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An Extension of the Morley Element on General Polytopal Partitions Using Weak Galerkin Methods 使用弱伽勒金方法扩展一般多面体分区上的莫利元素
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-10 DOI: 10.1007/s10915-024-02580-8
Dan Li, Chunmei Wang, Junping Wang
{"title":"An Extension of the Morley Element on General Polytopal Partitions Using Weak Galerkin Methods","authors":"Dan Li, Chunmei Wang, Junping Wang","doi":"10.1007/s10915-024-02580-8","DOIUrl":"https://doi.org/10.1007/s10915-024-02580-8","url":null,"abstract":"<p>This paper introduces an extension of the well-known Morley element for the biharmonic equation, extending its application from triangular elements to general polytopal elements using the weak Galerkin finite element methods. By leveraging the Schur complement of the weak Galerkin method, this extension not only preserves the same degrees of freedom as the Morley element on triangular elements but also expands its applicability to general polytopal elements. The numerical scheme is devised by locally constructing weak tangential derivatives and weak second-order partial derivatives. Error estimates for the numerical approximation are established in both the energy norm and the <span>(L^2)</span> norm. A series of numerical experiments are conducted to validate the theoretical developments.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"24 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529169","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
Developing and Analyzing Some Novel Finite Element Schemes for the Electromagnetic Rotation Cloak Model 为电磁旋转斗篷模型开发和分析一些新的有限元方案
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-08 DOI: 10.1007/s10915-024-02585-3
Yunqing Huang, Jichun Li, Bin He
{"title":"Developing and Analyzing Some Novel Finite Element Schemes for the Electromagnetic Rotation Cloak Model","authors":"Yunqing Huang, Jichun Li, Bin He","doi":"10.1007/s10915-024-02585-3","DOIUrl":"https://doi.org/10.1007/s10915-024-02585-3","url":null,"abstract":"<p>One potential application of metamaterials is for designing invisibility cloaks. In this paper, we are interested in a rotation cloak model. Here we carry out the mathematical analysis of this model for the first time. Through a careful analysis, we reformulate a new system of governing partial differential equations by reducing one unknown variable from the originally developed modeling equations in Yang et al. (Commun Comput Phys 25:135–154, 2019). Then some novel finite element schemes are proposed and their stability and optimal error estimate are proved. Numerical simulations are presented to demonstrate that the new schemes for the reduced modeling equations can effectively reproduce the rotation cloaking phenomenon.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"11 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512397","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 and Exact Multimarginal Optimal Transport with Pairwise Costs 具有成对成本的高效精确多边际优化运输
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-07 DOI: 10.1007/s10915-024-02572-8
Bohan Zhou, Matthew Parno
{"title":"Efficient and Exact Multimarginal Optimal Transport with Pairwise Costs","authors":"Bohan Zhou, Matthew Parno","doi":"10.1007/s10915-024-02572-8","DOIUrl":"https://doi.org/10.1007/s10915-024-02572-8","url":null,"abstract":"<p>We address the numerical solution to multimarginal optimal transport (MMOT) with pairwise costs. MMOT, as a natural extension from the classical two-marginal optimal transport, has many important applications including image processing, density functional theory and machine learning, but lacks efficient and exact numerical methods. The popular entropy-regularized method may suffer numerical instability and blurring issues. Inspired by the back-and-forth method introduced by Jacobs and Léger, we investigate MMOT problems with pairwise costs. We show that such problems have a graphical representation and leverage this structure to develop a new computationally gradient ascent algorithm to solve the dual formulation of such MMOT problems. Our method produces accurate solutions which can be used for the regularization-free applications, including the computation of Wasserstein barycenters with high resolution imagery.\u0000</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"112 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512398","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
High Order Asymptotic Preserving and Classical Semi-implicit RK Schemes for the Euler–Poisson System in the Quasineutral Limit 准中性极限中欧拉-泊松系统的高阶渐近保留和经典半隐式 RK 方案
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-06 DOI: 10.1007/s10915-024-02577-3
K. R. Arun, N. Crouseilles, S. Samantaray
{"title":"High Order Asymptotic Preserving and Classical Semi-implicit RK Schemes for the Euler–Poisson System in the Quasineutral Limit","authors":"K. R. Arun, N. Crouseilles, S. Samantaray","doi":"10.1007/s10915-024-02577-3","DOIUrl":"https://doi.org/10.1007/s10915-024-02577-3","url":null,"abstract":"<p>In this paper, the design and analysis of high order accurate IMEX finite volume schemes for the compressible Euler–Poisson (EP) equations in the quasineutral limit is presented. As the quasineutral limit is singular for the governing equations, the time discretisation is tantamount to achieving an accurate numerical method. To this end, the EP system is viewed as a differential algebraic equation system (DAEs) via static condensation. As a consequence of this vantage point, high order linearly semi-implicit (SI) time discretisation are realised by employing a novel combination of the direct approach used for implicit discretisation of DAEs and, two different classes of IMEX-RK schemes: the additive and the multiplicative. For both the time discretisation strategies, in order to account for rapid plasma oscillations in quasineutral regimes, the nonlinear Euler fluxes are split into two different combinations of stiff and non-stiff components. The high order scheme resulting from the additive approach is designated as a classical scheme while the one generated by the multiplicative approach possesses the asymptotic preserving (AP) property. Time discretisations for the classical and the AP schemes are performed by standard IMEX-RK and SI-IMEX-RK methods, respectively so that the stiff terms are treated implicitly and the non-stiff ones explicitly. In order to discretise in space a Rusanov-type central flux is used for the non-stiff part, and simple central differencing for the stiff part. Results of numerical experiments are presented, which confirm that the high order schemes based on the SI-IMEX-RK time discretisation achieve uniform second order convergence with respect to the Debye length and are AP in the quasineutral limit.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"20 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530303","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
Arbitrary High Order ADER-DG Method with Local DG Predictor for Solutions of Initial Value Problems for Systems of First-Order Ordinary Differential Equations 用局部 DG 预测器解决一阶常微分方程系统初值问题的任意高阶 ADER-DG 方法
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-04 DOI: 10.1007/s10915-024-02578-2
Ivan S. Popov
{"title":"Arbitrary High Order ADER-DG Method with Local DG Predictor for Solutions of Initial Value Problems for Systems of First-Order Ordinary Differential Equations","authors":"Ivan S. Popov","doi":"10.1007/s10915-024-02578-2","DOIUrl":"https://doi.org/10.1007/s10915-024-02578-2","url":null,"abstract":"<p>An adaptation of the arbitrary high order ADER-DG numerical method with local DG predictor for solving the IVP for a first-order non-linear ODE system is proposed. The proposed numerical method is a completely one-step ODE solver with uniform steps, and is simple in algorithmic and software implementations. It was shown that the proposed version of the ADER-DG numerical method is <b><i>A</i></b>-stable and <b><i>L</i></b>-stable. The ADER-DG numerical method demonstrates superconvergence with convergence order <span>({varvec{2N}}+textbf{1})</span> for the solution at grid nodes, while the local solution obtained using the local DG predictor has convergence order <span>({varvec{N}}+textbf{1})</span>. It was demonstrated that an important applied feature of this implementation of the numerical method is the possibility of using the local solution as a solution with a subgrid resolution, which makes it possible to obtain a detailed solution even on very coarse coordinate grids. The scale of the error of the local solution, when calculating using standard representations of single or double precision floating point numbers, using large values of the degree <b><i>N</i></b>, practically does not differ from the error of the solution at the grid nodes. The capabilities of the ADER-DG method for solving stiff ODE systems characterized by extreme stiffness are demonstrated. Estimates of the computational costs of the ADER-DG numerical method are obtained.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"101 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254642","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 Power Method for Computing the Dominant Eigenvalue of a Dual Quaternion Hermitian Matrix 计算双四元赫米矩阵主特征值的幂方法
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-04 DOI: 10.1007/s10915-024-02561-x
Chunfeng Cui, Liqun Qi
{"title":"A Power Method for Computing the Dominant Eigenvalue of a Dual Quaternion Hermitian Matrix","authors":"Chunfeng Cui, Liqun Qi","doi":"10.1007/s10915-024-02561-x","DOIUrl":"https://doi.org/10.1007/s10915-024-02561-x","url":null,"abstract":"<p>In this paper, we first study the projections onto the set of unit dual quaternions, and the set of dual quaternion vectors with unit norms. Then we propose a power method for computing the dominant eigenvalue of a dual quaternion Hermitian matrix. For a strict dominant eigenvalue, we show the sequence generated by the power method converges to the dominant eigenvalue and its corresponding eigenvector linearly. For a general dominant eigenvalue, we establish linear convergence of the standard part of the dominant eigenvalue. Based upon these, we reformulate the simultaneous localization and mapping problem as a rank-one dual quaternion completion problem. A two-block coordinate descent method is proposed to solve this problem. One block has a closed-form solution and the other block is the best rank-one approximation problem of a dual quaternion Hermitian matrix, which can be computed by the power method. Numerical experiments are presented to show the efficiency of our proposed power method.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"49 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254686","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 Sinc Rule for the Hankel Transform 汉克尔变换的 Sinc 规则
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-04 DOI: 10.1007/s10915-024-02575-5
Eleonora Denich, Paolo Novati
{"title":"A Sinc Rule for the Hankel Transform","authors":"Eleonora Denich, Paolo Novati","doi":"10.1007/s10915-024-02575-5","DOIUrl":"https://doi.org/10.1007/s10915-024-02575-5","url":null,"abstract":"<p>This paper deals with the computation of the Hankel transform by means of the sinc rule applied after a special exponential transformation. An error analysis, particularly suitable for meromorphic functions, together with the parameter selection strategy, is considered. A prototype algorithm for automatic integration is also presented.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"106 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254685","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 According to the Regularity of External Forces of a Semi-Implicit Difference Scheme for Time Fractional Navier–Stokes Equations 根据外力规则性对时间分式纳维-斯托克斯方程半隐式差分方案的稳定性分析
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-03 DOI: 10.1007/s10915-024-02564-8
HuiChol Choe, JongHyang Ri, SunAe Pak, YongDo Ri, SongGuk Jong
{"title":"Stability Analysis According to the Regularity of External Forces of a Semi-Implicit Difference Scheme for Time Fractional Navier–Stokes Equations","authors":"HuiChol Choe, JongHyang Ri, SunAe Pak, YongDo Ri, SongGuk Jong","doi":"10.1007/s10915-024-02564-8","DOIUrl":"https://doi.org/10.1007/s10915-024-02564-8","url":null,"abstract":"<p>In this paper, we discuss the stability of a semi-discrete implicit difference scheme of the time fractional Navier–Stokes equations which is applied in many physical processes, and the convergence of the difference approximate solution. First, we introduce the concept of the average characteristic of the sequence obtained by the difference scheme and the concept of partial stability of the scheme, and then obtain several stability results according to the normality of the external force term. We also prove the convergence of the difference approximation sequence to the unique solution of the equation.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"132 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259772","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
hp-Multigrid Preconditioner for a Divergence-Conforming HDG Scheme for the Incompressible Flow Problems 针对不可压缩流问题的发散顺应性 HDG 方案的 hp-Multigrid 预处理器
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-03 DOI: 10.1007/s10915-024-02568-4
Guosheng Fu, Wenzheng Kuang
{"title":"hp-Multigrid Preconditioner for a Divergence-Conforming HDG Scheme for the Incompressible Flow Problems","authors":"Guosheng Fu, Wenzheng Kuang","doi":"10.1007/s10915-024-02568-4","DOIUrl":"https://doi.org/10.1007/s10915-024-02568-4","url":null,"abstract":"<p>In this study, we present an <i>hp</i>-multigrid preconditioner for a divergence-conforming HDG scheme for the generalized Stokes and the Navier–Stokes equations using an augmented Lagrangian formulation. Our method relies on conforming simplicial meshes in two- and three-dimensions. The <i>hp</i>-multigrid algorithm is a multiplicative auxiliary space preconditioner that employs the lowest-order space as the auxiliary space, and we develop a geometric multigrid method as the auxiliary space solver. For the generalized Stokes problem, the crucial ingredient of the geometric multigrid method is the equivalence between the condensed lowest-order divergence-conforming HDG scheme and a Crouzeix–Raviart discretization with a pressure-robust treatment as introduced in Linke and Merdon (Comput Methods Appl Mech Engrg 311:304–326, 2022), which allows for the direct application of geometric multigrid theory on the Crouzeix–Raviart discretization. The numerical experiments demonstrate the robustness of the proposed <i>hp</i>-multigrid preconditioner with respect to mesh size and augmented Lagrangian parameter, with iteration counts insensitivity to polynomial order increase. Inspired by the works by Benzi and Olshanskii (SIAM J Sci Comput 28:2095–2113, 2006) and Farrell et al. (SIAM J Sci Comput 41:A3073–A3096, 2019), we further test the proposed preconditioner on the divergence-conforming HDG scheme for the Navier–Stokes equations. Numerical experiments show a mild increase in the iteration counts of the preconditioned GMRes solver with the rise in Reynolds number up to <span>(10^3)</span>.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"3 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254688","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
Gauss Newton Method for Solving Variational Problems of PDEs with Neural Network Discretizaitons 用高斯牛顿法解决带有神经网络离散性的 PDE 变分问题
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-03 DOI: 10.1007/s10915-024-02535-z
Wenrui Hao, Qingguo Hong, Xianlin Jin
{"title":"Gauss Newton Method for Solving Variational Problems of PDEs with Neural Network Discretizaitons","authors":"Wenrui Hao, Qingguo Hong, Xianlin Jin","doi":"10.1007/s10915-024-02535-z","DOIUrl":"https://doi.org/10.1007/s10915-024-02535-z","url":null,"abstract":"<p>The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based discretization has emerged as a powerful tool for solving differential equations by parameterizing a set of functions. Various approaches, such as the deep Ritz method and physics-informed neural networks, have been developed for numerical solutions. Training algorithms, including gradient descent and greedy algorithms, have been proposed to solve the resulting optimization problems. In this paper, we focus on the variational formulation of the problem and propose a Gauss–Newton method for computing the numerical solution. We provide a comprehensive analysis of the superlinear convergence properties of this method, along with a discussion on semi-regular zeros of the vanishing gradient. Numerical examples are presented to demonstrate the efficiency of the proposed Gauss–Newton method.\u0000</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"8 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254719","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
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