Advances in Computational Mathematics最新文献_第10页

A nonlocal osmosis model for enhanced multi-image fusion 一种增强多图像融合的非局部渗透模型

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2025-10-23 DOI: 10.1007/s10444-025-10259-3

Sabira Ben Alia, Mohammed Hachama

引用次数: 0

Tight frames over the quaternions and equiangular lines 四元数和等角线上的紧密帧

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2025-10-22 DOI: 10.1007/s10444-025-10264-6

Shayne Waldron

引用次数: 0

Closed form representations for the compactly supported radial basis functions of Buhmann, Wendland and Wu Buhmann， Wendland和Wu的紧支持径向基函数的封闭形式表示

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2025-10-20 DOI: 10.1007/s10444-025-10262-8

Simon Hubbert, Janin Jäger

{"title":"Closed form representations for the compactly supported radial basis functions of Buhmann, Wendland and Wu","authors":"Simon Hubbert, Janin Jäger","doi":"10.1007/s10444-025-10262-8","DOIUrl":"10.1007/s10444-025-10262-8","url":null,"abstract":"<div>The original compactly supported radial basis functions of Wendland (Adv. Comput. Math., 4, 389–396, 1995) and Wu (Adv. Comput. Math., 4, 283–292, 1995) have a polynomial form and are constructed using a two-step dimension walk strategy. Focussing on the Wendland functions, Schaback (Adv. Comput. Math., 34(1), 67–81, 2011) proposed a one-step dimension walk which is shown to recover the original Wendland functions at every second step but also introduces new examples, the so-called missing Wendland functions at the intermediate steps. In a recent paper (Science China Mathematics Published online, 2025), the analogue of Schaback’s work is presented for the Wu functions and so delivers the so-called missing Wu functions. The original and missing Wendland functions belong to a much wider class proposed by Buhmann (Math. Comput., 70(233), 307–318, 2001). The classical Buhmann functions, which are related to thin-plate spline radial basis functions, also belong to this much wider class. The theme uniting the classical Buhmann functions and the missing Wendland/Wu functions is that they are non-polynomial, and closed-form expressions are not known for all of them. In this paper, we revisit these functions and show how closed-form representations can be given using direct techniques. The results for the classical Buhmann and Wu functions are new, and the resulting expressions for the missing Wendland functions improve on those given in Hubbert (Adv. Comput. Math., 36, 115–136, 2012) and so their implementation should be more straightforward.</div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"51 6","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316363","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

Pathwise uniform convergence of a full discretization for a three-dimensional stochastic Allen-Cahn equation with multiplicative noise 具有乘性噪声的三维随机Allen-Cahn方程的全离散化的路径一致收敛

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2025-10-16 DOI: 10.1007/s10444-025-10261-9

Binjie Li, Qin Zhou

引用次数: 0

A conforming virtual element method for Emden-Fowler model over polygonal meshes 多边形网格上Emden-Fowler模型的一致性虚元法

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2025-10-16 DOI: 10.1007/s10444-025-10260-w

Zaffar Mehdi Dar, M. Arrutselvi, Chandru Muthusamy, Sundararajan Natarajan

引用次数: 0

A method of fundamental solutions for large-scale 3D elastance and mobility problems 一种大规模三维弹性和流动性问题的基本解方法

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2025-10-06 DOI: 10.1007/s10444-025-10258-4

Anna Broms, Alex H. Barnett, Anna-Karin Tornberg

{"title":"A method of fundamental solutions for large-scale 3D elastance and mobility problems","authors":"Anna Broms, Alex H. Barnett, Anna-Karin Tornberg","doi":"10.1007/s10444-025-10258-4","DOIUrl":"10.1007/s10444-025-10258-4","url":null,"abstract":"<div>The method of fundamental solutions (MFS) is known to be effective for solving 3D Laplace and Stokes Dirichlet boundary value problems in the exterior of a large collection of simple smooth objects. Here, we present new scalable MFS formulations for the corresponding elastance and mobility problems. The elastance problem computes the potentials of conductors with given net charges, while the mobility problem—crucial to rheology and complex fluid applications—computes rigid body velocities given net forces and torques on the particles. The key idea is orthogonal projection of the net charge (or forces and torques) in a rectangular variant of a “completion flow.” The proposal is compatible with one-body preconditioning, resulting in well-conditioned square linear systems amenable to fast multipole accelerated iterative solution, thus a cost linear in the particle number. For large suspensions with moderate lubrication forces, MFS sources on inner proxy-surfaces give accuracy on par with a well-resolved boundary integral formulation. Our several numerical tests include a suspension of 10,000 nearby ellipsoids, using (2.6times 10^7) total preconditioned degrees of freedom, where GMRES converges to five digits of accuracy in under two hours on one workstation.</div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"51 5","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-025-10258-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145256398","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

An iterative projection method for unsteady Navier–Stokes equations with high Reynolds numbers 高雷诺数非定常Navier-Stokes方程的迭代投影法

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2025-09-30 DOI: 10.1007/s10444-025-10257-5

Xiaoming Zheng, Kun Zhao, Jiahong Wu, Weiwei Hu, Dapeng Du

{"title":"An iterative projection method for unsteady Navier–Stokes equations with high Reynolds numbers","authors":"Xiaoming Zheng, Kun Zhao, Jiahong Wu, Weiwei Hu, Dapeng Du","doi":"10.1007/s10444-025-10257-5","DOIUrl":"10.1007/s10444-025-10257-5","url":null,"abstract":"<div>A new iterative projection method is proposed to solve the unsteady Navier–Stokes equations with high Reynolds numbers. The convectional projection method attempts to project the intermediate velocity to the divergence-free space only once per time step. However, such a velocity is not genuinely divergence-free in general practice, which can yield large errors when the Reynolds number is high. The new method has several important features: the BDF2 time discretization, the skew-symmetric convection in a semi-implicit form, two modulating parameters, and the iterative projections in each time step. A major difficulty in the proof of iteration convergence is the nonlinear convection. We solve this problem by first analyzing the non-convective scheme with a focus on the spectral properties of the iterative matrix and then employing a delicate perturbation analysis for the convective scheme. The work achieves the weakly divergence-free velocity (strongly divergence-free for divergence-free finite element spaces) and the rigorous stability and error analysis when the iterations converge The three-dimensional numerical tests confirm that this new method can effectively treat high Reynolds numbers with only a few iterations per time, where the convectional projection method and the iterative projection method with the explicit convection would fail.</div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"51 5","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145210928","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

A two-grid method with dispersion matching for finite-element Helmholtz problems 有限元亥姆霍兹问题的色散匹配双网格法

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2025-09-18 DOI: 10.1007/s10444-025-10256-6

Christiaan C. Stolk

引用次数: 0

A primal-dual adaptive finite element method for total variation minimization 全变分最小化的一种原对偶自适应有限元方法

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2025-08-21 DOI: 10.1007/s10444-025-10254-8

Martin Alkämper, Stephan Hilb, Andreas Langer

引用次数: 0

Two-level discretization of the 3D stationary Navier–Stokes equations with damping based on a difference finite element method 基于差分有限元法的含阻尼三维平稳Navier-Stokes方程的两级离散化

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2025-08-14 DOI: 10.1007/s10444-025-10255-7

Qi Zhang, Pengzhan Huang

{"title":"Two-level discretization of the 3D stationary Navier–Stokes equations with damping based on a difference finite element method","authors":"Qi Zhang, Pengzhan Huang","doi":"10.1007/s10444-025-10255-7","DOIUrl":"10.1007/s10444-025-10255-7","url":null,"abstract":"<div>A difference finite element method based on the mixed finite element pair (((P_1^b,P_1^b,P_1) times (P_1,P_1,P_1)))-((P_1 times P_0)) is presented for the three-dimensional stationary Navier–Stokes equations with damping. Moreover, based on this proposed method, a two-level discretization is constructed, which involves solving a problem of the Navier–Stokes equations with damping on coarse mesh with mesh sizes H and (mathcal {T}), and a general Stokes problem on fine mesh with mesh sizes (h = O(H^2)) and (tau = O(mathcal {T}^2)). This two-level difference finite element method provides an approximate solution with the same convergence rate as the difference finite element solution, which involves solving a problem of the Navier–Stokes equations with damping on fine mesh with mesh sizes h and (tau ). Hence, it can save a large amount of computational time. Finally, all computational results support the theoretical analysis and show the effectiveness of the two-level difference finite element method for solving the considered problem.</div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"51 4","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144832090","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