Journal of Scientific Computing最新文献_第8页

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

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":"210 1","pages":""},"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":"28 1","pages":""},"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

The Splitting Characteristic Finite Difference Domain Decomposition Scheme for Solving Time-Fractional MIM Nonlinear Advection–Diffusion Equations 求解时间-分数 MIM 非线性平流-扩散方程的分割特征有限差分域分解方案

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-07-01 DOI: 10.1007/s10915-024-02603-4

Zhongguo Zhou, Sihan Zhang, Wanshan Li

{"title":"The Splitting Characteristic Finite Difference Domain Decomposition Scheme for Solving Time-Fractional MIM Nonlinear Advection–Diffusion Equations","authors":"Zhongguo Zhou, Sihan Zhang, Wanshan Li","doi":"10.1007/s10915-024-02603-4","DOIUrl":"https://doi.org/10.1007/s10915-024-02603-4","url":null,"abstract":"In this paper, we develop a new splitting characteristic finite difference scheme for solving the time-fractional mobile-immobile nonlinear advection–diffusion equation by combining non-overlapping block-divided domain decomposition method, the operator splitting technique and the characteristic finite difference method. Over each sub-domain, the solutions and fluxes along x-direction in the interiors of sub-domains are computed by the implicit characteristic finite difference method while the intermediate fluxes on the interfaces of sub-domains are computed by local multi-point weighted average from the approximate solutions at characteristic tracking points which are solved by the quadratic interpolation. Secondly, the solutions and fluxes along y direction in the interiors of sub-domains are computed lastly by the implicit characteristic difference method while the time fractional derivative is approximated by L1-format and the intermediate fluxes on the interfaces of sub-domains are computed by local multi-point weighted average from the approximate solutions at characteristic tracking points are solved by the quadratic interpolation. Applying Brouwer fixed point theorem, we prove strictly the existence and uniqueness of the proposed scheme. The conditional stability and convergence with (Oleft( {varDelta t}+{varDelta t}^{2-alpha }+{h}^2+{H}^frac{5}{2}right) ) of the proposed scheme are given as well. Numerical experiments verify the theoretical results.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"215 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529162","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 Robust Randomized Indicator Method for Accurate Symmetric Eigenvalue Detection 用于精确对称特征值检测的稳健随机指标法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-06-28 DOI: 10.1007/s10915-024-02599-x

Zhongyuan Chen, Jiguang Sun, Jianlin Xia

{"title":"A Robust Randomized Indicator Method for Accurate Symmetric Eigenvalue Detection","authors":"Zhongyuan Chen, Jiguang Sun, Jianlin Xia","doi":"10.1007/s10915-024-02599-x","DOIUrl":"https://doi.org/10.1007/s10915-024-02599-x","url":null,"abstract":"We propose a robust randomized indicator method for the reliable detection of eigenvalue existence within an interval for symmetric matrices A. An indicator tells the eigenvalue existence based on some statistical norm estimators for a spectral projector. Previous work on eigenvalue indicators relies on a threshold which is empirically chosen, thus often resulting in under or over detection. In this paper, we use rigorous statistical analysis to guide the design of a robust indicator. Multiple randomized estimators for a contour integral operator in terms of A are analyzed. In particular, when A has eigenvalues inside a given interval, we show that the failure probability (for the estimators to return very small estimates) is extremely low. This enables to design a robust rejection indicator based on the control of the failure probability. We also give a prototype framework to illustrate how the indicator method may be applied numerically for eigenvalue detection and may potentially serve as a new way to design randomized symmetric eigenvalue solvers. Unlike previous indicator methods that only detect eigenvalue existence, the framework also provides a way to find eigenvectors with little extra cost by reusing computations from indicator evaluations. Extensive numerical tests show the reliability of the eigenvalue detection in multiple aspects.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"17 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532366","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 Multiscale Finite Element Method for an Elliptic Distributed Optimal Control Problem with Rough Coefficients and Control Constraints 具有粗糙系数和控制约束条件的椭圆分布式最优控制问题的多尺度有限元方法

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-06-28 DOI: 10.1007/s10915-024-02590-6

Susanne C. Brenner, José C. Garay, Li-yeng Sung

引用次数: 0