Applied Numerical Mathematics最新文献

英文中文

Discrete gradient methods for port-Hamiltonian differential-algebraic equations 波特-哈密顿微分代数方程的离散梯度方法

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2026-05-01 Epub Date: 2025-12-27 DOI: 10.1016/j.apnum.2025.12.006

Philipp L. Kinon , Riccardo Morandin , Philipp Schulze

Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient methods to the system class of nonlinear port-Hamiltonian differential-algebraic equations - as they emerge from the port- and energy-based modeling of physical systems in various domains. We introduce a novel numerical scheme tailored for semi-explicit differential-algebraic equations and further address more general settings using the concepts of discrete gradient pairs and Dirac-dissipative structures. Additionally, the behavior under system transformations is investigated and we demonstrate that under suitable assumptions port-Hamiltonian differential-algebraic equations admit a representation which consists of a parametrized port-Hamiltonian semi-explicit system and an unstructured equation. Finally, we present the application to multibody system dynamics and discuss numerical results to demonstrate the capabilities of our approach.

离散梯度方法是动力系统时间离散化的有力工具，因为无论总能量的形式如何，它们都是结构保持的。在这项工作中，我们讨论了离散梯度方法在非线性端口-哈密顿微分代数方程系统类中的应用，因为它们出现在各个领域的基于端口和能量的物理系统建模中。我们介绍了一种针对半显式微分代数方程的新型数值格式，并进一步使用离散梯度对和狄拉克耗散结构的概念解决了更一般的设置。此外，研究了系统变换下的行为，证明了在适当的假设下，port- hamilton微分代数方程允许由参数化port- hamilton半显式系统和非结构方程组成的表示。最后，我们介绍了该方法在多体系统动力学中的应用，并讨论了数值结果来证明我们方法的能力。

引用次数: 0

Two-grid mixed finite element method with backward Euler fully discrete scheme for the nonlinear schrödinger equation 用反向欧拉完全离散格式的两网格混合有限元法求解非线性schrödinger方程

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2026-05-01 Epub Date: 2026-01-03 DOI: 10.1016/j.apnum.2025.12.009

Zhikun Tian , Jianyun Wang , Jie Zhou

We consider the two-dimensional time-dependent nonlinear Schrödinger equation by the backward Euler fully discrete mixed finite element method and obtain optimal error order in L²-norm. We develop a two-grid algorithm within the backward Euler fully discrete mixed finite element scheme. This algorithm reduces the solution of the nonlinear Schrödinger equation on a fine grid to solving the original nonlinear problem on a much coarser grid, coupled with a linear problem on the fine grid. Moreover, we demonstrate that the two-grid solution achieves the same error order as the standard mixed finite element solution when the coarse and fine mesh sizes satisfy

H = O (h^{\frac{1}{2}})

. Finally, a numerical experiment in the RT₀ space is provided to partly verify theoretical results.

采用倒向欧拉完全离散混合有限元法对二维时变非线性Schrödinger方程进行了分析，得到了l2范数下的最优误差阶。在后向欧拉完全离散混合有限元格式中，提出了一种双网格算法。该算法将非线性Schrödinger方程在细网格上的求解简化为在更粗的网格上求解原非线性问题，并在细网格上求解线性问题。此外，我们还证明了当粗、细网格尺寸满足H=O（h12）时，两网格解与标准混合有限元解具有相同的误差阶。最后，通过RT0空间的数值实验对理论结果进行了部分验证。

引用次数: 0

Finite element simulation of modified Poisson-Nernst-Planck/Navier-Stokes model for compressible electrolytes under mechanical equilibrium 力学平衡下可压缩电解质修正Poisson-Nernst-Planck/Navier-Stokes模型的有限元模拟

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2026-05-01 Epub Date: 2026-01-23 DOI: 10.1016/j.apnum.2026.01.011

Ankur Ankur , Ram Jiwari , Satyvir Singh

This work presents a finite element method for a modified Poisson–Nernst–Planck/Navier–Stokes (PNP/NS) model under the mechanical equilibrium, developed for compressible electrolytes. The modification is based on the new model proposed by Dreyer, Guhlke and M

\ddot{u}

ller [1], where the diffusion flux in the classical PNP system is replaced with an implicitly involved new diffusion flux, leading to fractional nonlinearity. He and Sun [2] previously developed a numerical approach for another type of modification, where the Poisson equation in the PNP system was substituted with a fourth-order elliptic equation. Another key contribution of this work is the reduction of the equilibrium system to a modified Poisson–Boltzmann system. The proposed numerical scheme is capable of handling both compressible and incompressible regimes by employing a bulk modulus parameter, which governs the fluid’s compressibility and enables seamless transition between these regimes. To emphasize practical relevance, we discuss the implications of compressible electrolytes in the context of double-layer capacitance behavior. We also conduct numerical simulations over various domains to demonstrate its applicability under various operating conditions, including temperature fluctuations and variations in the bulk modulus. The numerical results validate the accuracy and robustness of our computational scheme and demonstrate that the observed limiting behavior for the incompressible regime aligns with the theoretical trends anticipated by Dreyer et al. [1].

本文提出了一种针对可压缩电解质的力学平衡下改进的泊松-能斯特-普朗克/纳维-斯托克斯（PNP/NS）模型的有限元方法。该修正基于Dreyer， Guhlke和Mu¨ller[1]提出的新模型，其中经典PNP系统中的扩散通量被隐式涉及的新扩散通量取代，导致分数阶非线性。他和Sun[2]之前为另一种类型的修正开发了一种数值方法，其中PNP系统中的泊松方程被四阶椭圆方程取代。这项工作的另一个关键贡献是将平衡系统还原为一个修正的泊松-玻尔兹曼系统。所提出的数值方案能够处理可压缩和不可压缩两种状态，通过采用体积模量参数来控制流体的可压缩性，并实现这些状态之间的无缝转换。为了强调实际意义，我们讨论了可压缩电解质在双层电容行为背景下的含义。我们还在各个领域进行了数值模拟，以证明其在各种操作条件下的适用性，包括温度波动和体积模量的变化。数值结果验证了我们的计算方案的准确性和鲁棒性，并表明观察到的不可压缩状态的极限行为与Dreyer等人预测的理论趋势一致。

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引用次数: 0

Efficient, accurate, and robust penalty-projection algorithm for parameterized stochastic Navier-Stokes flow problems 参数化随机Navier-Stokes流问题的有效、准确、鲁棒的惩罚-投影算法

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2026-05-01 Epub Date: 2026-01-21 DOI: 10.1016/j.apnum.2026.01.010

Neethu Suma Raveendran , Md. Abdul Aziz , Sivaguru S. Ravindran , Muhammad Mohebujjaman

This paper presents and analyzes a fast, robust, efficient, and optimally accurate fully discrete splitting algorithm for the Uncertainty Quantification (UQ) of convection-dominated flow problems modeled by parameterized Stochastic Navier-Stokes Equations (SNSEs). The time-stepping algorithm is an implicit backward-Euler linearized method, grad-div and Ensemble Eddy Viscosity (EEV) regularized, and split using discrete Hodge decomposition. Moreover, the scheme’s sub-problems are all designed to have different Right-Hand-Side (RHS) vectors but the same system matrix for all realizations at each time-step. The stability of the algorithm is rigorously proven, and it has been shown that appropriately large grad-div stabilization parameters cause the splitting error to vanish. The proposed UQ algorithm is then combined with the Stochastic Collocation Methods (SCMs). Several numerical experiments are presented to verify the predicted convergence rates and performance of this superior scheme on benchmark problems with high expected Reynolds numbers (Re).

本文提出并分析了一种快速、鲁棒、高效、最优精确的全离散分裂算法，用于参数化随机Navier-Stokes方程（SNSEs）模拟的对流主导流问题的不确定性量化（UQ）。时间步进算法采用隐式后向欧拉线性化方法，梯度梯度和集合涡动黏度（EEV）正则化，并采用离散Hodge分解进行分割。此外，该方案的子问题都被设计成具有不同的右手边（RHS）向量，但每个时间步的所有实现都具有相同的系统矩阵。严格证明了算法的稳定性，并表明适当大的梯度稳定参数可以使分裂误差消失。然后将提出的UQ算法与随机配置方法（SCMs）相结合。通过数值实验验证了该算法在高期望雷诺数（Re）基准问题上的收敛速度和性能。

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引用次数: 0

A stable multistep scheme for the transient Wigner equation: Efficient handling of scattering 瞬态Wigner方程的稳定多步格式：散射的有效处理

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2026-05-01 Epub Date: 2026-01-18 DOI: 10.1016/j.apnum.2026.01.009

Yidan Wang , Haiyan Jiang , Tiao Lu , Wenqi Yao

For the transient Wigner equation including scattering, we develop a second-order two-step scheme inspired by the Crank-Nicolson (CN) scheme. The resulting CN-like scheme retains favorable stability while exhibiting higher computational efficiency than any of the existing multi-stage one-step time integration schemes. Unconditional L²-stability and convergence of the CN-like scheme are rigorously proved. Numerical experiments are conducted by simulating a typical resonant tunneling diode, and the results validate the second-order temporal accuracy, remarkable stability and high efficiency of the CN-like scheme. We also reveal the effects of the scattering mechanism on the Wigner function, and the subsequent impact on the I-V characteristics and the electron densities.

对于包含散射的暂态Wigner方程，我们在Crank-Nicolson （CN）格式的启发下，提出了二阶两步格式。所得到的类神经网络方案保持了良好的稳定性，同时表现出比任何现有的多阶段一步时间积分方案更高的计算效率。严格证明了类cn格式的无条件l2稳定性和收敛性。通过模拟典型的谐振隧道二极管进行了数值实验，结果验证了该方案的二阶时间精度、良好的稳定性和高效率。我们还揭示了散射机制对Wigner函数的影响，以及随后对I-V特性和电子密度的影响。

引用次数: 0

Derivative-free convergence analysis for Steffensen-type schemes for nonlinear equations 非线性方程steffensen型格式的无导数收敛分析

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2026-05-01 Epub Date: 2026-01-09 DOI: 10.1016/j.apnum.2026.01.003

Santhosh George , Muniyasamy M , Laurence Grammont

Steffensen schemes have been constructed to approximate the solution of an operator equation, with the goal of avoiding the use of its derivatives. It is the reason why these schemes involve the first order divided difference operator. Until now, results on convergence order have been provided using Taylor series expansion, which implies that the operator must be several times differentiable. To be consistent with the nature of the Steffensen schemes, we propose a proof of the convergence order under assumptions that involve only the first and second order divided difference operators. In addition, the convergence order analysis for these Steffensen schemes is done here for the general case of Banach spaces, while it has been done only for finite-dimensional spaces so far. Until now, the assumptions required for semi-local analysis and those required for local analysis have been of a very different nature. A new idea was to unify these hypotheses; hence, we give a single set of convergence conditions. Moreover, our local convergence analysis provides consistently explicit convergence balls that are computable.

Steffensen格式被构造为近似算子方程的解，目的是避免使用其导数。这就是为什么这些格式涉及一阶微分算子的原因。到目前为止，已经用泰勒级数展开给出了收敛阶的结果，这意味着算子必须是多次可微的。为了与Steffensen格式的性质相一致，我们提出了在只涉及一阶和二阶可分差分算子的假设下收敛阶的证明。此外，本文还对这些Steffensen格式在Banach空间的一般情况下进行了收敛阶分析，而迄今为止只对有限维空间进行了收敛阶分析。到目前为止，半局部分析所需的假设和局部分析所需的假设具有非常不同的性质。一个新的想法是统一这些假设；因此，我们给出了一组收敛条件。此外，我们的局部收敛分析提供了一致的显式收敛球，这些球是可计算的。

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引用次数: 0

A separate preconditioned primal-dual splitting algorithm for composite monotone inclusion problems 复合单调包含问题的单独预条件原对偶分裂算法

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2026-04-01 Epub Date: 2025-12-27 DOI: 10.1016/j.apnum.2025.12.004

Xiaokai Chang , Xingran Zhao , Long Xu

We propose a separable preconditioned primal-dual splitting (SP-PDS) method for solving composite monotone inclusion problems. The linear subproblem arising in this method can be selected or generated by comprehensively considering factors such as computational complexity and numerical convergence speed. We prove weak convergence in Hilbert space by reformulating the proposed SP-PDS as a decomposed proximal point algorithm, where the preconditioner is decomposed nonsymmetrically. In particular, various efficient preconditioners are introduced in this framework for which only a few inner iterations are needed to implement preconditioning, instead of computing an inexact solution and controlling the error. The performance of separate preconditioning strategy is verified through preliminary numerical experiments on the image denoising and LASSO problems.

提出了一种解复合单调包含问题的可分离预条件原对偶分裂（SP-PDS）方法。该方法产生的线性子问题可以综合考虑计算复杂度和数值收敛速度等因素进行选择或生成。通过将所提出的SP-PDS重构为分解的近点算法，证明了该算法在Hilbert空间中的弱收敛性，其中预条件是非对称分解的。特别地，在该框架中引入了各种有效的预条件，只需要几个内部迭代就可以实现预条件，而不是计算不精确的解并控制误差。通过对图像去噪和LASSO问题的初步数值实验，验证了分离预处理策略的性能。

引用次数: 0

Error analysis on the mixed finite element method for a quad-curl problem with low-order terms in three dimensions 三维低阶项四旋度问题的混合有限元法误差分析

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2026-04-01 Epub Date: 2025-12-02 DOI: 10.1016/j.apnum.2025.11.011

Jikun Zhao , Kangcheng Deng , Chao Wang , Bei Zhang

This paper aims to develop a mixed finite element method for the three-dimensional quad-curl problem with low-order terms. We prove the regularity estimates on the solution to the primal weak problem under the assumption that the domain is a convex polyhedron. Subsequently, we introduce an auxiliary variable to reformulate the original problem as a mixed problem that consists of two curl-curl equations. Based on the regularity estimates, we establish the equivalence between the primal and mixed formulations. In this mixed finite element method, the primal and auxiliary variables are discretized by the Nédélec’s edge elements. We first derive the suboptimal error estimates for the mixed finite element method. In order to prove the optimal convergence, we construct a special projection with some good properties by using the Maxwell equation under the natural boundary condition. Then, by the duality argument, we prove the optimal error estimates for the approximation to the primal solution in the quad-curl equation. The numerical results illustrate the viability and optimal convergence of this method.

本文旨在建立一种求解低阶项三维四旋度问题的混合有限元方法。在假设区域是凸多面体的情况下，证明了原始弱问题解的正则性估计。随后，我们引入一个辅助变量，将原问题重新表述为由两个旋度方程组成的混合问题。基于正则性估计，我们建立了原始公式和混合公式之间的等价性。在这种混合有限元方法中，主变量和辅助变量通过nsamdsamlec的边缘单元离散化。首先推导了混合有限元法的次优误差估计。为了证明最优收敛性，我们利用自然边界条件下的麦克斯韦方程构造了一个具有良好性质的特殊投影。然后，利用对偶论证，证明了四旋度方程原解近似的最优误差估计。数值结果表明了该方法的可行性和最优收敛性。

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引用次数: 0

Linear minimum-variance approximants for noisy data 噪声数据的线性最小方差近似

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2026-04-01 Epub Date: 2025-12-09 DOI: 10.1016/j.apnum.2025.12.002

Sergio López-Ureña, Dionisio F. Yáñez

Inspired by recent developments in subdivision schemes founded on the Weighted Least Squares technique, we construct linear approximants for noisy data in which the weighting strategy minimizes the output variance, thereby establishing a direct correspondence with the Generalized Least Squares and the Minimum-Variance Formulas methodologies. By introducing annihilation-operators for polynomial spaces, we derive usable formulas that are optimal for general correlated non-uniform noise. We show that earlier subdivision rules are optimal for uncorrelated non-uniform noise and, finally, we present numerical evidence to confirm that, in the correlated case, the proposed approximants are better than those currently used in the subdivision literature.

受基于加权最小二乘技术的细分方案的最新发展的启发，我们为噪声数据构建了线性近似，其中加权策略使输出方差最小化，从而与广义最小二乘和最小方差公式方法建立了直接对应关系。通过引入多项式空间的湮灭算子，我们推导出了适用于一般相关非均匀噪声的最优公式。我们证明了先前的细分规则对于不相关的非均匀噪声是最优的，最后，我们提供了数值证据来证实，在相关情况下，所提出的近似比目前在细分文献中使用的近似更好。

引用次数: 0

High-order orthogonal spline collocation schemes for two-dimensional nonlinear problems 二维非线性问题的高阶正交样条配置格式

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2026-04-01 Epub Date: 2025-12-06 DOI: 10.1016/j.apnum.2025.12.001

Meirong Cheng, Qimin Li, Leijie Qiao

To address the nonlinear control of transverse vibrations in a clamped square plate, we design and analyze an orthogonal spline collocation (OSC) scheme combined with a discrete-time approximation. Two new Crank–Nicolson (CN) OSC variants are introduced for temporal discretization. By applying a Taylor expansion to the nonlinear term, the original fourth-order nonlinear problem is transformed into a linear one, enabling efficient computation. The theoretical investigation is provided. Numerical experiments on several practical examples confirm the effectiveness of the schemes, achieving second-order temporal accuracy and optimal spatial convergence.

为了解决夹持方形板横向振动的非线性控制问题，我们设计并分析了一种结合离散时间近似的正交样条配置（OSC）方案。引入了两个新的Crank-Nicolson (CN) OSC变量进行时间离散化。通过对非线性项进行泰勒展开式，将原来的四阶非线性问题转化为线性问题，实现了高效的计算。并进行了理论研究。几个实例的数值实验验证了该方法的有效性，取得了二阶时间精度和最佳空间收敛性。

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全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

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Applied Numerical Mathematics

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