Applied Numerical Mathematics最新文献_第2页

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 : 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":"2025-09-12","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 numerical method on a posteriori mesh for a singularly perturbed Riccati equation 奇异摄动Riccati方程的后验网格数值解法

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-09-10 DOI: 10.1016/j.apnum.2025.09.003

Zhongdi Cen, Jian Huang, Aimin Xu

引用次数: 0

A high-order Haar wavelet approach to solve differential equations of fifth-order with simple, two-point and two-point integral conditions 用高阶Haar小波方法求解五阶微分方程的简单、两点和两点积分条件

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-09-10 DOI: 10.1016/j.apnum.2025.09.004

Maher Alwuthaynani , Muhammad Ahsan , Weidong Lei , Muhammad Abuzar , Masood Ahmad , Aditya Sharma

引用次数: 0

Comments on: “Two efficient iteration methods for solving the absolute value equations” 点评：“求解绝对值方程的两种有效迭代方法”

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-09-09 DOI: 10.1016/j.apnum.2025.09.005

Chun-Hua Guo

引用次数: 0

An adaptive HDG method for the pointwise tracking optimal control problem of elliptic equations 椭圆型方程点跟踪最优控制问题的自适应HDG方法

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-09-07 DOI: 10.1016/j.apnum.2025.09.001

Yanping Chen , Haitao Leng

引用次数: 0

Superconvergence of the local discontinuous Galerkin method with generalized numerical fluxes for one-dimensional linearized KdV equations 一维线性化KdV方程局部不连续Galerkin方法的超收敛性

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-09-03 DOI: 10.1016/j.apnum.2025.08.011

Yan Xu, Boying Wu, Xiong Meng

{"title":"Superconvergence of the local discontinuous Galerkin method with generalized numerical fluxes for one-dimensional linearized KdV equations","authors":"Yan Xu, Boying Wu, Xiong Meng","doi":"10.1016/j.apnum.2025.08.011","DOIUrl":"10.1016/j.apnum.2025.08.011","url":null,"abstract":"<div><div>In this paper, we analyze the local discontinuous Galerkin (LDG) method with generalized numerical fluxes to study the superconvergent properties of one-dimensional linearized KdV equations. Compared with traditional upwind and alternating fluxes, a slower error growth of the LDG solution using generalized numerical fluxes can be obtained for long time simulations. By establishing five energy identities and properties of correction functions with the appropriate numerical initial condition, we derive the supercloseness between the LDG solution and the interpolation function. The errors of the numerical fluxes as well as the cell averages achieve the <span><math><mrow><mo>(</mo><mn>2</mn><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>th-order superconvergence. In addition, we prove that the superconvergent rates of the function and derivative values at the interior generalized Radau points are <span><math><mrow><mi>k</mi><mo>+</mo><mn>2</mn></mrow></math></span> and <span><math><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></math></span>, respectively. An extension to mixed boundary conditions is given, for which we present the generalized skew-symmetry property and propose an appropriate conservation property for the numerical initial condition. Numerical experiments are shown to demonstrate the theoretical results, including cases with other boundary conditions and nonlinear KdV equations.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"219 ","pages":"Pages 99-121"},"PeriodicalIF":2.4,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145057114","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

On the recovery of boundary impedance for 3-dimensional obstacle by acoustic wave scattering using modified Kaczmarz iteration algorithm 基于改进Kaczmarz迭代算法的声波散射反演三维障碍物边界阻抗研究

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-09-03 DOI: 10.1016/j.apnum.2025.08.010

Yingdi Yi, Jijun Liu

引用次数: 0

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 : 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 : 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":"2025-09-02","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

Robust globally divergence-free HDG finite element method for steady thermally coupled incompressible MHD flow 稳定热耦合不可压缩MHD流动的鲁棒全局无散度HDG有限元方法

IF 2.4 2区数学

Applied Numerical Mathematics Pub Date : 2025-08-29 DOI: 10.1016/j.apnum.2025.08.007

Min Zhang , Zimo Zhu , Qijia Zhai , Xiaoping Xie

{"title":"Robust globally divergence-free HDG finite element method for steady thermally coupled incompressible MHD flow","authors":"Min Zhang , Zimo Zhu , Qijia Zhai , Xiaoping Xie","doi":"10.1016/j.apnum.2025.08.007","DOIUrl":"10.1016/j.apnum.2025.08.007","url":null,"abstract":"<div><div>This paper develops a hybridizable discontinuous Galerkin (HDG) finite element method of arbitrary order for the steady thermally coupled incompressible Magnetohydrodynamics (MHD) flow. The HDG scheme uses piecewise polynomials of degrees <span><math><mrow><mi>k</mi><mo>(</mo><mi>k</mi><mo>≥</mo><mn>1</mn><mo>)</mo><mo>,</mo><mi>k</mi><mo>,</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>,</mo><mi>k</mi><mo>−</mo><mn>1</mn></mrow></math></span> and <span><math><mi>k</mi></math></span> respectively for the approximations of the velocity, the magnetic field, the pressure, the magnetic pseudo-pressure, and the temperature in the interior of elements, and uses piecewise polynomials of degree <span><math><mi>k</mi></math></span> for their numerical traces on the interfaces of elements. The method is shown to yield globally divergence-free approximations of the velocity and magnetic fields. Existence and uniqueness results for the discrete scheme are given and <span><math><mrow><mi>O</mi><mo>(</mo><msup><mi>h</mi><mi>k</mi></msup><mo>)</mo></mrow></math></span>- optimal error estimates are derived for all the variables. Numerical experiments are provided to verify the obtained theoretical results.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"219 ","pages":"Pages 19-40"},"PeriodicalIF":2.4,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144989796","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