Journal of Scientific Computing最新文献_第6页

Block Diagonalization of Block Circulant Quaternion Matrices and the Fast Calculation for T-Product of Quaternion Tensors 块环四元数矩阵的块对角化和四元张量 T 积的快速计算

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-21 DOI: 10.1007/s10915-024-02623-0

Meng-Meng Zheng, Guyan Ni

{"title":"Block Diagonalization of Block Circulant Quaternion Matrices and the Fast Calculation for T-Product of Quaternion Tensors","authors":"Meng-Meng Zheng, Guyan Ni","doi":"10.1007/s10915-024-02623-0","DOIUrl":"https://doi.org/10.1007/s10915-024-02623-0","url":null,"abstract":"With quaternion matrices and quaternion tensors being gradually used in the color image and color video processing, the block diagonalization of block circulant quaternion matrices has become a key issue in the establishment of T-product based methods for quaternion tensors. Out of this consideration, we aim at establishing a fast calculation approach for the block diagonalization of block circulant quaternion matrices with the help of the fast Fourier transform (FFT). We first show that the discrete Fourier matrix (mathbf {F_p}) cannot diagonalize (ptimes p) circulant quaternion matrices, nor can the unitary quaternion matrices (mathbf {F_p}textbf{j}) and (mathbf {F_p}(1+textbf{j})/sqrt{2}) with (textbf{j}) being an imaginary unit of quaternion algebra. Then we prove that the unitary octonion matrix (mathbf {F_p}textbf{p}) with (textbf{p}=textbf{l},textbf{il}) or ((textbf{l}+textbf{il})/sqrt{2}) ((textbf{l}, textbf{il}) being imaginary units of octonion algebra) can diagonalize a circulant quaternion matrix of size (ptimes p), which further means that a block circulant quaternion matrix of size (mptimes np) can be block diagonalized at the cost of (O(mnplog p)) via the FFT. As one of applications, we give a fast algorithm to speed up the calculation of the T-product between (mtimes ntimes p) and (ntimes stimes p) third-order quaternion tensors via FFTs, whose computational magnitude is almost 1/p of the original one. As another application, we propose an effective compression strategy for third-order quaternion tensors with a certain low-rankness. Simulations on the color image and color video compression demonstrate that our compression strategy with no QSVD involved, can achieve higher quality compression in terms of PSNR values at much less time costs, compared with the QSVD-based methods.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141738109","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 Solution Existence for Collocation Discretizations of Time-Fractional Subdiffusion Equations 论时间-分数子扩散方程对位离散化的解存在性

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-18 DOI: 10.1007/s10915-024-02619-w

Sebastian Franz, Natalia Kopteva

引用次数: 0

A Structure-Preserving Semi-implicit IMEX Finite Volume Scheme for Ideal Magnetohydrodynamics at all Mach and Alfvén Numbers 所有马赫数和阿尔弗文数下理想磁流体力学的保结构半隐式 IMEX 有限体积方案

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-17 DOI: 10.1007/s10915-024-02606-1

Walter Boscheri, Andrea Thomann

{"title":"A Structure-Preserving Semi-implicit IMEX Finite Volume Scheme for Ideal Magnetohydrodynamics at all Mach and Alfvén Numbers","authors":"Walter Boscheri, Andrea Thomann","doi":"10.1007/s10915-024-02606-1","DOIUrl":"https://doi.org/10.1007/s10915-024-02606-1","url":null,"abstract":"We present a divergence-free semi-implicit finite volume scheme for the simulation of the ideal magnetohydrodynamics (MHD) equations which is stable for large time steps controlled by the local transport speed at all Mach and Alfvén numbers. An operator splitting technique allows to treat the convective terms explicitly while the hydrodynamic pressure and the magnetic field contributions are integrated implicitly, yielding two decoupled linear implicit systems. The linearity of the implicit part is achieved by means of a semi-implicit time linearization. This structure is favorable as second-order accuracy in time can be achieved relying on the class of semi-implicit IMplicit–EXplicit Runge–Kutta (IMEX-RK) methods. In space, implicit cell-centered finite difference operators are designed to discretely preserve the divergence-free property of the magnetic field on three-dimensional Cartesian meshes. The new scheme is also particularly well suited for low Mach number flows and for the incompressible limit of the MHD equations, since no explicit numerical dissipation is added to the implicit contribution and the time step is scale independent. Likewise, highly magnetized flows can benefit from the implicit treatment of the magnetic fluxes, hence improving the computational efficiency of the novel method. The convective terms undergo a shock-capturing second order finite volume discretization to guarantee the effectiveness of the proposed method even for high Mach number flows. The new scheme is benchmarked against a series of test cases for the ideal MHD equations addressing different acoustic and Alfvén Mach number regimes where the performance and the stability of the new scheme is assessed.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719073","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

Very High-Order Accurate Discontinuous Galerkin Method for Curved Boundaries with Polygonal Meshes 多边形网格曲面边界的极高阶精确非连续伽勒金方法

IF 2.8 2区数学

Journal of Scientific Computing Pub Date : 2024-07-16 DOI: 10.1007/s10915-024-02613-2

Milene Santos, Adérito Araújo, S. Barbeiro, S. Clain, Ricardo Costa, Gaspar J. Machado

引用次数: 0

A Mass-Conservative Reduced-Order Algorithm in Solving Optimal Control of Convection-Diffusion Equation 解决对流扩散方程优化控制的质量守恒降序算法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-14 DOI: 10.1007/s10915-024-02620-3

Junpeng Song, Qiuqin Wu, Yi Shi

{"title":"A Mass-Conservative Reduced-Order Algorithm in Solving Optimal Control of Convection-Diffusion Equation","authors":"Junpeng Song, Qiuqin Wu, Yi Shi","doi":"10.1007/s10915-024-02620-3","DOIUrl":"https://doi.org/10.1007/s10915-024-02620-3","url":null,"abstract":"This paper introduces a novel approach, the mass-conservative reduced-order characteristic finite element (MCROCFE) method, designed for optimal control problem governed by convection-diffusion equation. The study delves into scenarios where the original state equation exhibits mass-conservation, yet the velocity field is non-divergence-free. The key points of emphasis are: (1) The method effectively addresses convection-dominated diffusion systems through the application of the characteristic technique; (2) Its efficiency is underscored by leveraging the proper orthogonal decomposition (POD) technique, significantly reducing the scale of solving algebraic equation systems; (3) The proposed scheme, based on the mass-conservative characteristic finite element (MCCFE) method framework and the classical POD technique with a slight adjustment to reduce-order space, maintains mass-conservation for the state variable. A priori error estimates are derived for the mass-conservative reduced-order scheme. Theoretical results are validated through numerical comparisons with the MCCFE method, emphasizing the mass-conservation, accuracy and efficiency of the MCROCFE method.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141609467","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 Preconditioned MINRES Method for Block Lower Triangular Toeplitz Systems 块下三角托普利兹系统的预处理 MINRES 方法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-13 DOI: 10.1007/s10915-024-02611-4

Congcong Li, Xuelei Lin, Sean Hon, Shu-Lin Wu

{"title":"A Preconditioned MINRES Method for Block Lower Triangular Toeplitz Systems","authors":"Congcong Li, Xuelei Lin, Sean Hon, Shu-Lin Wu","doi":"10.1007/s10915-024-02611-4","DOIUrl":"https://doi.org/10.1007/s10915-024-02611-4","url":null,"abstract":"In this study, a novel preconditioner based on the absolute-value block (alpha )-circulant matrix approximation is developed, specifically designed for nonsymmetric dense block lower triangular Toeplitz (BLTT) systems that emerge from the numerical discretization of evolutionary equations. Our preconditioner is constructed by taking an absolute-value of a block (alpha )-circulant matrix approximation to the BLTT matrix. To apply our preconditioner, the original BLTT linear system is converted into a symmetric form by applying a time-reversing permutation transformation. Then, with our preconditioner, the preconditioned minimal residual method (MINRES) solver is employed to solve the symmetrized linear system. With properly chosen (alpha ), the eigenvalues of the preconditioned matrix are proven to be clustered around (pm 1) without any significant outliers. With the clustered spectrum, we show that the preconditioned MINRES solver for the preconditioned system has a convergence rate independent of system size. The efficacy of the proposed preconditioner is corroborated by our numerical experiments, which reveal that it attains optimal convergence.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141614425","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

Stability Analysis and Error Estimate of the Explicit Single-Step Time-Marching Discontinuous Galerkin Methods with Stage-Dependent Numerical Flux Parameters for a Linear Hyperbolic Equation in One Dimension 一维线性双曲方程的显式单步时间行进非连续伽勒金方法与阶段性数值通量参数的稳定性分析和误差估计

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-13 DOI: 10.1007/s10915-024-02621-2

Yuan Xu, Chi-Wang Shu, Qiang Zhang

{"title":"Stability Analysis and Error Estimate of the Explicit Single-Step Time-Marching Discontinuous Galerkin Methods with Stage-Dependent Numerical Flux Parameters for a Linear Hyperbolic Equation in One Dimension","authors":"Yuan Xu, Chi-Wang Shu, Qiang Zhang","doi":"10.1007/s10915-024-02621-2","DOIUrl":"https://doi.org/10.1007/s10915-024-02621-2","url":null,"abstract":"In this paper, we present the (hbox {L}^2)-norm stability analysis and error estimate for the explicit single-step time-marching discontinuous Galerkin (DG) methods with stage-dependent numerical flux parameters, when solving a linear constant-coefficient hyperbolic equation in one dimension. Two well-known examples of this method include the Runge–Kutta DG method with the downwind treatment for the negative time marching coefficients, as well as the Lax–Wendroff DG method with arbitrary numerical flux parameters to deal with the auxiliary variables. The stability analysis framework is an extension and an application of the matrix transferring process based on the temporal differences of stage solutions, and a new concept, named as the averaged numerical flux parameter, is proposed to reveal the essential upwind mechanism in the fully discrete status. Distinguished from the traditional analysis, we have to present a novel way to obtain the optimal error estimate in both space and time. The main tool is a series of space–time approximation functions for a given spatial function, which preserve the local structure of the fully discrete schemes and the balance of exact evolution under the control of the partial differential equation. Finally some numerical experiments are given to validate the theoretical results proposed in this paper.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141614426","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

Superconvergence Analysis of a Robust Orthogonal Gauss Collocation Method for 2D Fourth-Order Subdiffusion Equations 二维四阶次扩散方程的鲁棒正交高斯配位法的超收敛性分析

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-12 DOI: 10.1007/s10915-024-02616-z

Xuehua Yang, Zhimin Zhang

{"title":"Superconvergence Analysis of a Robust Orthogonal Gauss Collocation Method for 2D Fourth-Order Subdiffusion Equations","authors":"Xuehua Yang, Zhimin Zhang","doi":"10.1007/s10915-024-02616-z","DOIUrl":"https://doi.org/10.1007/s10915-024-02616-z","url":null,"abstract":"In this paper, we study the orthogonal Gauss collocation method (OGCM) with an arbitrary polynomial degree for the numerical solution of a two-dimensional (2D) fourth-order subdiffusion model. This numerical method involves solving a coupled system of partial differential equations by using OGCM in space together with the L1 scheme in time on a graded mesh. The approximations (w^n_h) and (v^n_h) of (w(cdot , t_n)) and (varDelta w(cdot , t_n)) are constructed. The stability of (w^n_h) and (v^n_h) are proved, and the a priori bounds of (Vert w^n_hVert ) and (Vert v^n_hVert ) are established, remaining (alpha )-robust as (alpha rightarrow 1^{-}). Then, the error (Vert w(cdot , t_n)- w^n_hVert ) and (Vert varDelta w(cdot , t_n)-v^n_hVert ) are estimated with (alpha )-robust at each time level. In addition, superconvergence results of the first-order and second-order derivative approximations are proved. These new error bounds are desirable and natural, as that they are optimal in both temporal and spatial mesh parameters for each fixed (alpha ). Finally some numerical results are provided to support our theoretical findings.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141609468","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

Gradient-Based Monte Carlo Methods for Relaxation Approximations of Hyperbolic Conservation Laws 基于梯度的蒙特卡罗方法用于双曲守恒定律的松弛逼近

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-11 DOI: 10.1007/s10915-024-02614-1

Giulia Bertaglia, Lorenzo Pareschi, Russel E. Caflisch

{"title":"Gradient-Based Monte Carlo Methods for Relaxation Approximations of Hyperbolic Conservation Laws","authors":"Giulia Bertaglia, Lorenzo Pareschi, Russel E. Caflisch","doi":"10.1007/s10915-024-02614-1","DOIUrl":"https://doi.org/10.1007/s10915-024-02614-1","url":null,"abstract":"Particle methods based on evolving the spatial derivatives of the solution were originally introduced to simulate reaction-diffusion processes, inspired by vortex methods for the Navier–Stokes equations. Such methods, referred to as gradient random walk methods, were extensively studied in the ’90s and have several interesting features, such as being grid-free, automatically adapting to the solution by concentrating elements where the gradient is large, and significantly reducing the variance of the standard random walk approach. In this work, we revive these ideas by showing how to generalize the approach to a larger class of partial differential equations, including hyperbolic systems of conservation laws. To achieve this goal, we first extend the classical Monte Carlo method to relaxation approximation of systems of conservation laws, and subsequently consider a novel particle dynamics based on the spatial derivatives of the solution. The methodology, combined with asymptotic-preserving splitting discretization, yields a way to construct a new class of gradient-based Monte Carlo methods for hyperbolic systems of conservation laws. Several results in one spatial dimension for scalar equations and systems of conservation laws show that the new methods are very promising and yield remarkable improvements compared to standard Monte Carlo approaches, either in terms of variance reduction as well as in describing the shock structure.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141587806","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

Weakly Compressible Two-Layer Shallow-Water Flows Along Channels 弱可压缩两层浅水水道流

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-11 DOI: 10.1007/s10915-024-02608-z

Sarswati Shah, Gerardo Hernández-Dueñas

引用次数: 0