Applied Numerical Mathematics最新文献_第7页

A highly accurate symplectic-preserving scheme for Gross-Pitaevskii equation Gross-Pitaevskii方程的高精度保辛格式

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2026-01-01 Epub Date: 2025-09-03 DOI: 10.1016/j.apnum.2025.08.006

Lan Wang , Yiyang Luo , Meng Chen , Pengfei Zhu

引用次数: 0

CSCMO: Relative permittivity-based complex shifted operator preconditioning method for solving time-harmonic Maxwell equations 基于相对介电常数的复移算子预处理方法求解时谐Maxwell方程

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2026-01-01 Epub Date: 2025-09-02 DOI: 10.1016/j.apnum.2025.08.009

Zikang Qin , Xiaoyu Duan , Hengbin An , Haoxuan Zhang , Shaoliang Hu

{"title":"CSCMO: Relative permittivity-based complex shifted operator preconditioning method for solving time-harmonic Maxwell equations","authors":"Zikang Qin , Xiaoyu Duan , Hengbin An , Haoxuan Zhang , Shaoliang Hu","doi":"10.1016/j.apnum.2025.08.009","DOIUrl":"10.1016/j.apnum.2025.08.009","url":null,"abstract":"<div><div>In electromagnetic field modeling and simulation, a critical challenge lies in solving discretized time-harmonic Maxwell equations. The inherent complexity of these systems – including matrix indefiniteness and solution oscillations – poses significant difficulties for efficient numerical solutions. Preconditioned Krylov subspace methods have emerged as a standard approach for solving the large scale discretized time-harmonic Maxwell equations, where the construction of effective preconditioners remains pivotal. The shifted operator method represents a prominent preconditioning technique for Maxwell equations. Typically, a purely imaginary shift to the original differential operator is used, since this capitalizes on the observed phenomenon where solution oscillatory behavior diminishes with increasing modulus of the imaginary component of relative permittivity. In this paper, we propose a novel preconditioning technique by shifting both the real and imaginary parts of the relative permittivity. The motivation for proposing this kind of shifted operator preconditioning is based on theoretical analysis, which shows that decreasing the real part of the relative permittivity will improve the positive definiteness of the discretized matrix. The resulting preconditioned system admits efficient solution via multigrid methods. Some analysis shows that the spectral distribution of the preconditioned matrix is more clustered than the purely imaginary shift preconditioned matrix. Also, theoretical analysis for a special model shows that the condition number of the preconditioned system is less than its purely imaginary-shifted counterpart. Numerical results demonstrate that the proposed preconditioning is more effective than the other two state-of-the-art shift operator preconditioning methods.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"219 ","pages":"Pages 145-169"},"PeriodicalIF":2.4,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106356","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

Adaptive SIPG method for approximations of parabolic boundary control problems with bilateral box constraints on Neumann boundary Neumann边界上双侧框约束抛物型边界控制问题逼近的自适应SIPG方法

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2026-01-01 Epub Date: 2025-08-13 DOI: 10.1016/j.apnum.2025.08.002

Ram Manohar , B․ V․ Rathish Kumar , Kedarnath Buda , Rajen Kumar Sinha

{"title":"Adaptive SIPG method for approximations of parabolic boundary control problems with bilateral box constraints on Neumann boundary","authors":"Ram Manohar , B․ V․ Rathish Kumar , Kedarnath Buda , Rajen Kumar Sinha","doi":"10.1016/j.apnum.2025.08.002","DOIUrl":"10.1016/j.apnum.2025.08.002","url":null,"abstract":"<div><div>This study presents an a posteriori error analysis of adaptive finite element approximations of parabolic boundary control problems with bilateral box constraints that act on a Neumann boundary. The control problem is discretized using the symmetric interior penalty Galerkin (SIPG) technique. We derive both reliable and efficient type residual-based error estimators coupling with the data oscillations. The implementation of these error estimators serves as a guide for the adaptive mesh refinement process, indicating whether or not more refinement is required. Although the control error estimator accurately captured control approximation errors, it had limitations in terms of guiding refinement localization in critical circumstances. To overcome this, an alternative control indicator was used in numerical tests. The results demonstrated the clear superiority of adaptive refinements over uniform refinements, confirming the proposed approach’s effectiveness in achieving accurate solutions while optimizing computational efficiency. Numerical experiments showcase the effectiveness of the derived error estimators.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"219 ","pages":"Pages 170-201"},"PeriodicalIF":2.4,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106357","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

Point-wise error estimates of two mass- and energy-preserving schemes for two-dimensional Schrödinger–Poisson equations 二维Schrödinger-Poisson方程的两种质量和能量守恒方案的点误差估计

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2026-01-01 Epub Date: 2025-09-12 DOI: 10.1016/j.apnum.2025.09.006

Jialing Wang , Anxin Kong , Tingchun Wang , Wenjun Cai

{"title":"Point-wise error estimates of two mass- and energy-preserving schemes for two-dimensional Schrödinger–Poisson equations","authors":"Jialing Wang , Anxin Kong , Tingchun Wang , Wenjun Cai","doi":"10.1016/j.apnum.2025.09.006","DOIUrl":"10.1016/j.apnum.2025.09.006","url":null,"abstract":"<div><div>This work presents two implicit and linear finite difference schemes that simultaneously preserve both mass and energy conservation properties for the two-dimensional Schrödinger–Poisson equations. The conservation, existence, uniqueness, as well as the convergence to the exact solution with the order <span><math><mrow><mi>O</mi><mo>(</mo><msup><mi>τ</mi><mn>2</mn></msup><mo>+</mo><msubsup><mi>h</mi><mi>x</mi><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>h</mi><mi>y</mi><mn>2</mn></msubsup><mo>)</mo></mrow></math></span> in discrete <span><math><msup><mi>L</mi><mn>2</mn></msup></math></span> and <span><math><msup><mi>L</mi><mi>∞</mi></msup></math></span> norms are established for these two schemes, where <span><math><mi>τ</mi></math></span> and <span><math><mrow><msub><mi>h</mi><mi>x</mi></msub><mo>,</mo><msub><mi>h</mi><mi>y</mi></msub></mrow></math></span> represent temporal and spatial step sizes. In contrast to the existing analysis techniques that rely on an <em>a priori</em> <span><math><msup><mi>L</mi><mi>∞</mi></msup></math></span> estimate of numerical solutions or impose restrictions on initial data, our approaches guarantee the unconditional convergence for SP equations with both attractive and repulsive forces. Besides the standard energy method, our analytical framework employs the cut-off method for the implicit scheme and the mathematical induction argument for the linear scheme, where the “lifting” technique is utilized in the two schemes to eliminate the constraints on grid ratios. Numerical experiments are provided to illustrate discrete conservation properties and validate the achieved convergence results.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"219 ","pages":"Pages 202-218"},"PeriodicalIF":2.4,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106358","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 posteriori error estimates for the finite element approximation of the convection–diffusion–reaction equation based on the variational multiscale concept 基于变分多尺度概念的对流扩散反应方程有限元近似的后验误差估计

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-12-01 Epub Date: 2025-08-11 DOI: 10.1016/j.apnum.2025.08.003

Ramon Codina , Hauke Gravenkamp , Sheraz Ahmed Khan

{"title":"A posteriori error estimates for the finite element approximation of the convection–diffusion–reaction equation based on the variational multiscale concept","authors":"Ramon Codina , Hauke Gravenkamp , Sheraz Ahmed Khan","doi":"10.1016/j.apnum.2025.08.003","DOIUrl":"10.1016/j.apnum.2025.08.003","url":null,"abstract":"<div><div>In this study, we employ the variational multiscale (VMS) concept to develop a posteriori error estimates for the stationary convection-diffusion-reaction equation. The variational multiscale method is based on splitting the continuous part of the problem into a resolved scale (coarse scale) and an unresolved scale (fine scale). The unresolved scale (also known as the sub-grid scale) is modeled by choosing it proportional to the component of the residual orthogonal to the finite element space, leading to the orthogonal sub-grid scale (OSGS) method. The idea is then to use the modeled sub-grid scale as an error estimator, considering its contribution in the element interiors and on the edges. We present the results of the a priori analysis and two different strategies for the a posteriori error analysis for the OSGS method. Our proposal is to use a scaled norm of the sub-grid scales as an a posteriori error estimate in the so-called stabilized norm of the problem. This norm has control over the convective term, which is necessary for convection-dominated problems. Numerical examples show the reliable performance of the proposed error estimator compared to other error estimators belonging to the variational multiscale family.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"218 ","pages":"Pages 238-260"},"PeriodicalIF":2.4,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886791","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

Fractional convection-diffusion systems in complex 2D and 3D geometries: A Bernoulli polynomial-based kernel method 复杂二维和三维几何中的分数对流扩散系统：基于伯努利多项式的核方法

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-12-01 Epub Date: 2025-08-15 DOI: 10.1016/j.apnum.2025.08.004

Mojtaba Fardi , Mahmoud A. Zaky , Babak Azarnavid

{"title":"Fractional convection-diffusion systems in complex 2D and 3D geometries: A Bernoulli polynomial-based kernel method","authors":"Mojtaba Fardi , Mahmoud A. Zaky , Babak Azarnavid","doi":"10.1016/j.apnum.2025.08.004","DOIUrl":"10.1016/j.apnum.2025.08.004","url":null,"abstract":"<div><div>This study presents an accurate meshless method for the efficient solution of nonlinear time-fractional convection-diffusion systems in complex two- and three-dimensional geometries. The proposed approach combines spatial discretization using a Bernoulli polynomial kernel function with temporal discretization via the backward differentiation formula. By employing positive definite kernels, the method achieves high spatial accuracy, while the use of the backward differentiation formula ensures high-order temporal accuracy. Convergence conditions and error bounds are rigorously analyzed using the Mittag-Leffler function. Error estimates are derived based on the spectral properties of the associated matrices, and inequalities describing error propagation over time are established. The method is tested on a variety of benchmark problems, including the Brusselator model and nonlinear coupled convection-diffusion systems, across both 2D and 3D domains. Extensive numerical experiments are carried out on various geometries-such as rectangular, circular, and spherical shapes-demonstrating the method’s robustness and accuracy in handling both regular and irregular computational domains.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"218 ","pages":"Pages 275-297"},"PeriodicalIF":2.4,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896067","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 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 : 2025-12-01 Epub 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":"2025-12-01","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

Algebraic multigrid methods for uncertainty quantification of source-type flows through randomly heterogeneous porous media 随机非均质多孔介质中源型流动不确定性量化的代数多重网格方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-12-01 Epub Date: 2025-07-03 DOI: 10.1016/j.apnum.2025.06.015

Vincenzo Schiano Di Cola , Salvatore Cuomo , Gerardo Severino , Marco Berardi

引用次数: 0

A boundary-corrected weak Galerkin mixed finite method for elliptic interface problems with curved interfaces 具有弯曲界面的椭圆界面问题的边界修正弱Galerkin混合有限方法

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-12-01 Epub Date: 2025-08-06 DOI: 10.1016/j.apnum.2025.08.001

Yongli Hou , Yi Liu , Yanqiu Wang

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