Journal of Scientific Computing最新文献_第2页

A Robustness-Enhanced Reconstruction Based on Discontinuity Feedback Factor for High-Order Finite Volume Scheme 基于不连续反馈因子的高阶有限体积方案的鲁棒性增强重构

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-04 DOI: 10.1007/s10915-024-02655-6

Hong Zhang, Xing Ji, Yue Zhao, Yuan Ding, Kun Xu

引用次数: 0

A Modified Interior Penalty Virtual Element Method for Fourth-Order Singular Perturbation Problems 四阶奇异扰动问题的修正内部惩罚虚拟元素法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-04 DOI: 10.1007/s10915-024-02665-4

Fang Feng, Yue Yu

引用次数: 0

Multi-dimensional Scaling from K-Nearest Neighbourhood Distances 根据 K 最近邻距离进行多维扩展

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-02 DOI: 10.1007/s10915-024-02662-7

Wenjian Du, Jia Li

{"title":"Multi-dimensional Scaling from K-Nearest Neighbourhood Distances","authors":"Wenjian Du, Jia Li","doi":"10.1007/s10915-024-02662-7","DOIUrl":"https://doi.org/10.1007/s10915-024-02662-7","url":null,"abstract":"Multi-dimensional scaling (MDS) with incomplete distance information represents a significant challenging inverse problem in computational geometry. This technique finds expensive applications in the fields of surface, manifold, and cubicle reconstructions, and is also relevant in the context of social networks. While a majority of existing methodologies tend to provide accurate results primarily when the missing distance indices are chosen randomly or when the omission rate is below 50%, our research proposes an innovative approach. We present a robust MDS framework when distances to the k-nearest neighbors (kNN) are known, even in situations characterized by a high coherence of missing indices. Our proposed strategy starts with a local reconstruction phase based on local correlation. Subsequently, the global reconstruction phase is realized through two distinct models: one based on low-rank semi-definite programming (SDP) and the other rooted in a model utilizing the Frobenius norm. Throughout the global reconstruction, we incorporate the alternating direction method of multipliers (ADMM) and the Riemann gradient descent algorithm (RGrad). Numerical Simulations have demonstrated that for MDS from kNN distances, our proposed model and algorithm outperforms the existed SDP models in terms of the visual effect and error of Gram matrix. We further validate that our approach can reconstruct surfaces from as mere as 1% of kNN distances, which shows that the proposed model is robust to the high coherence of missing indices. Additionally, we propose another MDS model which is applicable from kNN distances with additive noise.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183712","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

High-Accuracy Numerical Methods and Convergence Analysis for Schrödinger Equation with Incommensurate Potentials 具有不相称势垒的薛定谔方程的高精度数值方法和收敛性分析

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-29 DOI: 10.1007/s10915-024-02658-3

Kai Jiang, Shifeng Li, Juan Zhang

引用次数: 0

A Fast Algorithm for Rank-(L, M, N) Block Term Decomposition of Multi-Dimensional Data 多维数据的 Rank-(L, M, N) 块项分解快速算法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-28 DOI: 10.1007/s10915-024-02653-8

Hao Zhang, Ting-Zhu Huang, Xi-Le Zhao, Maolin Che

{"title":"A Fast Algorithm for Rank-(L, M, N) Block Term Decomposition of Multi-Dimensional Data","authors":"Hao Zhang, Ting-Zhu Huang, Xi-Le Zhao, Maolin Che","doi":"10.1007/s10915-024-02653-8","DOIUrl":"https://doi.org/10.1007/s10915-024-02653-8","url":null,"abstract":"Attribute to its powerful representation ability, block term decomposition (BTD) has recently attracted many views of multi-dimensional data processing, e.g., hyperspectral image unmixing and blind source separation. However, the popular alternating least squares algorithm for rank-(L, M, N) BTD (BTD-ALS) suffers expensive time and space costs from Kronecker products and solving low-rank approximation subproblems, hindering the deployment of BTD for real applications, especially for large-scale data. In this paper, we propose a fast sketching-based Kronecker product-free algorithm for rank-(L, M, N) BTD (termed as KPF-BTD), which is suitable for real-world multi-dimensional data. Specifically, we first decompose the original optimization problem into several rank-(L, M, N) approximation subproblems, and then we design the bilateral sketching to obtain the approximate solutions of these subproblems instead of the exact solutions, which allows us to avoid Kronecker products and rapidly solve rank-(L, M, N) approximation subproblems. As compared with BTD-ALS, the time and space complexities (mathcal {O}{(2(p+1)(I^3LR+I^2L^2R+IL^3R)+I^3LR)}) and (mathcal {O}{(I^3)}) of KPF-BTD are significantly cheaper than (mathcal {O}{(I^3L^6R^2+I^3L^3R+I^3LR+I^2L^3R^2+I^2L^2R)}) and (mathcal {O}{(I^3L^3R)}) of BTD-ALS, where (p ll I). Moreover, we establish the theoretical error bound for KPF-BTD. Extensive synthetic and real experiments show KPF-BTD achieves substantial speedup and memory saving while maintaining accuracy (e.g., for a (150times 150times 150) synthetic tensor, the running time 0.2 seconds per iteration of KPF-BTD is significantly faster than 96.2 seconds per iteration of BTD-ALS while their accuracies are comparable).","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183457","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

Poissonian Image Restoration Via the $$L_1/L_2$$ -Based Minimization 通过基于 L_1/L_2$$ 的最小化实现泊松图像复原

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-28 DOI: 10.1007/s10915-024-02657-4

Mujibur Rahman Chowdhury, Chao Wang, Yifei Lou

引用次数: 0

Flexible Ultra-convergence Structures for the Finite Volume Element Method 有限体积元素法的灵活超收敛结构

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-26 DOI: 10.1007/s10915-024-02654-7

Xiang Wang, Yuqing Zhang, Zhimin Zhang

引用次数: 0

An Alternating Direction Multiplier Method for the Inversion of FDEM Data 用于反演 FDEM 数据的交替方向乘法器方法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-24 DOI: 10.1007/s10915-024-02652-9

Alessandro Buccini, Patricia Díaz de Alba, Federica Pes

引用次数: 0

A Multigrid Solver for PDE-Constrained Optimization with Uncertain Inputs 用于具有不确定输入的 PDE 受限优化的多网格求解器

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-24 DOI: 10.1007/s10915-024-02646-7

Gabriele Ciaramella, Fabio Nobile, Tommaso Vanzan

{"title":"A Multigrid Solver for PDE-Constrained Optimization with Uncertain Inputs","authors":"Gabriele Ciaramella, Fabio Nobile, Tommaso Vanzan","doi":"10.1007/s10915-024-02646-7","DOIUrl":"https://doi.org/10.1007/s10915-024-02646-7","url":null,"abstract":"In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence analysis of collective smoothers and collective two-level methods. The multigrid algorithm is based on a collective smoother that at each iteration sweeps over the nodes of the computational mesh, and solves a reduced saddle-point system whose size is proportional to the number N of samples used to discretized the probability space. We show that this reduced system can be solved with optimal O(N) complexity. The multigrid method is tested both as a stationary method and as a preconditioner for GMRES on three problems: a linear-quadratic problem, possibly with a local or a boundary control, for which the multigrid method is used to solve directly the linear optimality system; a nonsmooth problem with box constraints and (L^1)-norm penalization on the control, in which the multigrid scheme is used as an inner solver within a semismooth Newton iteration; a risk-averse problem with the smoothed CVaR risk measure where the multigrid method is called within a preconditioned Newton iteration. In all cases, the multigrid algorithm exhibits excellent performances and robustness with respect to the parameters of interest.\u0000","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183462","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

Analysis of Weak Galerkin Mixed Finite Element Method Based on the Velocity–Pseudostress Formulation for Navier–Stokes Equation on Polygonal Meshes 基于多边形网格上 Navier-Stokes 方程速度-伪应力公式的弱 Galerkin 混合有限元法分析

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-22 DOI: 10.1007/s10915-024-02651-w

Zeinab Gharibi, Mehdi Dehghan

{"title":"Analysis of Weak Galerkin Mixed Finite Element Method Based on the Velocity–Pseudostress Formulation for Navier–Stokes Equation on Polygonal Meshes","authors":"Zeinab Gharibi, Mehdi Dehghan","doi":"10.1007/s10915-024-02651-w","DOIUrl":"https://doi.org/10.1007/s10915-024-02651-w","url":null,"abstract":"The present article introduces, mathematically analyzes, and numerically validates a new weak Galerkin mixed finite element method based on Banach spaces for the stationary Navier–Stokes equation in pseudostress–velocity formulation. Specifically, a modified pseudostress tensor, which depends on the pressure as well as the diffusive and convective terms, is introduced as an auxiliary unknown, and the incompressibility condition is then used to eliminate the pressure, which is subsequently computed using a postprocessing formula. Consequently, to discretize the resulting mixed formulation, it is sufficient to provide a tensorial weak Galerkin space for the pseudostress and a space of piecewise polynomial vectors of total degree at most ’k’ for the velocity. Moreover, the weak gradient/divergence operator is utilized to propose the weak discrete bilinear forms, whose continuous version involves the classical gradient/divergence operators. The well-posedness of the numerical solution is proven using a fixed-point approach and the discrete versions of the Babuška–Brezzi theory and the Banach–Nečas–Babuška theorem. Additionally, an a priori error estimate is derived for the proposed method. Finally, several numerical results illustrating the method’s good performance and confirming the theoretical rates of convergence are presented.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183497","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