Advances in Computational Mathematics最新文献_第7页

L((theta ))-stable peer methods with reused stages for advection–diffusion-reaction problems L((theta ))-稳定的对等方法与重复使用的阶段平流扩散反应问题

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-05-25 DOI: 10.1007/s10444-026-10315-6

Giovanni Pagano, Luis Rández

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引用次数: 0

Spectral analysis of the banded preconditioning with adjustable shift compensation for solving two-dimensional Riesz space-fractional diffusion equations 二维Riesz空间-分数扩散方程可调移位补偿带状预处理的谱分析

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-05-13 DOI: 10.1007/s10444-026-10312-9

Ying Sun, Kang-Ya Lu, Zong-Han Li, Jun-Heng Niu, Yu-Fan Cao

引用次数: 0

A locally conservative enriched virtual element method for elliptic problems 椭圆型问题的局部保守富虚元法

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-05-13 DOI: 10.1007/s10444-026-10308-5

Xinyu Zhao, Hongxing Rui, Gang Wang

引用次数: 0

A variable time-step IMEX BDF2 scheme for the incompressible MHD system 不可压缩MHD系统的可变时间步长IMEX BDF2方案

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-05-04 DOI: 10.1007/s10444-026-10311-w

Qianqian Ding, Yifan Luo, Shipeng Mao

引用次数: 0

A discretization theory of meshfree collocation for nonlinear systems of partial differential equations 非线性偏微分方程组无网格配置的离散化理论

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-05-04 DOI: 10.1007/s10444-026-10310-x

Zhiyong Liu, Qiuyan Xu

{"title":"A discretization theory of meshfree collocation for nonlinear systems of partial differential equations","authors":"Zhiyong Liu, Qiuyan Xu","doi":"10.1007/s10444-026-10310-x","DOIUrl":"10.1007/s10444-026-10310-x","url":null,"abstract":"<div><p>This paper extends for the first time B<span>(ddot{text {o}})</span>hmer/Schaback’s nonlinear discretization theory (J. Comput. Appl. Math., 254\u0000(2013), pp. 204–219) to nonlinear systems of partial differential equations. A direct collocation method is used to solve the coupled nonlinear systems. There are no restrictions on the nonlinear operators; in particular, there is no ellipticity, compactness, or self-adjointness assumed. The trial spaces might include a large class of finite-dimensional approximation spaces such as radial basis functions spaces, spline functions spaces, local Lagrange functions spaces, spectral techniques, and finite element spaces. A general framework for proving the convergence of collocation methods for solving well-posed nonlinear operator equations is presented. The theoretical results cover error bounds and convergence rates. In order to show how the general theoretical framework can be set to work, we take the meshfree method for solving the Navier–Stokes equations as an illustration and derive specific convergence rates in Sobolev spaces. Several numerical examples are provided to deal with numerical efficiency.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829210","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

Bivariate polynomial histopolation techniques on Padua, Fekete, and Leja triangles 在Padua， Fekete和Leja三角形上的二元多项式组织定位技术

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-05-04 DOI: 10.1007/s10444-026-10309-4

Ludovico Bruni Bruno, Francesco Dell’Accio, Wolfgang Erb, Federico Nudo

{"title":"Bivariate polynomial histopolation techniques on Padua, Fekete, and Leja triangles","authors":"Ludovico Bruni Bruno, Francesco Dell’Accio, Wolfgang Erb, Federico Nudo","doi":"10.1007/s10444-026-10309-4","DOIUrl":"10.1007/s10444-026-10309-4","url":null,"abstract":"<div><p>This paper explores the reconstruction of a real-valued function <i>f</i> defined over a domain <span>(varOmega subset mathbb {R}^2)</span> using bivariate polynomials that satisfy triangular histopolation conditions. More precisely, we assume that only the averages of <i>f</i> over a given triangulation <span>(mathcal {T}_N)</span> of <span>(varOmega )</span> are available and seek a bivariate polynomial that approximates <i>f</i> using a histopolation approach, potentially flanked by an additional regression technique. This methodology relies on the selection of a subset of triangles <span>(mathcal {T}_M subset mathcal {T}_N)</span> for histopolation, ensuring both the solvability and the well-conditioning of the problem. The remaining triangles can potentially be used to enhance the accuracy of the polynomial approximation through a simultaneous regression. We will introduce histopolation and combined histopolation-regression methods using the Padua points, discrete Leja sequences, and approximate Fekete nodes. The proposed algorithms are implemented and evaluated through numerical experiments that demonstrate their effectiveness in function approximation.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-026-10309-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829113","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

A new magnetic-coupled binary phase-field crystal model and its efficient fully discrete decoupled energy-stable scheme 一种新的磁耦合二元相场晶体模型及其高效的全离散解耦能量稳定格式

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-04-30 DOI: 10.1007/s10444-026-10313-8

Hengrui Xu, Kejia Pan, Xiaofeng Yang

{"title":"A new magnetic-coupled binary phase-field crystal model and its efficient fully discrete decoupled energy-stable scheme","authors":"Hengrui Xu, Kejia Pan, Xiaofeng Yang","doi":"10.1007/s10444-026-10313-8","DOIUrl":"10.1007/s10444-026-10313-8","url":null,"abstract":"<div><p>Despite extensive research on ferromagnetic materials and binary alloys, the interplay between magnetic fields and binary microstructure formation has not yet been systematically modeled within the phase-field crystal (PFC) framework. In this work, we propose a novel magnetic-coupled binary PFC model which, to the best of our knowledge, is the first to integrate ferromagnetic ordering and binary atomic density evolution within a unified formulation. The resulting system consists of three strongly coupled and highly nonlinear partial differential equations: two mass-conserved Allen–Cahn type equations for the binary density fields, and a third Allen-Cahn type equation governing the magnetization field dynamics, derived via a Ginzburg–Landau approach. To solve this challenging system efficiently, we further develop a fully discrete scheme that combines the Invariant Energy Quadratization (IEQ) and Zero-Energy-Contribution (ZEC) approaches for time discretization with a Fourier spectral method for spatial discretization. The proposed scheme is linear, fully decoupled, unconditionally energy stable, and second-order accurate in time, enabling robust and efficient simulation of magneto-structural dynamics. Extensive two- and three-dimensional numerical experiments demonstrate the method’s capability to capture magnetically driven phenomena such as crystal growth and phase transitions. This work not only establishes a new theoretical framework for modeling magnetic field-coupled binary systems but also provides an effective computational tool for simulating complex ferromagnetic material behavior.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-026-10313-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147797206","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

Which transmission condition is the best in optimized Schwarz waveform relaxation for viscoelastic equation: Robin or characteristic? 粘弹性方程优化施瓦茨波形松弛时，哪种传输条件最好：Robin还是characteristic？

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-04-29 DOI: 10.1007/s10444-026-10305-8

Fu Li, Yingxiang Xu

{"title":"Which transmission condition is the best in optimized Schwarz waveform relaxation for viscoelastic equation: Robin or characteristic?","authors":"Fu Li, Yingxiang Xu","doi":"10.1007/s10444-026-10305-8","DOIUrl":"10.1007/s10444-026-10305-8","url":null,"abstract":"<div><p>The viscoelastic equation introduces a viscoelastic damping term in the classical wave equation, thus exhibiting properties of parabolic systems accompanied by hyperbolic properties. On the other hand, it is well known that for parabolic systems, when solved using the optimized Schwarz waveform relaxation (OSWR) method, Robin transmission condition is preferred; however, the characteristic transmission condition is good for hyperbolic systems. In this paper, we investigate what transmission condition should be applied according to different strengths of damping. The results show that, in the OSWR algorithm, for weak damping the characteristic transmission condition is preferred, while for strong damping one should use Robin instead, as anticipated. It is also observed that the convergence depends on the relationship between the temporal and spatial mesh sizes applied, which shows that overlap may not accelerate the convergence. In addition, we find numerically that a mix of both transmission conditions can only improve the convergence for strong damping, and it remains an interesting problem to look for transmission conditions that are more robust in the damping strength.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147797127","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

Well-posedness for an improved time-fractional reaction-diffusion systems 改进的时间分数反应扩散系统的适定性

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-04-29 DOI: 10.1007/s10444-026-10307-6

Ziad Zaabouli, Lekbir Afraites, Aissam Hadri, Amine Laghrib

引用次数: 0

Stabilized gradient flow schemes of phase field model for shape and topology optimization in diffusion 扩散过程中形状和拓扑优化的相场模型的稳定梯度流格式

IF 2.1 3区数学

Advances in Computational Mathematics Pub Date : 2026-04-24 DOI: 10.1007/s10444-026-10303-w

Jiajie Li, Hui Yang, Shengfeng Zhu

引用次数: 0