Journal of Scientific Computing最新文献_第4页

Spectrally Constrained Optimization 光谱约束优化

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-06 DOI: 10.1007/s10915-024-02636-9

Casey Garner, Gilad Lerman, Shuzhong Zhang

引用次数: 0

Preconditioned Nonsymmetric/Symmetric Discontinuous Galerkin Method for Elliptic Problem with Reconstructed Discontinuous Approximation 用重构非连续逼近椭圆问题的预条件非对称/对称非连续伽勒金方法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-06 DOI: 10.1007/s10915-024-02639-6

Ruo Li, Qicheng Liu, Fanyi Yang

{"title":"Preconditioned Nonsymmetric/Symmetric Discontinuous Galerkin Method for Elliptic Problem with Reconstructed Discontinuous Approximation","authors":"Ruo Li, Qicheng Liu, Fanyi Yang","doi":"10.1007/s10915-024-02639-6","DOIUrl":"https://doi.org/10.1007/s10915-024-02639-6","url":null,"abstract":"In this paper, we propose and analyze an efficient preconditioning method for the elliptic problem based on the reconstructed discontinuous approximation method. This method is originally proposed in Li et al. (J Sci Comput 80(1):268–288, 2019) that an arbitrarily high-order approximation space with one unknown per element is reconstructed by solving a local least squares fitting problem. This space can be directly used with the symmetric/nonsymmetric interior penalty discontinuous Galerkin methods. The least squares problem is modified in this paper, which allows us to establish a norm equivalence result between the reconstructed high-order space and the piecewise constant space. This property further inspires us to construct a preconditioner from the piecewise constant space. The preconditioner is shown to be optimal that the upper bound of the condition number to the preconditioned symmetric/nonsymmetric system is independent of the mesh size. In addition, we can enjoy the advantage on the efficiency of the approximation in number of degrees of freedom compared with the standard DG method. Numerical experiments are provided to demonstrate the validity of the theory and the efficiency of the proposed method.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944493","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

On the Global Complexity of a Derivative-Free Levenberg-Marquardt Algorithm via Orthogonal Spherical Smoothing 通过正交球形平滑法论无衍生莱文伯格-马夸特算法的全局复杂性

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-06 DOI: 10.1007/s10915-024-02649-4

Xi Chen, Jinyan Fan

引用次数: 0

Two Finite Element Approaches for the Porous Medium Equation That Are Positivity Preserving and Energy Stable 多孔介质方程的两种有限元方法，既保证正向性，又保证能量稳定

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-06 DOI: 10.1007/s10915-024-02642-x

Arjun Vijaywargiya, Guosheng Fu

{"title":"Two Finite Element Approaches for the Porous Medium Equation That Are Positivity Preserving and Energy Stable","authors":"Arjun Vijaywargiya, Guosheng Fu","doi":"10.1007/s10915-024-02642-x","DOIUrl":"https://doi.org/10.1007/s10915-024-02642-x","url":null,"abstract":"In this work, we present the construction of two distinct finite element approaches to solve the porous medium equation (PME). In the first approach, we transform the PME to a log-density variable formulation and construct a continuous Galerkin method. In the second approach, we introduce additional potential and velocity variables to rewrite the PME into a system of equations, for which we construct a mixed finite element method. Both approaches are first-order accurate, mass conserving, and proved to be unconditionally energy stable for their respective energies. The mixed approach is shown to preserve positivity under a CFL condition, while a much stronger property of unconditional bound preservation is proved for the log-density approach. A novel feature of our schemes is that they can handle compactly supported initial data without the need for any perturbation techniques. Furthermore, the log-density method can handle unstructured grids in any number of dimensions, while the mixed method can handle unstructured grids in two dimensions. We present results from several numerical experiments to demonstrate these properties.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944488","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 Quasi-Conservative Alternative WENO Finite Difference Scheme for Solving Compressible Multicomponent Flows 解决可压缩多组分流动的准保守替代 WENO 有限差分方案

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-06 DOI: 10.1007/s10915-024-02645-8

Yanan Yang, Hua Shen, Zhiwei He

引用次数: 0

Very High-Order A-Stable Stiffly Accurate Diagonally Implicit Runge-Kutta Methods with Error Estimators 带误差估计器的极高阶 A 级稳定、刚性、精确对角隐含 Runge-Kutta 方法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-05 DOI: 10.1007/s10915-024-02627-w

Yousef Alamri, David I. Ketcheson

{"title":"Very High-Order A-Stable Stiffly Accurate Diagonally Implicit Runge-Kutta Methods with Error Estimators","authors":"Yousef Alamri, David I. Ketcheson","doi":"10.1007/s10915-024-02627-w","DOIUrl":"https://doi.org/10.1007/s10915-024-02627-w","url":null,"abstract":"A numerical search approach is used to design high-order diagonally implicit Runge-Kutta (DIRK) time stepping schemes equipped with embedded error estimators, some of which have identical diagonal elements (i.e., SDIRK) and explicit first stage (i.e., ESDIRK). In each of these classes, we present new A-stable schemes of order six (the highest order of previously known A-stable DIRK-type schemes) up to order eight. For each order, we include one scheme that is only A-stable as well as several schemes that are L-stable, stiffly accurate, and/or have stage order two. The latter types require more stages, but yield better convergence rates for differential-algebraic equations (DAEs), and particularly those which have stage order two result in better accuracy for moderately stiff problems. The development of the eighth-order schemes requires, in addition to imposing A-stability, finding highly accurate numerical solutions for a system of 200 equations in over 100 variables, which is accomplished via a combination of global and local optimization strategies. The accuracy, stability, and adaptive stepsize control of the schemes are demonstrated on diverse problems.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944492","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

Asymptotic and Invariant-Domain Preserving Schemes for Scalar Conservation Equations with Stiff Source Terms and Multiple Equilibrium Points 具有刚性源项和多个平衡点的标量守恒方程的渐近和无变量域保恒方案

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-02 DOI: 10.1007/s10915-024-02628-9

Alexandre Ern, Jean-Luc Guermond, Zuodong Wang

引用次数: 0

A High-Order Discontinuous Galerkin Method for One-Fluid Two-Temperature Euler Non-equilibrium Hydrodynamics 单流体双温欧拉非平衡流体力学的高阶非连续伽勒金方法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-02 DOI: 10.1007/s10915-024-02640-z

Jian Cheng

引用次数: 0

A Hodge Decomposition Finite Element Method for the Quad-Curl Problem on Polyhedral Domains 多面体域上四曲面问题的霍奇分解有限元法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-01 DOI: 10.1007/s10915-024-02626-x

Susanne C. Brenner, Casey Cavanaugh, Li-yeng Sung

引用次数: 0

An Efficient and Versatile Variational Method for High-Dimensional Data Classification 用于高维数据分类的高效多变方法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-01 DOI: 10.1007/s10915-024-02644-9

Xiaohao Cai, Raymond H. Chan, Xiaoyu Xie, Tieyong Zeng

{"title":"An Efficient and Versatile Variational Method for High-Dimensional Data Classification","authors":"Xiaohao Cai, Raymond H. Chan, Xiaoyu Xie, Tieyong Zeng","doi":"10.1007/s10915-024-02644-9","DOIUrl":"https://doi.org/10.1007/s10915-024-02644-9","url":null,"abstract":"High-dimensional data classification is a fundamental task in machine learning and imaging science. In this paper, we propose an efficient and versatile multi-class semi-supervised classification method for classifying high-dimensional data and unstructured point clouds. To begin with, a warm initialization is generated by using a fuzzy classification method such as the standard support vector machine or random labeling. Then an unconstraint convex variational model is proposed to purify and smooth the initialization, followed by a step which is to project the smoothed partition obtained previously to a binary partition. These steps can be repeated, with the latest result as a new initialization, to keep improving the classification quality. We show that the convex model of the smoothing step has a unique solution and can be solved by a specifically designed primal–dual algorithm whose convergence is guaranteed. We test our method and compare it with the state-of-the-art methods on several benchmark data sets. Thorough experimental results demonstrate that our method is superior in both the classification accuracy and computation speed for high-dimensional data and point clouds.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141887063","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