632","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

Randomized GCUR decompositions 随机 GCUR 分解

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-18 DOI: 10.1007/s10444-024-10168-x

Zhengbang Cao, Yimin Wei, Pengpeng Xie

引用次数: 0

Macro-micro decomposition for consistent and conservative model order reduction of hyperbolic shallow water moment equations: a study using POD-Galerkin and dynamical low-rank approximation 对双曲浅水矩方程进行一致和保守模型阶次缩减的宏观-微观分解：使用 POD-Galerkin 和动态低阶近似的研究

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-16 DOI: 10.1007/s10444-024-10175-y

Julian Koellermeier, Philipp Krah, Jonas Kusch

{"title":"Macro-micro decomposition for consistent and conservative model order reduction of hyperbolic shallow water moment equations: a study using POD-Galerkin and dynamical low-rank approximation","authors":"Julian Koellermeier, Philipp Krah, Jonas Kusch","doi":"10.1007/s10444-024-10175-y","DOIUrl":"10.1007/s10444-024-10175-y","url":null,"abstract":"<div><p>Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques that allow for efficient and accurate simulations while guaranteeing physical properties like mass conservation. In this paper, we develop the first model reduction for the hyperbolic shallow water moment equations and achieve mass conservation. This is accomplished using a macro-micro decomposition of the model into a macroscopic (conservative) part and a microscopic (non-conservative) part with subsequent model reduction using either POD-Galerkin or dynamical low-rank approximation only on the microscopic (non-conservative) part. Numerical experiments showcase the performance of the new model reduction methods including high accuracy and fast computation times together with guaranteed conservation and consistency properties.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10175-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141625059","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

Augmented Lagrangian method for tensor low-rank and sparsity models in multi-dimensional image recovery 多维图像复原中张量低阶和稀疏模型的增量拉格朗日法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-16 DOI: 10.1007/s10444-024-10170-3

Hong Zhu, Xiaoxia Liu, Lin Huang, Zhaosong Lu, Jian Lu, Michael K. Ng

引用次数: 0