Journal of Scientific Computing最新文献_第7页

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

Gradient-Robust Hybrid DG Discretizations for the Compressible Stokes Equations 可压缩斯托克斯方程的梯度-稳健混合 DG 离散法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-04 DOI: 10.1007/s10915-024-02605-2

P. L. Lederer, C. Merdon

引用次数: 0

Error Analysis of Serendipity Virtual Element Methods for Semilinear Parabolic Integro-Differential Equations 半线性抛物线积分微分方程 Serendipity 虚拟元素方法的误差分析

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-04 DOI: 10.1007/s10915-024-02610-5

Yang Xu, Zhenguo Zhou, Jingjun Zhao

{"title":"Error Analysis of Serendipity Virtual Element Methods for Semilinear Parabolic Integro-Differential Equations","authors":"Yang Xu, Zhenguo Zhou, Jingjun Zhao","doi":"10.1007/s10915-024-02610-5","DOIUrl":"https://doi.org/10.1007/s10915-024-02610-5","url":null,"abstract":"The main objective of this study is to evaluate the performance of serendipity virtual element methods in solving semilinear parabolic integro-differential equations with variable coefficients. The primary advantage of this method, in comparison to the standard (enhanced) virtual element methods, lies in the reduction of internal-moment degrees of freedom, which can speed up the iterative algorithms when using the quasi-interpolation operators to approximate nonlinear terms. The temporal discretization is obtained with the backward-Euler scheme. To maintain consistency with the accuracy order of the backward-Euler scheme, the integral term is approximated using the left rectangular quadrature rule. Within the serendipity virtual element framework, we introduced a Ritz–Volterra projection and conducted a comprehensive analysis of its approximation properties. Building upon this analysis, we ultimately provided optimal (H^1)-seminorm and (L^2)-norm error estimates for both the semi-discrete and fully discrete schemes. Finally, two numerical examples that serve to illustrate and validate the theoretical findings are presented.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"29 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547110","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

Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport 线性玻尔兹曼输运的高效高阶空间-角度-能量多拓扑非连续伽勒金有限元方法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-02 DOI: 10.1007/s10915-024-02569-3

Paul Houston, Matthew E. Hubbard, Thomas J. Radley, Oliver J. Sutton, Richard S. J. Widdowson

{"title":"Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport","authors":"Paul Houston, Matthew E. Hubbard, Thomas J. Radley, Oliver J. Sutton, Richard S. J. Widdowson","doi":"10.1007/s10915-024-02569-3","DOIUrl":"https://doi.org/10.1007/s10915-024-02569-3","url":null,"abstract":"We introduce an hp-version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new method is that, while offering arbitrary order convergence rates, it may be implemented in an almost identical form to standard multigroup discrete ordinates methods, meaning that solutions can be computed efficiently with high accuracy and in parallel within existing software. This method provides a unified discretisation of the space, angle, and energy domains of the underlying integro-differential equation and naturally incorporates both local mesh and local polynomial degree variation within each of these computational domains. Moreover, general polytopic elements can be handled by the method, enabling efficient discretisations of problems posed on complicated spatial geometries. We study the stability and hp-version a priori error analysis of the proposed method, by deriving suitable hp-approximation estimates together with a novel inf-sup bound. Numerical experiments highlighting the performance of the method for both polyenergetic and monoenergetic problems are presented.\u0000","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"5 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512484","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