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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":"<p>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 <i>x</i>-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 <i>y</i> direction in the interiors of sub-domains are computed lastly by the implicit characteristic difference method while the time fractional derivative is approximated by <i>L</i>1-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 <span>(Oleft( {varDelta t}+{varDelta t}^{2-alpha }+{h}^2+{H}^frac{5}{2}right) )</span> of the proposed scheme are given as well. Numerical experiments verify the theoretical results.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"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":"<p>We propose a robust randomized indicator method for the reliable detection of eigenvalue existence within an interval for symmetric matrices <i>A</i>. 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 <i>A</i> are analyzed. In particular, when <i>A</i> 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.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"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
{"title":"A Multiscale Finite Element Method for an Elliptic Distributed Optimal Control Problem with Rough Coefficients and Control Constraints","authors":"Susanne C. Brenner, José C. Garay, Li-yeng Sung","doi":"10.1007/s10915-024-02590-6","DOIUrl":"https://doi.org/10.1007/s10915-024-02590-6","url":null,"abstract":"<p>We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the multiscale finite element method is similar to the performance of standard finite element methods for smooth problems and present corroborating numerical results.\u0000</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512483","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
On the Immersed Boundary Method with Time-Filter-SAV for Solving Fluid–Structure Interaction Problem 用时间滤波-SAV沉浸边界法解决流固耦合问题
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-27 DOI: 10.1007/s10915-024-02591-5
Qixing Chen, Li Cai, Feifei Jing, Pengfei Ma, Xiaoyu Luo, Hao Gao
{"title":"On the Immersed Boundary Method with Time-Filter-SAV for Solving Fluid–Structure Interaction Problem","authors":"Qixing Chen, Li Cai, Feifei Jing, Pengfei Ma, Xiaoyu Luo, Hao Gao","doi":"10.1007/s10915-024-02591-5","DOIUrl":"https://doi.org/10.1007/s10915-024-02591-5","url":null,"abstract":"<p>In this work, the immersed boundary method with time filter and scalar auxiliary variable techniques is studied to solve the fluid–structure interaction problems. For the fluid flow, we first use the backward Euler differentiation formula in temporal discretization, we then employ the time filter technique to improve its convergence order, the scalar auxiliary variable strategy is visited to decouple the fluid equations and achieve fast solutions. We adopt the immersed boundary method to build the connection between the fluid and the structure, as well as characterize the deformations of the structure. We approximate the fluid–structure interaction model by the finite element method in space. The semi-discrete and fully-discrete implicit numerical schemes are proposed followed with unconditionally stability properties. We carry out several numerical experiments to validate the convergence behaviors and efficiency of the algorithms.\u0000</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530302","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
Hybridizable Discontinuous Galerkin Methods for the Two-Dimensional Monge–Ampère Equation 二维蒙日-安培方程的可混合非连续伽勒金方法
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-27 DOI: 10.1007/s10915-024-02604-3
Ngoc Cuong Nguyen, Jaime Peraire
{"title":"Hybridizable Discontinuous Galerkin Methods for the Two-Dimensional Monge–Ampère Equation","authors":"Ngoc Cuong Nguyen, Jaime Peraire","doi":"10.1007/s10915-024-02604-3","DOIUrl":"https://doi.org/10.1007/s10915-024-02604-3","url":null,"abstract":"<p>We introduce two hybridizable discontinuous Galerkin (HDG) methods for numerically solving the two-dimensional Monge–Ampère equation. The first HDG method is devised to solve the nonlinear elliptic Monge–Ampère equation by using Newton’s method. The second HDG method is devised to solve a sequence of the Poisson equation until convergence to a fixed-point solution of the Monge–Ampère equation is reached. Numerical examples are presented to demonstrate the convergence and accuracy of the HDG methods. Furthermore, the HDG methods are applied to <i>r</i>-adaptive mesh generation by redistributing a given scalar density function via the optimal transport theory. This <i>r</i>-adaptivity methodology leads to the Monge–Ampère equation with a nonlinear Neumann boundary condition arising from the optimal transport of the density function to conform the resulting high-order mesh to the boundary. Hence, we extend the HDG methods to treat the nonlinear Neumann boundary condition. Numerical experiments are presented to illustrate the generation of <i>r</i>-adaptive high-order meshes on planar and curved domains.\u0000</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529164","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
First-Order Greedy Invariant-Domain Preserving Approximation for Hyperbolic Problems: Scalar Conservation Laws, and p-System 双曲问题的一阶贪婪无域保留逼近：标量守恒定律和 p 系统
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-27 DOI: 10.1007/s10915-024-02592-4
Jean-Luc Guermond, Matthias Maier, Bojan Popov, Laura Saavedra, Ignacio Tomas
{"title":"First-Order Greedy Invariant-Domain Preserving Approximation for Hyperbolic Problems: Scalar Conservation Laws, and p-System","authors":"Jean-Luc Guermond, Matthias Maier, Bojan Popov, Laura Saavedra, Ignacio Tomas","doi":"10.1007/s10915-024-02592-4","DOIUrl":"https://doi.org/10.1007/s10915-024-02592-4","url":null,"abstract":"<p>The paper focuses on first-order invariant-domain preserving approximations of hyperbolic systems. We propose a new way to estimate the artificial viscosity that has to be added to make explicit, conservative, consistent numerical methods invariant-domain preserving and entropy inequality compliant. Instead of computing an upper bound on the maximum wave speed in Riemann problems, we estimate a minimum wave speed in the said Riemann problems such that the approximation satisfies predefined invariant-domain properties and predefined entropy inequalities. This technique eliminates non-essential fast waves from the construction of the artificial viscosity, while preserving pre-assigned invariant-domain properties and entropy inequalities.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512485","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
Convergent Authalic Energy Minimization for Disk Area-Preserving Parameterizations 磁盘面积保全参数化的收敛性自证能量最小化
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-25 DOI: 10.1007/s10915-024-02594-2
Shu-Yung Liu, Mei-Heng Yueh
{"title":"Convergent Authalic Energy Minimization for Disk Area-Preserving Parameterizations","authors":"Shu-Yung Liu, Mei-Heng Yueh","doi":"10.1007/s10915-024-02594-2","DOIUrl":"https://doi.org/10.1007/s10915-024-02594-2","url":null,"abstract":"<p>An area-preserving parameterization of a surface is a bijective mapping that maps the surface onto a specified domain and preserves the local area. This paper formulates the computation of disk area-preserving parameterization as an improved optimization problem and develops a preconditioned nonlinear conjugate gradient method with guaranteed theoretical convergence for solving the problem. Numerical experiments indicate that our new approach has significantly improved area-preserving accuracy and computational efficiency compared to other state-of-the-art algorithms. Furthermore, we present an application of surface registration to illustrate the practical utility of area-preserving mappings as parameterizations of surfaces.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529165","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
Stabilizing Discontinuous Galerkin Methods Using Dafermos’ Entropy Rate Criterion: II—Systems of Conservation Laws and Entropy Inequality Predictors 使用 Dafermos 的熵率标准稳定非连续 Galerkin 方法：II-守恒定律系统和熵不等式预测器
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-24 DOI: 10.1007/s10915-024-02595-1
Simon-Christian Klein
{"title":"Stabilizing Discontinuous Galerkin Methods Using Dafermos’ Entropy Rate Criterion: II—Systems of Conservation Laws and Entropy Inequality Predictors","authors":"Simon-Christian Klein","doi":"10.1007/s10915-024-02595-1","DOIUrl":"https://doi.org/10.1007/s10915-024-02595-1","url":null,"abstract":"<p>A novel approach for the stabilization of the Discontinuous Galerkin method based on the Dafermos entropy rate crition is presented. First, estimates for the maximal possible entropy dissipation rate of a weak solution are derived. Second, families of conservative Hilbert–Schmidt operators are identified to dissipate entropy. Steering these operators using the bounds on the entropy dissipation results in high-order accurate shock-capturing DG schemes for the one-dimensional Euler equations, satisfying the entropy rate criterion and an entropy inequality. Other testcases include the one-dimensional Buckley–Leverett equation.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512487","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
Sharp Error Bounds for a Fractional Collocation Method for Weakly Singular Volterra Integral Equations with Variable Exponent 带可变指数的弱奇异 Volterra 积分方程的分式配位法的尖锐误差边界
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-24 DOI: 10.1007/s10915-024-02593-3
Zheng Ma, Martin Stynes
{"title":"Sharp Error Bounds for a Fractional Collocation Method for Weakly Singular Volterra Integral Equations with Variable Exponent","authors":"Zheng Ma, Martin Stynes","doi":"10.1007/s10915-024-02593-3","DOIUrl":"https://doi.org/10.1007/s10915-024-02593-3","url":null,"abstract":"<p>Variable-exponent weakly singular Volterra integral equations of the second kind with integral kernels of the form <span>((t-s)^{-alpha (t)})</span> are considered. In Liang and Stynes (IMA J Numer Anal 19:drad072, 2023) it is shown that a typical solution of such an equation exhibits a weak singularity at the initial time <span>(t=0)</span>, similarly to the case where <span>(alpha (t))</span> is constant. Our paper extends this analysis further by giving a decomposition for the exact solution. To solve the problem numerically, a fractional polynomial collocation method is applied on a graded mesh. The convergence of the collocation solution to the exact solution is analysed rigorously and it is proved that specific choices of the fractional polynomials and mesh grading yield optimal-order convergence of the computed solution. Superconvergence properties of the iterated collocation solution are also analysed. Numerical experiments illustrate the sharpness of our theoretical results.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512486","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
Enhancing the Convergence of the Multigrid-Reduction-in-Time Method for the Euler and Navier–Stokes Equations 增强欧拉和纳维-斯托克斯方程多网格-时间还原法的收敛性
IF 2.5 2区 数学
Journal of Scientific Computing Pub Date : 2024-06-21 DOI: 10.1007/s10915-024-02596-0
Meiyuan Zhen, Xuejun Ding, Kun Qu, Jinsheng Cai, Shucheng Pan
{"title":"Enhancing the Convergence of the Multigrid-Reduction-in-Time Method for the Euler and Navier–Stokes Equations","authors":"Meiyuan Zhen, Xuejun Ding, Kun Qu, Jinsheng Cai, Shucheng Pan","doi":"10.1007/s10915-024-02596-0","DOIUrl":"https://doi.org/10.1007/s10915-024-02596-0","url":null,"abstract":"<p>Excessive spatial parallelization can introduce a performance bottleneck due to the communication overhead. While time-parallel method multigrid-reduction-in-time (MGRIT) provides an alternative to enhance concurrency, it generally requires large numbers of iterations to converge or even fails when applied to advection-dominated problems. To enhance the convergence of MGRIT, we propose the use of consecutive-step coarse-grid operators in MGRIT, rather than the standard rediscretized coarse-grid operators. The consecutive-step coarse-grid operator is defined as the multiplication of several fine-grid operators, which is able to track the advective characteristic more accurately than the standard rediscretized one. Numerical results show that multilevel MGRIT using the proposed operator is more efficient than the one using the standard rediscretized operator when applied to linear advection problems. Moreover, we perform time-parallel computing of the Euler equations and the Navier–Stokes equations by using the proposed method. Spatial coarsening is also considered. Compared with the MGRIT using the standard rediscretization approach, the developed method demonstrates enhanced robustness and efficiency in handling complex flow problems, including cases involving multidimensional shock waves and contact discontinuities.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512488","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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