Journal of Scientific Computing最新文献_第2页

Quadrature Rules on Triangles and Tetrahedra for Multidimensional Summation-By-Parts Operators 多维分项求和算子的三角形和正四面体正交规则

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-09 DOI: 10.1007/s10915-024-02656-5

Zelalem Arega Worku, Jason E. Hicken, David W. Zingg

{"title":"Quadrature Rules on Triangles and Tetrahedra for Multidimensional Summation-By-Parts Operators","authors":"Zelalem Arega Worku, Jason E. Hicken, David W. Zingg","doi":"10.1007/s10915-024-02656-5","DOIUrl":"https://doi.org/10.1007/s10915-024-02656-5","url":null,"abstract":"Multidimensional diagonal-norm summation-by-parts (SBP) operators with collocated volume and facet nodes, known as diagonal-( textsf{E}) operators, are attractive for entropy-stable discretizations from an efficiency standpoint. However, there is a limited number of such operators, and those currently in existence often have a relatively high node count for a given polynomial order due to a scarcity of suitable quadrature rules. We present several new symmetric positive-weight quadrature rules on triangles and tetrahedra that are suitable for construction of diagonal-( textsf{E}) SBP operators. For triangles, quadrature rules of degree one through twenty with facet nodes that correspond to the Legendre-Gauss-Lobatto and Legendre-Gauss quadrature rules are derived. For tetrahedra, quadrature rules of degree one through ten are presented along with the corresponding facet quadrature rules. All of the quadrature rules are provided in a supplementary data repository. The quadrature rules are used to construct novel SBP diagonal-( textsf{E}) operators, whose accuracy and maximum time-step restrictions are studied numerically.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"24 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183706","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 High-Accuracy Mode Solver for Acoustic Scattering by a Periodic Array of Axially Symmetric Obstacles 轴对称障碍物周期性阵列声散射的高精度模式求解器

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-05 DOI: 10.1007/s10915-024-02659-2

Hangya Wang, Wangtao Lu

{"title":"A High-Accuracy Mode Solver for Acoustic Scattering by a Periodic Array of Axially Symmetric Obstacles","authors":"Hangya Wang, Wangtao Lu","doi":"10.1007/s10915-024-02659-2","DOIUrl":"https://doi.org/10.1007/s10915-024-02659-2","url":null,"abstract":"This paper is concerned with guided modes of an acoustic wave propagation problem on a periodic array of axially symmetric obstacles. A guided mode refers to a quasi-periodic eigenfield that propagates along the obstacles but decays exponentially away from them in the absence of incidences. Thus, the problem can be studied in an unbound unit cell due to the quasi-periodicity. We truncate the unit cell onto a cylinder enclosing the interior obstacle in terms of utilizing Rayleigh’s expansion to design an exact condition on the lateral boundary. We derive a new boundary integral equation (BIE) only involving the free-space Green function on the boundary of each homogeneous region within the cylinder. Due to the axial symmetry of the boundaries, each BIE is decoupled via the Fourier transform to curve BIEs and they are discretized with high-accuracy quadratures. With the lateral boundary condition and the side quasi-periodic condition, the discretized BIEs lead to a homogeneous linear system governing the propagation constant of a guided mode at a given frequency. The propagation constant is determined by enforcing that the coefficient matrix is singular. The accuracy of the proposed method is demonstrated by a number of examples even when the obstacles have sharp edges or corners.\u0000","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"26 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183708","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

Stabilized Variational Formulations of Chorin-Type and Artificial Compressibility Methods for the Stochastic Stokes–Darcy Equations 用于随机斯托克斯-达西方程的乔林型和人工可压缩性方法的稳定变分公式

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-09-04 DOI: 10.1007/s10915-024-02663-6

Huangxin Chen, Can Huang, Shuyu Sun, Yahong Xiang

{"title":"Stabilized Variational Formulations of Chorin-Type and Artificial Compressibility Methods for the Stochastic Stokes–Darcy Equations","authors":"Huangxin Chen, Can Huang, Shuyu Sun, Yahong Xiang","doi":"10.1007/s10915-024-02663-6","DOIUrl":"https://doi.org/10.1007/s10915-024-02663-6","url":null,"abstract":"In this paper, we consider two different types of numerical schemes for the nonstationary stochastic Stokes–Darcy equations with multiplicative noise. Firstly, we consider the Chorin-type time-splitting scheme for the Stokes equation in the free fluid region. The Darcy equation and an elliptic equation for the intermediate velocity of free fluid coupled with the interface conditions are solved, and then the velocity and pressure in free fluid region are updated by an elliptic system. Secondly, we further consider the artificial compressibility method (ACM) which separates the fully coupled Stokes–Darcy model into two smaller subphysics problems. The ACM reduces the storage and the computational time at each time step, and allows parallel computing for the decoupled problems. The pressure in free fluid region only needs to be updated at each time step without solving an elliptic system. We utilize the RT(_1)-P(_1) pair finite element space and the interior penalty discontinuous Galerkin (IPDG) scheme based on the BDM(_1)-P(_0) finite element space in the spatial discretizations. Under usual assumptions for the multiplicative noise, we prove that both of the Chorin-type scheme and the ACM are unconditionally stable. We present the error estimates for the time semi-discretization of the Chorin-type scheme. Numerical examples are provided to verify the stability estimates for both of schemes. Moreover, we test the convergence rate for the velocity in time for both of schemes, and the convergence rate for the pressure approximation in time average is also tested.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"1 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183709","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 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":"23 1","pages":""},"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":"4 1","pages":""},"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