Applied Numerical Mathematics最新文献

Semi-implicit fully exactly well-balanced schemes for the two-layer shallow water system 双层浅水系统的半隐式完全精确平衡方案

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-29 DOI: 10.1016/j.apnum.2025.07.014

C. Caballero-Cárdenas , M.J. Castro , C. Chalons , T. Morales de Luna , M.L. Muñoz-Ruiz

引用次数: 0

A fast Fourier-Galerkin method for solving boundary integral equations on non-axisymmetric toroidal surfaces 求解非轴对称环面边界积分方程的快速傅立叶-伽辽金方法

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-24 DOI: 10.1016/j.apnum.2025.07.013

Yiying Fang , Ying Jiang , Jiafeng Su

{"title":"A fast Fourier-Galerkin method for solving boundary integral equations on non-axisymmetric toroidal surfaces","authors":"Yiying Fang , Ying Jiang , Jiafeng Su","doi":"10.1016/j.apnum.2025.07.013","DOIUrl":"10.1016/j.apnum.2025.07.013","url":null,"abstract":"<div><div>We propose a fast Fourier–Galerkin method for solving boundary integral equations (BIEs) on smooth, non-axisymmetric toroidal surfaces. Our approach begins by analyzing the structure of the integral kernel, revealing an exponential decay pattern in the Fourier coefficients after a shear transformation. Leveraging this decay, we design a truncation strategy that compresses the dense representation matrix into a sparse form with only <span><math><mi>O</mi><mo>(</mo><mi>N</mi><msup><mrow><mi>ln</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⁡</mo><mi>N</mi><mo>)</mo></math></span> nonzero entries, where <em>N</em> denotes the degrees of freedom. We rigorously prove that the truncated system retains the stability of the original Fourier–Galerkin formulation and achieves a quasi-optimal convergence rate of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mi>p</mi><mo>/</mo><mn>2</mn></mrow></msup><mi>ln</mi><mo>⁡</mo><mi>N</mi><mo>)</mo></math></span>, with <em>p</em> denoting the regularity of the exact solution. Numerical experiments corroborate our theoretical results, demonstrating both high accuracy and computational efficiency. Furthermore, we extend the proposed strategy to BIEs defined on surfaces diffeomorphic to the sphere, confirming the sparsity structure remains exploitable under broader geometric settings.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"218 ","pages":"Pages 73-90"},"PeriodicalIF":2.4,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144720943","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

Space-time parallel solvers for reaction-diffusion problems forming Turing patterns 形成图灵模式的反应扩散问题的时空并行求解器

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-23 DOI: 10.1016/j.apnum.2025.07.012

Andrés Arrarás , Francisco J. Gaspar , Iñigo Jimenez-Ciga , Laura Portero

{"title":"Space-time parallel solvers for reaction-diffusion problems forming Turing patterns","authors":"Andrés Arrarás , Francisco J. Gaspar , Iñigo Jimenez-Ciga , Laura Portero","doi":"10.1016/j.apnum.2025.07.012","DOIUrl":"10.1016/j.apnum.2025.07.012","url":null,"abstract":"<div><div>In recent years, parallelization has become a strong tool to avoid the limits of classical sequential computing. In the present paper, we introduce four space-time parallel methods that combine the parareal algorithm with suitable splitting techniques for the numerical solution of reaction-diffusion problems. In particular, we consider a suitable partition of the elliptic operator that enables the parallelization in space by using splitting time integrators. Those schemes are then chosen as the propagators of the parareal algorithm, a well-known parallel-in-time method. Both first- and second-order time integrators are considered for this task. The resulting space-time parallel methods are applied to integrate reaction-diffusion problems that model Turing pattern formation. This phenomenon appears in chemical reactions due to diffusion-driven instabilities, and rules the pattern formation for animal coat markings. Such reaction-diffusion problems require fine space and time meshes for their numerical integration, so we illustrate the usefulness of the proposed methods by solving several models of practical interest.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"218 ","pages":"Pages 91-108"},"PeriodicalIF":2.4,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144720946","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

Robust globally divergence-free weak Galerkin variational data assimilation method for convection-dominated Oseen equations 对流占优Oseen方程的鲁棒全局无发散弱Galerkin变分数据同化方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-22 DOI: 10.1016/j.apnum.2025.07.011

Xian Zhang, Ya Min, Minfu Feng

{"title":"Robust globally divergence-free weak Galerkin variational data assimilation method for convection-dominated Oseen equations","authors":"Xian Zhang, Ya Min, Minfu Feng","doi":"10.1016/j.apnum.2025.07.011","DOIUrl":"10.1016/j.apnum.2025.07.011","url":null,"abstract":"<div><div>This paper presents a weak Galerkin (WG) finite element method based on the variational approach for data assimilation of the unsteady convection-dominated Oseen equation. The WG scheme uses piecewise polynomials of degrees <em>k</em>(<span><math><mi>k</mi><mo>≥</mo><mn>1</mn></math></span>) and <span><math><mi>k</mi><mo>−</mo><mn>1</mn></math></span> respectively for the approximations of the velocity and the pressure in the interior of elements, and uses piecewise polynomials of degree <em>k</em> for their numerical traces on the interfaces of elements. The method is shown to yield globally divergence-free approximations of the velocity and initial value. It is proved that the velocity error in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm has a Reynolds-robust error bound with quasi-optimal convergence order <span><math><mi>k</mi><mo>+</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span> in the convection-dominated region. To solve the discrete optimality system efficiently, the conjugate gradient iterative algorithm is developed, which also preserves the globally divergence-free property of WG scheme. Numerical experiments are provided to verify the obtained theoretical results.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"218 ","pages":"Pages 22-42"},"PeriodicalIF":2.2,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686025","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

H(div)-conforming IPDG FEM with pointwise divergence-free velocity field for the micropolar Navier-Stokes equations 微极Navier-Stokes方程的H（div）型无点发散速度场IPDG有限元

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-18 DOI: 10.1016/j.apnum.2025.07.007

Xinran Huang, Haiyan Su, Xinlong Feng

引用次数: 0

A novel amplifying methodology in Gauss-Legendre IRK integrations to cope with high-frequency stiff problems 高斯-勒让德IRK积分中处理高频刚性问题的一种新的放大方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-17 DOI: 10.1016/j.apnum.2025.07.006

Sanaz Hami Hassan Kiyadeh , Hosein Saadat , Ramin Goudarzi Karim , Ali Safaie , Fayyaz Khodadosti

{"title":"A novel amplifying methodology in Gauss-Legendre IRK integrations to cope with high-frequency stiff problems","authors":"Sanaz Hami Hassan Kiyadeh , Hosein Saadat , Ramin Goudarzi Karim , Ali Safaie , Fayyaz Khodadosti","doi":"10.1016/j.apnum.2025.07.006","DOIUrl":"10.1016/j.apnum.2025.07.006","url":null,"abstract":"<div><div>This work presents a new amplification methodology based on the widely used Gauss-Legendre implicit Runge-Kutta integrations by addressing the phase lag and amplification factor. The novel methodology focuses on these two elements, which are the complex amplifiers associated with the GLIRK integrations.</div><div>To enhance the amplifier capabilities of the GLIRK integrations, we introduce two novel equations that clarify the relationships between the amplification factor and phase lag. This paper culminates in the improvement of two well-defined GLIRK integrations, each carefully designed to eliminate both the phase lag and the amplification factor in practical applications. The examination of absolute stability regions in the complex plane, as well as stability regions in the <em>z</em>-<em>v</em> plane, is relevant to the new GLIRK integrations presented.</div><div>To satisfy the admissibility of the new methodology, we establish a competitive environment alongside the classical GLIRK integration.</div><div>This competitive space includes numerical examples that demonstrate the low cost of the new amplified GLIRK integrations in addressing stiff problems with high frequency. Ultimately, this cost-effectiveness and superiority become increasingly evident as the frequency of the stiff problems increases.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"218 ","pages":"Pages 43-57"},"PeriodicalIF":2.2,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144694462","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 third-order finite difference weighted essentially non-oscillatory scheme with shallow neural network 具有浅层神经网络的三阶有限差分加权本质非振荡格式

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-14 DOI: 10.1016/j.apnum.2025.07.005

Kwanghyuk Park , Xinjuan Chen , Dongjin Lee , Jiaxi Gu , Jae-Hun Jung

引用次数: 0

Error estimates of a two-grid BDF2 virtual element scheme for semilinear parabolic equation 半线性抛物方程双网格BDF2虚元格式的误差估计

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-10 DOI: 10.1016/j.apnum.2025.07.002

Peixuan Wu, Xiaohui Wu, Yang Wang, Ruqing Wang

{"title":"Error estimates of a two-grid BDF2 virtual element scheme for semilinear parabolic equation","authors":"Peixuan Wu, Xiaohui Wu, Yang Wang, Ruqing Wang","doi":"10.1016/j.apnum.2025.07.002","DOIUrl":"10.1016/j.apnum.2025.07.002","url":null,"abstract":"<div><div>In this article, we present a new two-grid discretization for the approximation of semilinear parabolic equation found on virtual element method (VEM). The two-step backward differentiation formula (BDF2) is comtemplated in the time dimension, while the VEM is utilized in spatial dimension. The two-grid VEM primarily computes the numerical solution <span><math><msubsup><mrow><mi>W</mi></mrow><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> from solving a nonlinear system on a coarse mesh with size <em>H</em> and then gets the numerical solution <span><math><msubsup><mrow><mi>W</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> to a linear system built by the earlier result <span><math><msubsup><mrow><mi>W</mi></mrow><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> on a fine mesh with size <em>h</em> (<span><math><mi>h</mi><mo>≪</mo><mi>H</mi></math></span>). Consequently, our proposed scheme not only reduces total computational expense, but also achieves same accuracy as the single-grid VEM. The convergence analysis in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and semi-<span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norm for both the VEM and the two-grid VEM methods are provided concretely.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 451-475"},"PeriodicalIF":2.2,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631126","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 linear-decoupled and unconditionally energy stable fully discrete scheme for Peterlin viscoelastic model Peterlin粘弹性模型的线性解耦无条件能量稳定全离散格式

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-09 DOI: 10.1016/j.apnum.2025.07.001

Qi Wang , Kun Wang , Guanyu Zhou

{"title":"A linear-decoupled and unconditionally energy stable fully discrete scheme for Peterlin viscoelastic model","authors":"Qi Wang , Kun Wang , Guanyu Zhou","doi":"10.1016/j.apnum.2025.07.001","DOIUrl":"10.1016/j.apnum.2025.07.001","url":null,"abstract":"<div><div>In this paper, we design a linear-decoupled and unconditionally energy stable scheme utilizing the ZEC (“zero-energy-contribution”) technique for the diffusion Peterlin viscoelastic model. This model includes a diffusion term with an arbitrary small diffusion coefficient <em>ε</em> for the conformation tensor <strong><em>C</em></strong>. A specific ODE is introduced to deal with the nonlinear coupling terms for velocity <strong><em>u</em></strong> and <strong><em>C</em></strong> satisfying the ZEC property. We approximate the coupled nonlinear terms using the previous time-step results while still maintaining energy stability, allowing us to solve a linear-decoupled system at each time-step. Moreover, each component of <strong><em>C</em></strong> can be computed in parallel. We prove the unique solvability and energy stability of the fully discrete scheme. Additionally, we derive an error bound <span><math><mi>C</mi><mo>(</mo><mi>τ</mi><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> for the P2/P1/P2 element, where the constant <span><math><mi>C</mi></math></span> is not explicitly dependent on the reciprocal of <em>ε</em>. Several numerical experiments are presented to demonstrate the accuracy and performance of the proposed scheme. Comparison with a linear-decoupled scheme excluding the ZEC technique indicates that the proposed algorithm offers superior stability and performance.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 412-435"},"PeriodicalIF":2.2,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144597209","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 higher-order solver for the FitzHugh-Nagumo equation by combining nonstandard and compact finite difference scheme 结合非标准与紧致有限差分格式求解FitzHugh-Nagumo方程的高阶解

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-09 DOI: 10.1016/j.apnum.2025.07.004

Zhi-Chen Li , Yang-Wen Yu , Xiao-Yu Zhang , Qing Fang

引用次数: 0