Journal of Scientific Computing最新文献_第10页

A Staggered Scheme for the Compressible Euler Equations on General 3D Meshes 一般三维网格上可压缩欧拉方程的交错方案

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-06-14 DOI: 10.1007/s10915-024-02560-y

Aubin Brunel, Raphaèle Herbin, Jean-Claude Latché

{"title":"A Staggered Scheme for the Compressible Euler Equations on General 3D Meshes","authors":"Aubin Brunel, Raphaèle Herbin, Jean-Claude Latché","doi":"10.1007/s10915-024-02560-y","DOIUrl":"https://doi.org/10.1007/s10915-024-02560-y","url":null,"abstract":"We develop and analyze in this paper a momentum convection operator for variable density flows, and apply it to obtain a finite volume scheme for the Euler equations. The mesh is composed of triangular and quadrangular cells, in the two-dimensional case, and of hexahedral, tetrahedral, prismatic and pyramidal cells in three space dimensions. The approximation is staggered: the scalar variables (pressure, density and internal energy) are associated with the cells while the velocity approximation is face-centred. The derivation of the momentum convection operator extends to pyramids and prisms an already proposed construction for the other above-mentioned cells. The resulting operator takes the form of a finite volume operator, but is obtained by an algebraic process using as input the mass fluxes through the primal faces appearing in the mass balance for the definition of the velocity fluxes, with the only guideline to satisfy a discrete local kinetic energy identity. Its consistency thus deserves to be studied, and we show that this process yields a consistent convection operator in the Lax-Wendroff sense. Numerical tests confirm the expected scheme convergence, with a first-order rate on a pure shock solution.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512494","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 $$tau $$ -Preconditioner for Space Fractional Diffusion Equation with Non-separable Variable Coefficients 具有不可分割可变系数的空间分数扩散方程的 $$tau $$ - 前提器

IF 2.5 2区数学

Journal of Scientific Computing Pub Date : 2024-06-11 DOI: 10.1007/s10915-024-02574-6

Xue-Lei Lin, Michael K. Ng

{"title":"A $$tau $$ -Preconditioner for Space Fractional Diffusion Equation with Non-separable Variable Coefficients","authors":"Xue-Lei Lin, Michael K. Ng","doi":"10.1007/s10915-024-02574-6","DOIUrl":"https://doi.org/10.1007/s10915-024-02574-6","url":null,"abstract":"In this paper, we study a (tau )-matrix approximation based preconditioner for the linear systems arising from discretization of unsteady state Riesz space fractional diffusion equation with non-separable variable coefficients. The structure of coefficient matrices of the linear systems is identity plus summation of diagonal-times-multilevel-Toeplitz matrices. In our preconditioning technique, the diagonal matrices are approximated by scalar identity matrices and the Toeplitz matrices are approximated by (tau )-matrices (a type of matrices diagonalizable by discrete sine transforms). The proposed preconditioner is fast invertible through the fast sine transform (FST) algorithm. Theoretically, we show that the GMRES solver for the preconditioned systems has an optimal convergence rate (a convergence rate independent of discretization stepsizes). To the best of our knowledge, this is the first preconditioning method with the optimal convergence rate for the variable-coefficients space fractional diffusion equation. Numerical results are reported to demonstrate the efficiency of the proposed method.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529167","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

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

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

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

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":"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.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"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":"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 A-stable and L-stable. The ADER-DG numerical method demonstrates superconvergence with convergence order ({varvec{2N}}+textbf{1}) for the solution at grid nodes, while the local solution obtained using the local DG predictor has convergence order ({varvec{N}}+textbf{1}). 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 N, 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.","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"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

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

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

引用次数: 0