Journal of Scientific Computing最新文献_第7页

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

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

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":null,"pages":null},"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 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":null,"pages":null},"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":null,"pages":null},"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

Anisotropic Weakly Over-Penalised Symmetric Interior Penalty Method for the Stokes Equation 斯托克斯方程的各向异性弱过度惩罚对称内部惩罚法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-02 DOI: 10.1007/s10915-024-02598-y

Hiroki Ishizaka

引用次数: 0

Optimal Balanced-Norm Error Estimate of the LDG Method for Reaction–Diffusion Problems I: The One-Dimensional Case 反应扩散问题 LDG 方法的最优平衡正态误差估计 I：一维情况

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-02 DOI: 10.1007/s10915-024-02602-5

Yao Cheng, Xuesong Wang, Martin Stynes

{"title":"Optimal Balanced-Norm Error Estimate of the LDG Method for Reaction–Diffusion Problems I: The One-Dimensional Case","authors":"Yao Cheng, Xuesong Wang, Martin Stynes","doi":"10.1007/s10915-024-02602-5","DOIUrl":"https://doi.org/10.1007/s10915-024-02602-5","url":null,"abstract":"A singularly perturbed reaction–diffusion problem in 1D is solved numerically by a local discontinuous Galerkin (LDG) finite element method. For this type of problem the standard energy norm is too weak to capture the contribution of the boundary layer component of the true solution, so balanced norms have been used by many authors to give more satisfactory error bounds for solutions computed using various types of finite element method. But for the LDG method, up to now no optimal-order balanced-norm error estimate has been derived. In this paper, we consider an LDG method with central numerical flux on a Shishkin mesh. Using the superconvergence property of the local (L^2) projector and some local coupled projections around the two transition points of the mesh, we prove an optimal-order balanced-norm error estimate for the computed solution; that is, when piecewise polynomials of degree k are used on a Shishkin mesh with N mesh intervals, in the balanced norm we establish (O((N^{-1}ln N)^{k+1})) convergence when k is even and (O((N^{-1}ln N)^{k})) when k is odd. Numerical experiments confirm the sharpness of these error bounds.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512482","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

Discretization of Non-uniform Rational B-Spline (NURBS) Models for Meshless Isogeometric Analysis 非均匀有理 B-样条线 (NURBS) 模型的离散化，用于无网格等距分析

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-02 DOI: 10.1007/s10915-024-02597-z

Urban Duh, Varun Shankar, Gregor Kosec

{"title":"Discretization of Non-uniform Rational B-Spline (NURBS) Models for Meshless Isogeometric Analysis","authors":"Urban Duh, Varun Shankar, Gregor Kosec","doi":"10.1007/s10915-024-02597-z","DOIUrl":"https://doi.org/10.1007/s10915-024-02597-z","url":null,"abstract":"We present an algorithm for fast generation of quasi-uniform and variable-spacing nodes on domains whose boundaries are represented as computer-aided design (CAD) models, more specifically non-uniform rational B-splines (NURBS). This new algorithm enables the solution of partial differential equations within the volumes enclosed by these CAD models using (collocation-based) meshless numerical discretizations. Our hierarchical algorithm first generates quasi-uniform node sets directly on the NURBS surfaces representing the domain boundary, then uses the NURBS representation in conjunction with the surface nodes to generate nodes within the volume enclosed by the NURBS surface. We provide evidence for the quality of these node sets by analyzing them in terms of local regularity and separation distances. Finally, we demonstrate that these node sets are well-suited (both in terms of accuracy and numerical stability) for meshless radial basis function generated finite differences discretizations of the Poisson, Navier-Cauchy, and heat equations. Our algorithm constitutes an important step in bridging the field of node generation for meshless discretizations with isogeometric analysis.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512480","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