Advances in Computational Mathematics最新文献_第10页

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

Inverse problem for determining free parameters of a reduced turbulent transport model for tokamak plasma 确定托卡马克等离子体简化湍流输运模型自由参数的逆问题

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-05-02 DOI: 10.1007/s10444-024-10135-6

Louis Lamérand, Didier Auroux, Philippe Ghendrih, Francesca Rapetti, Eric Serre

{"title":"Inverse problem for determining free parameters of a reduced turbulent transport model for tokamak plasma","authors":"Louis Lamérand, Didier Auroux, Philippe Ghendrih, Francesca Rapetti, Eric Serre","doi":"10.1007/s10444-024-10135-6","DOIUrl":"10.1007/s10444-024-10135-6","url":null,"abstract":"<div><p>Two-dimensional transport codes for the simulation of tokamak plasma are reduced version of full 3D fluid models where plasma turbulence has been smoothed out by averaging. One of the main issues nowadays in such reduced models is the accurate modelling of transverse transport fluxes resulting from the averaging of stresses due to fluctuations. Transverse fluxes are assumed driven by local gradients, and characterised by ad hoc diffusion coefficients (turbulent eddy viscosity), adjusted by hand in order to match numerical solutions with experimental measurements. However, these coefficients vary substantially depending on the machine used, type of experiment and even the location inside the device, reducing drastically the predictive capabilities of these codes for a new configuration. To mitigate this issue, we recently proposed an innovative path for fusion plasma simulations by adding two supplementary transport equations to the mean-flow system for turbulence characteristic variables (here the turbulent kinetic energy <i>k</i> and its dissipation rate <span>(epsilon )</span>) to estimate the turbulent eddy viscosity. The remaining free parameters are more driven by the underlying transport physics and hence vary much less between machines and between locations in the plasma. In this paper, as a proof of concept, we explore, on the basis of digital twin experiments, the efficiency of the assimilation of data to fix these free parameters involved in the transverse turbulent transport models in the set of averaged equations in 2D.</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":"140819394","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

Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry 具有二面对称性的二维图形的拉普拉卡特征值计算

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-05-02 DOI: 10.1007/s10444-024-10138-3

David Berghaus, Robert Stephen Jones, Hartmut Monien, Danylo Radchenko

{"title":"Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry","authors":"David Berghaus, Robert Stephen Jones, Hartmut Monien, Danylo Radchenko","doi":"10.1007/s10444-024-10138-3","DOIUrl":"10.1007/s10444-024-10138-3","url":null,"abstract":"<div><p>We numerically compute the lowest Laplacian eigenvalues of several two-dimensional shapes with dihedral symmetry at arbitrary precision arithmetic. Our approach is based on the method of particular solutions with domain decomposition. We are particularly interested in asymptotic expansions of the eigenvalues <span>(lambda (n))</span> of shapes with <i>n</i> edges that are of the form <span>(lambda (n) sim xsum _{k=0}^{infty } frac{C_k(x)}{n^k})</span> where <i>x</i> is the limiting eigenvalue for <span>(nrightarrow infty )</span>. Expansions of this form have previously only been known for regular polygons with Dirichlet boundary conditions and (quite surprisingly) involve Riemann zeta values and single-valued multiple zeta values, which makes them interesting to study. We provide numerical evidence for closed-form expressions of higher order <span>(C_k(x))</span> and give more examples of shapes for which such expansions are possible (including regular polygons with Neumann boundary condition, regular star polygons, and star shapes with sinusoidal boundary).</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":"https://link.springer.com/content/pdf/10.1007/s10444-024-10138-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140819260","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

Spatial best linear unbiased prediction: a computational mathematics approach for high dimensional massive datasets 空间最佳线性无偏预测：针对高维海量数据集的计算数学方法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-04-30 DOI: 10.1007/s10444-024-10132-9

Julio Enrique Castrillón-Candás

{"title":"Spatial best linear unbiased prediction: a computational mathematics approach for high dimensional massive datasets","authors":"Julio Enrique Castrillón-Candás","doi":"10.1007/s10444-024-10132-9","DOIUrl":"10.1007/s10444-024-10132-9","url":null,"abstract":"<div><p>With the advent of massive data sets, much of the computational science and engineering community has moved toward data-intensive approaches in regression and classification. However, these present significant challenges due to increasing size, complexity, and dimensionality of the problems. In particular, covariance matrices in many cases are numerically unstable, and linear algebra shows that often such matrices cannot be inverted accurately on a finite precision computer. A common ad hoc approach to stabilizing a matrix is application of a so-called nugget. However, this can change the model and introduce error to the original solution. <i>It is well known from numerical analysis that ill-conditioned matrices cannot be accurately inverted.</i> In this paper, we develop a multilevel computational method that scales well with the number of observations and dimensions. A multilevel basis is constructed adapted to a kd-tree partitioning of the observations. Numerically unstable covariance matrices with large condition numbers can be transformed into well-conditioned multilevel ones without compromising accuracy. Moreover, it is shown that the multilevel prediction <i>exactly</i> solves the best linear unbiased predictor (BLUP) and generalized least squares (GLS) model, but is numerically stable. The multilevel method is tested on numerically unstable problems of up to 25 dimensions. Numerical results show speedups of up to 42,050 times for solving the BLUP problem, but with the same accuracy as the traditional iterative approach. For very ill-conditioned cases, the speedup is infinite. In addition, decay estimates of the multilevel covariance matrices are derived based on high dimensional interpolation techniques from the field of numerical analysis. This work lies at the intersection of statistics, uncertainty quantification, high performance computing, and computational applied mathematics.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140819271","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