Journal of Scientific Computing最新文献_第7页

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":"108 1","pages":""},"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":"23 1","pages":""},"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":"36 1","pages":""},"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":"57 1","pages":""},"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":"45 1","pages":""},"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

A Penalty-Free and Essentially Stabilization-Free DG Method for Convection-Dominated Second-Order Elliptic Problems 针对对流主导的二阶椭圆问题的无罚金且基本无稳定的 DG 方法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-09 DOI: 10.1007/s10915-024-02615-0

Huoyuan Duan, Junhua Ma

引用次数: 0

Inexact Fixed-Point Proximity Algorithm for the $$ell _0$$ Sparse Regularization Problem $$ell _0$$ 稀疏正则化问题的非精确定点邻近算法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-08 DOI: 10.1007/s10915-024-02600-7

Ronglong Fang, Yuesheng Xu, Mingsong Yan

{"title":"Inexact Fixed-Point Proximity Algorithm for the $$ell _0$$ Sparse Regularization Problem","authors":"Ronglong Fang, Yuesheng Xu, Mingsong Yan","doi":"10.1007/s10915-024-02600-7","DOIUrl":"https://doi.org/10.1007/s10915-024-02600-7","url":null,"abstract":"We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the (ell _0) norm. Specifically, the (ell _0) model has an objective function that is the sum of a convex fidelity term and a Moreau envelope of the (ell _0) norm regularization term. Such an (ell _0) model is non-convex. Existing exact algorithms for solving the problems require the availability of closed-form formulas for the proximity operator of convex functions involved in the objective function. When such formulas are not available, numerical computation of the proximity operator becomes inevitable. This leads to inexact iteration algorithms. We investigate in this paper how the numerical error for every step of the iteration should be controlled to ensure global convergence of the inexact algorithms. We establish a theoretical result that guarantees the sequence generated by the proposed inexact algorithm converges to a local minimizer of the optimization problem. We implement the proposed algorithms for three applications of practical importance in machine learning and image science, which include regression, classification, and image deblurring. The numerical results demonstrate the convergence of the proposed algorithm and confirm that local minimizers of the (ell _0) models found by the proposed inexact algorithm outperform global minimizers of the corresponding (ell _1) models, in terms of approximation accuracy and sparsity of the solutions.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"141 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141566994","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 Combined Mixed Hybrid and Hybridizable Discontinuous Galerkin Method for Darcy Flow and Transport 达西流与传输的混合可混合非连续伽勒金方法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-08 DOI: 10.1007/s10915-024-02607-0

Keegan L. A. Kirk, Beatrice Riviere

引用次数: 0

A Parallel Finite Element Discretization Scheme for the Natural Convection Equations 自然对流方程的并行有限元离散化方案

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-04 DOI: 10.1007/s10915-024-02601-6

Yueqiang Shang

引用次数: 0