Advances in Computational Mathematics最新文献_第10页

Error analysis of a collocation method on graded meshes for a fractional Laplacian problem 针对分数拉普拉斯问题的梯度网格上的拼合方法的误差分析

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-05-20 DOI: 10.1007/s10444-024-10146-3

Minghua Chen, Weihua Deng, Chao Min, Jiankang Shi, Martin Stynes

引用次数: 0

An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations 非光滑抛物型偏微分方程的自适应认证时空还原基方法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-05-15 DOI: 10.1007/s10444-024-10137-4

Marco Bernreuther, Stefan Volkwein

引用次数: 0

Local behaviors of Fourier expansions for functions of limited regularities 有限正则函数傅里叶展开的局部行为

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-05-09 DOI: 10.1007/s10444-024-10136-5

Shunfeng Yang, Shuhuang Xiang

引用次数: 0

Optimally convergent mixed finite element methods for the time-dependent 2D/3D stochastic closed-loop geothermal system with multiplicative noise 具有乘法噪声的时变二维/三维随机闭环地热系统的最佳收敛混合有限元方法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-05-08 DOI: 10.1007/s10444-024-10122-x

Xinyue Gao, Yi Qin, Jian Li

引用次数: 0

A Lagrangian approach for solving an axisymmetric thermo-electromagnetic problem. Application to time-varying geometry processes 解决轴对称热电磁问题的拉格朗日方法。时变几何过程的应用

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-05-08 DOI: 10.1007/s10444-024-10121-y

Marta Benítez, Alfredo Bermúdez, Pedro Fontán, Iván Martínez, Pilar Salgado

{"title":"A Lagrangian approach for solving an axisymmetric thermo-electromagnetic problem. Application to time-varying geometry processes","authors":"Marta Benítez, Alfredo Bermúdez, Pedro Fontán, Iván Martínez, Pilar Salgado","doi":"10.1007/s10444-024-10121-y","DOIUrl":"10.1007/s10444-024-10121-y","url":null,"abstract":"<div><p>The aim of this work is to introduce a thermo-electromagnetic model for calculating the temperature and the power dissipated in cylindrical pieces whose geometry varies with time and undergoes large deformations; the motion will be a known data. The work will be a first step towards building a complete thermo-electromagnetic-mechanical model suitable for simulating electrically assisted forming processes, which is the main motivation of the work. The electromagnetic model will be obtained from the time-harmonic eddy current problem with an in-plane current; the source will be given in terms of currents or voltages defined at some parts of the boundary. Finite element methods based on a Lagrangian weak formulation will be used for the numerical solution. This approach will avoid the need to compute and remesh the thermo-electromagnetic domain along the time. The numerical tools will be implemented in FEniCS and validated by using a suitable test also solved in Eulerian coordinates.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10121-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140895489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stray field computation by inverted finite elements: a new method in micromagnetic simulations 用倒置有限元计算杂散场：微磁模拟中的一种新方法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-05-07 DOI: 10.1007/s10444-024-10139-2

Tahar Z. Boulmezaoud, Keltoum Kaliche

引用次数: 0

Unconditional superconvergence analysis of a structure-preserving finite element method for the Poisson-Nernst-Planck equations 针对泊松-纳斯特-普朗克方程的保结构有限元法的无条件超收敛分析

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-05-06 DOI: 10.1007/s10444-024-10145-4

Huaijun Yang, Meng Li

{"title":"Unconditional superconvergence analysis of a structure-preserving finite element method for the Poisson-Nernst-Planck equations","authors":"Huaijun Yang, Meng Li","doi":"10.1007/s10444-024-10145-4","DOIUrl":"10.1007/s10444-024-10145-4","url":null,"abstract":"<div><p>In this paper, a linearized structure-preserving Galerkin finite element method is investigated for Poisson-Nernst-Planck (PNP) equations. By making full use of the high accuracy estimation of the bilinear element, the mean value technique and rigorously dealing with the coupled nonlinear term, not only the unconditionally optimal error estimate in <span>(L^2)</span>-norm but also the unconditionally superclose error estimate in <span>(H^1)</span>-norm for the related variables are obtained. Then, the unconditionally global superconvergence error estimate in <span>(H^1)</span>-norm is derived by a simple and efficient interpolation post-processing approach, without any coupling restriction condition between the time step size and the space mesh width. Finally, numerical results are provided to confirm the theoretical findings. The numerical scheme preserves the global mass conservation and the electric energy decay, and this work has a great improvement of the error estimate results given in Prohl and Schmuck (Numer. Math. <b>111</b>, 591–630 2009) and Gao and He (J. Sci. Comput. <b>72</b>, 1269–1289 2017).</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140845221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Dominant subspaces of high-fidelity polynomial structured parametric dynamical systems and model reduction 高保真多项式结构参数动态系统的主子空间与模型还原

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-05-03 DOI: 10.1007/s10444-024-10133-8

Pawan Goyal, Igor Pontes Duff, Peter Benner

{"title":"Dominant subspaces of high-fidelity polynomial structured parametric dynamical systems and model reduction","authors":"Pawan Goyal, Igor Pontes Duff, Peter Benner","doi":"10.1007/s10444-024-10133-8","DOIUrl":"10.1007/s10444-024-10133-8","url":null,"abstract":"<div><p>In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically, we consider a class of nonlinear dynamical systems whose nonlinear terms are polynomial functions, and the linear part corresponds to a linear structured model, such as second-order, time-delay, or fractional-order systems. Our approach relies on the Volterra series representation of these dynamical systems. Using this representation, we identify the kernels and, thus, the generalized multivariate transfer functions associated with these systems. Consequently, we present results allowing the construction of reduced-order models whose generalized transfer functions interpolate these of the original system at pre-defined frequency points. For efficient calculations, we also need the concept of a symmetric Kronecker product representation of a tensor and derive particular properties of them. Moreover, we propose an algorithm that extracts dominant subspaces from the prescribed interpolation conditions. This allows the construction of reduced-order models that preserve the structure. We also extend these results to parametric systems and a special case (delay in input/output). We demonstrate the efficiency of the proposed method by means of various numerical benchmarks.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10133-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140845245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the maximum principle and high-order, delay-free integrators for the viscous Cahn–Hilliard equation 关于粘性卡恩-希利亚德方程的最大值原理和高阶无延迟积分器

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-05-03 DOI: 10.1007/s10444-024-10143-6

Hong Zhang, Gengen Zhang, Ziyuan Liu, Xu Qian, Songhe Song

{"title":"On the maximum principle and high-order, delay-free integrators for the viscous Cahn–Hilliard equation","authors":"Hong Zhang, Gengen Zhang, Ziyuan Liu, Xu Qian, Songhe Song","doi":"10.1007/s10444-024-10143-6","DOIUrl":"10.1007/s10444-024-10143-6","url":null,"abstract":"<div><p>The stabilization approach has been known to permit large time-step sizes while maintaining stability. However, it may “slow down the convergence rate” or cause “delayed convergence” if the time-step rescaling is not well resolved. By considering a fourth-order-in-space viscous Cahn–Hilliard (VCH) equation, we propose a class of up to the fourth-order single-step methods that are able to capture the correct physical behaviors with high-order accuracy and without time delay. By reformulating the VCH as a system consisting of a second-order diffusion term and a nonlinear term involving the operator <span>(({I} - nu Delta )^{-1})</span>, we first develop a general approach to estimate the maximum bound for the VCH equation equipped with either the Ginzburg–Landau or Flory–Huggins potential. Then, by taking advantage of new recursive approximations and adopting a time-step-dependent stabilization, we propose a class of stabilization Runge–Kutta methods that preserve the maximum principle for any time-step size without harming the convergence. Finally, we transform the stabilization method into a parametric Runge–Kutta formulation, estimate the rescaled time-step, and remove the time delay by means of a relaxation technique. When the stabilization parameter is chosen suitably, the proposed parametric relaxation integrators are rigorously proven to be mass-conserving, maximum-principle-preserving, and the convergence in the <span>(l^infty )</span>-norm is estimated with <i>p</i>th-order accuracy under mild regularity assumption. Numerical experiments on multi-dimensional benchmark problems are carried out to demonstrate the stability, accuracy, and structure-preserving properties of the proposed schemes.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140845425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Fast numerical integration of highly oscillatory Bessel transforms with a Cauchy type singular point and exotic oscillators 带有考奇型奇异点和奇异振荡器的高振荡贝塞尔变换的快速数值积分

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-05-02 DOI: 10.1007/s10444-024-10134-7

Hongchao Kang, Qi Xu, Guidong Liu

{"title":"Fast numerical integration of highly oscillatory Bessel transforms with a Cauchy type singular point and exotic oscillators","authors":"Hongchao Kang, Qi Xu, Guidong Liu","doi":"10.1007/s10444-024-10134-7","DOIUrl":"10.1007/s10444-024-10134-7","url":null,"abstract":"<div><p>In this article, we propose an efficient hybrid method to calculate the highly oscillatory Bessel integral <span>(int _{0}^{1} frac{f(x)}{x-tau } J_{m} (omega x^{gamma } )textrm{d}x)</span> with the Cauchy type singular point, where <span>( 0< tau < 1, m ge 0, 2gamma in N^{+}. )</span> The hybrid method is established by combining the complex integration method with the Clenshaw– Curtis– Filon– type method. Based on the special transformation of the integrand and the additivity of the integration interval, we convert the integral into three integrals. The explicit formula of the first one is expressed in terms of the Meijer G function. The second is computed by using the complex integration method and the Gauss– Laguerre quadrature rule. For the third, we adopt the Clenshaw– Curtis– Filon– type method to obtain the quadrature formula. In particular, the important recursive relationship of the required modified moments is derived by utilizing the Bessel equation and the properties of Chebyshev polynomials. Importantly, the strict error analysis is performed by a large amount of theoretical analysis. Our proposed methods only require a few nodes and interpolation multiplicities to achieve very high accuracy. Finally, numerical examples are provided to verify the validity of our theoretical analysis and the accuracy of the proposed methods.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140819265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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