Journal of Scientific Computing最新文献_第4页

High-Order BDF Convolution Quadrature for Fractional Evolution Equations with Hyper-singular Source Term 带超正弦源项的分数演化方程的高阶 BDF 卷积正交

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-17 DOI: 10.1007/s10915-024-02641-y

Jiankang Shi, Minghua Chen, Jianxiong Cao

{"title":"High-Order BDF Convolution Quadrature for Fractional Evolution Equations with Hyper-singular Source Term","authors":"Jiankang Shi, Minghua Chen, Jianxiong Cao","doi":"10.1007/s10915-024-02641-y","DOIUrl":"https://doi.org/10.1007/s10915-024-02641-y","url":null,"abstract":"Anomalous diffusion in the presence or absence of an external force field is often modelled in terms of the fractional evolution equations, which can involve the hyper-singular source term. For this case, conventional time stepping methods may exhibit a severe order reduction. Although a second-order numerical algorithm is provided for the subdiffusion model with a simple hyper-singular source term (t^{mu }), (-2<mu <-1) in [arXiv:2207.08447], the convergence analysis remain to be proved. To fill in these gaps, we present a simple and robust smoothing method for the hyper-singular source term, where the Hadamard finite-part integral is introduced. This method is based on the smoothing/IDm-BDFk method proposed by Shi and Chen (SIAM J Numer Anal 61:2559–2579, 2023) for the subdiffusion equation with a weakly singular source term. We prove that the kth-order convergence rate can be restored for the diffusion-wave case (gamma in (1,2)) and sketch the proof for the subdiffusion case (gamma in (0,1)), even if the source term is hyper-singular and the initial data is not compatible. Numerical experiments are provided to confirm the theoretical results.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"390 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183465","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

Convergence Analysis for the Wave Equation Discretized with Hybrid Methods in Space (HHO, HDG and WG) and the Leapfrog Scheme in Time 用空间混合方法（HHO、HDG 和 WG）和时间跃迁方案离散化波浪方程的收敛性分析

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-13 DOI: 10.1007/s10915-024-02609-y

Alexandre Ern, Morgane Steins

引用次数: 0

Local Discontinuous Galerkin Methods with Multistep Implicit–Explicit Time Discretization for Nonlinear Schrödinger Equations 针对非线性薛定谔方程的多步隐式-显式时间离散化局部非连续伽勒金方法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-13 DOI: 10.1007/s10915-024-02647-6

Ying Li, Hui Shi, Xinghui Zhong

引用次数: 0

An Efficient and Accurate Penalty-projection Eddy Viscosity Algorithm for Stochastic Magnetohydrodynamic Flow Problems 针对随机磁流体动力流问题的高效、精确的惩罚性投影涡流粘度算法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-13 DOI: 10.1007/s10915-024-02633-y

Muhammad Mohebujjaman, Julian Miranda, Md. Abdullah Al Mahbub, Mengying Xiao

{"title":"An Efficient and Accurate Penalty-projection Eddy Viscosity Algorithm for Stochastic Magnetohydrodynamic Flow Problems","authors":"Muhammad Mohebujjaman, Julian Miranda, Md. Abdullah Al Mahbub, Mengying Xiao","doi":"10.1007/s10915-024-02633-y","DOIUrl":"https://doi.org/10.1007/s10915-024-02633-y","url":null,"abstract":"We propose, analyze, and test a penalty projection-based robust efficient and accurate algorithm for the Uncertainty Quantification (UQ) of the time-dependent Magnetohydrodynamic (MHD) flow problems in convection-dominated regimes. The algorithm uses the Elsässer variables formulation and discrete Hodge decomposition to decouple the stochastic MHD system into four sub-problems (at each time-step for each realization) which are much easier to solve than solving the coupled saddle point problems. Each of the sub-problems is designed in a sophisticated way so that at each time-step the system matrix remains the same for all the realizations but with different right-hand-side vectors which allows saving a huge amount of computer memory and computational time. Moreover, the scheme is equipped with Ensemble Eddy Viscosity (EEV) and grad-div stabilization terms. The unconditional stability with respect to the time-step size of the algorithm is proven rigorously. We prove the proposed scheme converges to an equivalent non-projection-based coupled MHD scheme for large grad-div stabilization parameter values. We examine how Stochastic Collocation Methods (SCMs) can be combined with the proposed penalty projection UQ algorithm. Finally, a series of numerical experiments are given which verify the predicted convergence rates, show the algorithm’s performance on benchmark channel flow over a rectangular step, a regularized lid-driven cavity problem with high random Reynolds number and high random magnetic Reynolds number, and the impact of the EEV stabilization in the MHD UQ algorithm.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"24 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183502","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

Riemannian Newton Methods for Energy Minimization Problems of Kohn–Sham Type 用于 Kohn-Sham 类型能量最小化问题的黎曼牛顿方法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-13 DOI: 10.1007/s10915-024-02612-3

R. Altmann, D. Peterseim, T. Stykel

引用次数: 0

A New Alternative WENO Scheme Based on Exponential Polynomial Interpolation with an Improved Order of Accuracy 基于指数多项式插值的新 WENO 替代方案，精度更高

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-13 DOI: 10.1007/s10915-024-02635-w

Youngsoo Ha, Chang Ho Kim, Hyoseon Yang, Jungho Yoon

{"title":"A New Alternative WENO Scheme Based on Exponential Polynomial Interpolation with an Improved Order of Accuracy","authors":"Youngsoo Ha, Chang Ho Kim, Hyoseon Yang, Jungho Yoon","doi":"10.1007/s10915-024-02635-w","DOIUrl":"https://doi.org/10.1007/s10915-024-02635-w","url":null,"abstract":"In this study, we present a new alternative formulation of a conservative weighted essentially non-oscillatory (WENO) scheme that improves the performance of the known fifth-order alternative WENO (AWENO) schemes. In the formulation of the fifth-order AWENO scheme, the numerical flux can be written in two terms: a low-order flux and a high-order correction flux. The low-order numerical flux is constructed by a fifth-order WENO interpolator, and the high-order correction flux includes terms of the second and fourth derivatives, yielding the sixth-order truncation error. Noticing the difference in the convergence rates between these two approximations, this study first aims to fill the accuracy gap by enhancing the approximation order of the low-order numerical flux. To this end, the WENO interpolator for the low-order term is implemented using exponential polynomials with a shape parameter. Selecting a locally optimized shape parameter, the proposed WENO interpolator achieves an additional order of improvement, resulting in the overall sixth order of accuracy of the final reconstruction, under the same fifth-order AWENO framework. In addition, since a linear approximation to the high-order correction term may cause some oscillations in the vicinity of strong shocks, we present a new strategy for the limiting procedure to deal with the second derivative term in the high-order correction flux. Several numerical results for the well-known benchmark test problems confirm the reliability of our AWENO method.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"1 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183501","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

Quaternion Tensor Left Ring Decomposition and Application for Color Image Inpainting 四元张量左环分解及其在彩色图像绘制中的应用

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-08-13 DOI: 10.1007/s10915-024-02624-z

Jifei Miao, Kit Ian Kou, Hongmin Cai, Lizhi Liu

{"title":"Quaternion Tensor Left Ring Decomposition and Application for Color Image Inpainting","authors":"Jifei Miao, Kit Ian Kou, Hongmin Cai, Lizhi Liu","doi":"10.1007/s10915-024-02624-z","DOIUrl":"https://doi.org/10.1007/s10915-024-02624-z","url":null,"abstract":"In recent years, tensor networks have emerged as powerful tools for solving large-scale optimization problems. One of the most promising tensor networks is the tensor ring (TR) decomposition, which achieves circular dimensional permutation invariance in the model through the utilization of the trace operation and equitable treatment of the latent cores. On the other hand, more recently, quaternions have gained significant attention and have been widely utilized in color image processing tasks due to their effectiveness in encoding color pixels by considering the three color channels as a unified entity. Therefore, in this paper, based on the left quaternion matrix multiplication, we propose the quaternion tensor left ring (QTLR) decomposition, which inherits the powerful and generalized representation abilities of the TR decomposition while leveraging the advantages of quaternions for color pixel representation. In addition to providing the definition of QTLR decomposition and an algorithm for learning the QTLR format, the paper further proposes a low-rank quaternion tensor completion (LRQTC) model and its algorithm for color image inpainting based on the defined QTLR decomposition. Finally, extensive experiments on color image inpainting demonstrate that the proposed LRQTC method is highly competitive.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"23 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183498","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

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":"41 1","pages":""},"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