Computers & Mathematics with Applications最新文献

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A high-order discontinuous Galerkin method for the numerical modeling of epileptic seizures 癫痫发作数值模拟的高阶不连续伽辽金方法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-01 Epub Date: 2025-12-29 DOI: 10.1016/j.camwa.2025.12.017

Caterina B. Leimer Saglio, Stefano Pagani, Mattia Corti, Paola F. Antonietti

Epilepsy is a neurological disorder characterized by recurrent and spontaneous seizures consisting of abnormal high-frequency electrical activity in the brain. In this condition, the transmembrane potential dynamics are characterized by rapid and sharp wavefronts traveling along the heterogeneous and anisotropic conduction pathways of the brain. This work employs the monodomain model, coupled with specific models characterizing ion concentration dynamics, to mathematically describe brain tissue electrophysiology in grey and white matter at the organ scale. This multiscale model is discretized in space with the high-order discontinuous Galerkin method on polygonal and polyhedral grids (PolyDG) and advanced in time with a Crank-Nicolson scheme. This ensures efficient and accurate simulations of the high-frequency electrical activity that is responsible for epileptic seizure, and keeps reasonably low the computational costs by a suitable combination of high-order approximations and agglomerated polytopal meshes. We numerically investigate synthetic test cases on a two-dimensional heterogeneous squared domain discretized with a polygonal grid, and on a two-dimensional brainstem in a sagittal plane with an agglomerated polygonal grid that takes advantage of the flexibility of the PolyDG approximation of the semidiscrete formulation. Finally, we provide a theoretical analysis of stability and an a-priori convergence analysis for a simplified mathematical problem.

癫痫是一种神经系统疾病，其特征是反复发作和自发发作，包括大脑中异常的高频电活动。在这种情况下，跨膜电位动力学的特点是沿大脑的非均质和各向异性传导通路快速而尖锐的波前。本研究采用单域模型，结合表征离子浓度动力学的特定模型，在器官尺度上对灰质和白质的脑组织电生理进行数学描述。该多尺度模型在多边形和多面体网格（PolyDG）上采用高阶不连续Galerkin方法在空间上离散化，并采用Crank-Nicolson格式在时间上推进。这确保了对导致癫痫发作的高频电活动的有效和准确的模拟，并通过高阶近似和聚集多边形网格的适当组合保持合理的低计算成本。我们在用多边形网格离散的二维非均匀平方域和利用半离散公式的PolyDG近似的灵活性利用聚类多边形网格在矢状面上的二维脑干上进行了数值研究。最后，我们对一个简化的数学问题进行了稳定性的理论分析和先验收敛分析。

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引用次数: 0

Efficient matching boundary conditions of two-dimensional honeycomb lattice for atomic simulations 二维蜂窝晶格原子模拟的有效匹配边界条件

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-01 Epub Date: 2025-12-29 DOI: 10.1016/j.camwa.2025.12.015

Baiyili Liu , Songsong Ji , Gang Pang , Shaoqiang Tang , Lei Zhang

In this paper, we design a series of matching boundary conditions for a two-dimensional compound honeycomb lattice, which has an explicit and simple form, high computing efficiency and good effectiveness of suppressing boundary reflections. First, we formulate the dynamic equations and calculate the dispersion relation for the harmonic honeycomb lattice, then symmetrically choose specific atoms near the boundary to design different forms of matching boundary conditions. The boundary coefficients are determined by matching a residual function at some selected wavenumbers. Several atomic simulations are performed to test the effectiveness of matching boundary conditions in the example of a harmonic honeycomb lattice and a nonlinear honeycomb lattice with the FPU-β potential. Numerical results illustrate that the low-order matching boundary conditions mainly treat long waves, while the high-order matching boundary conditions can efficiently suppress short waves and long waves simultaneously. Decaying kinetic energy curves indicate the stability of matching boundary conditions in numerical simulations.

本文针对二维复合蜂窝晶格设计了一系列匹配边界条件，其形式明确简单，计算效率高，抑制边界反射效果好。首先，我们建立了谐波蜂窝晶格的动力学方程并计算了色散关系，然后在边界附近对称地选择特定的原子来设计不同形式的匹配边界条件。边界系数是通过在一些选定的波数上匹配残差函数来确定的。以谐波蜂窝晶格和具有FPU-β电位的非线性蜂窝晶格为例，进行了原子模拟，验证了边界条件匹配的有效性。数值结果表明，低阶匹配边界条件主要处理长波，而高阶匹配边界条件可以有效地同时抑制短波和长波。在数值模拟中，动能衰减曲线表明了匹配边界条件的稳定性。

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引用次数: 0

Accelerating the Lax-Wendroff time discretization method for the first-order acoustic wave equation simulation by designing proper SGFD schemes 通过设计合适的SGFD格式，加速一阶声波方程模拟的Lax-Wendroff时间离散化方法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-01 Epub Date: 2026-01-02 DOI: 10.1016/j.camwa.2025.12.025

Wenquan Liang , Yanfei Wang

The Lax-Wendroff high-order time discretization method is well known for its larger stability range and its ability to reduce temporal dispersion introduced by large time steps. However, the Lax-Wendroff high-order time discretization method substantially increases the computation burden since it requires computing many more spatial derivatives. In this paper, we propose two novel finite-difference schemes for the high-order Lax-Wendroff time discretization. With comparable accuracy, the proposed finite-difference schemes reduce numerical simulation time by approximately 50 % and 63 %, respectively, compared with a conventional finite-difference implementation of the Lax-Wendroff time discretization method. We then present dispersion error analyses and derive the stability conditions. Finally, numerical experiments with progressively larger time steps validate the accuracy and efficiency of the proposed finite-difference schemes.

Lax-Wendroff高阶时间离散方法以其较大的稳定范围和降低大时间步长引起的时间色散的能力而闻名。然而，由于需要计算更多的空间导数，Lax-Wendroff高阶时间离散化方法大大增加了计算量。本文提出了高阶Lax-Wendroff时间离散化的两种新的有限差分格式。与传统的有限差分实现的Lax-Wendroff时间离散化方法相比，所提出的有限差分格式分别减少了大约50%和63%的数值模拟时间。然后给出了色散误差分析，并推导了稳定性条件。最后，逐步增大时间步长的数值实验验证了所提出的有限差分格式的准确性和有效性。

引用次数: 0

Analysis of the weighted shifted boundary method for the Poisson and Stokes problems 泊松和斯托克斯问题的加权移边法分析

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-01 Epub Date: 2025-12-27 DOI: 10.1016/j.camwa.2025.12.011

Nabil M. Atallah , Claudio Canuto , Guglielmo Scovazzi

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by properly shifting the location and values of the boundary conditions. This avoids integration over cut cells and the associated implementation issues. Recently, the Weighted SBM (WSBM) was proposed for the Navier-Stokes equations with free surfaces and the Stokes flow with moving boundaries. The attribute “weighted” in the name WSBM stems from the fact that its variational form is weighted with the elemental volume fraction of active fluid. The motivation for the development of the WSBM was the preservation of the volume of active fluid to a higher degree of accuracy, which in turn resulted in improved stability and robustness characteristics in moving-boundary, time-dependent simulations. In this article, we present the numerical analysis of the WSBM formulations for the Poisson and Stokes problems. We give mathematical conditions under which the bilinear forms defining the discrete variational formulations are uniformly coercive (Poisson problem) or inf-sup stable (Stokes problem). By these results, stability and optimal convergence is proven in the natural norm; L²-error estimates can also be derived.

平移边界法（SBM）属于一类非拟合（或浸入或嵌入）有限元方法，它依赖于在代理（近似）计算域上重新表述原始边值问题。通过适当地移动边界条件的位置和值来保持精度。这避免了对切割单元的集成和相关的实现问题。最近，针对具有自由曲面的Navier-Stokes方程和具有运动边界的Stokes流，提出了加权SBM （WSBM）。WSBM名称中的“加权”属性源于其变分形式是用活性流体的元素体积分数加权的。开发WSBM的动机是在更高的精度下保持活动流体的体积，这反过来又提高了移动边界、依赖时间的模拟的稳定性和鲁棒性。在本文中，我们给出了泊松和斯托克斯问题的WSBM公式的数值分析。给出了定义离散变分公式的双线性形式是一致强制的（泊松问题）或不稳定的（斯托克斯问题）的数学条件。通过这些结果，证明了算法在自然范数下的稳定性和最优收敛性；l2误差估计也可以推导出来。

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引用次数: 0

Unconditionally convergent fourth-order compact difference methods for Quasi-linear convection-diffusion equations 拟线性对流扩散方程的无条件收敛四阶紧致差分方法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-01 Epub Date: 2026-01-19 DOI: 10.1016/j.camwa.2026.01.018

Mengling Wu , Hongling Hu , Kejia Pan , Wei Wu

In this paper, we propose an unconditionally convergent implicit compact difference method for the quasi-linear convective diffusion equation. First, we use Taylor expansion combined with the truncation error residual correction method to discretize the first-order derivative in the temporal direction, while the first- and second-order derivatives in the spatial direction are approximated by the consistent fourth-order boundary schemes and the fourth-order difference method, respectively. We develop a two-level scheme with

O (τ^{2} + h^{4})

. Secondly, the convergence of the scheme in the L^∞ norm has been proven. To further improve computational efficiency, we apply Richardson extrapolation to improve the temporal accuracy of the scheme to fourth-order, i.e.,

O (τ^{4} + h^{4})

. Finally, we present numerical examples to verify the theoretical analysis and the efficiency of our proposed method.

本文给出了拟线性对流扩散方程的一种无条件收敛隐式紧差分法。首先，采用Taylor展开式结合截断误差残差校正方法对时间方向上的一阶导数进行离散化，而空间方向上的一阶导数和二阶导数分别采用一致的四阶边界格式和四阶差分法进行逼近。我们开发了一个具有O（τ2+h4）的两能级格式。其次，证明了该方案在L∞范数上的收敛性。为了进一步提高计算效率，我们采用Richardson外推将格式的时间精度提高到四阶，即O（τ4+h4）。最后，通过数值算例验证了理论分析和所提方法的有效性。

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引用次数: 0

Solving fluid flow problems in space-time with multiscale stabilization: Formulation and examples 用多尺度稳定方法求解时空流体流动问题：公式和实例

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-01 Epub Date: 2025-12-30 DOI: 10.1016/j.camwa.2025.12.019

Biswajit Khara , Robert Dyja , Kumar Saurabh , Anupam Sharma , Baskar Ganapathysubramanian

We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The finite element problem is posed on the “full” space-time domain, considering time as another dimension. We provide a rigorous analysis of the stability and convergence of the stabilized formulation. And finally, we apply this method on two benchmark problems in computational fluid dynamics, namely, lid-driven cavity flow and flow past a circular cylinder. We validate the current method with existing results from literature and show that very large space-time blocks can be solved using our approach.

给出了求解不可压缩Navier-Stokes方程的一种时空连续galerkin有限元方法。为了保证离散变分问题的稳定性，我们应用了变分多尺度方法的思想。有限元问题是在“全”时空域中提出的，将时间视为另一个维度。我们对稳定公式的稳定性和收敛性进行了严格的分析。最后，将该方法应用于计算流体力学中的两个基准问题，即盖子驱动的空腔流动和经过圆柱的流动。我们用文献中的现有结果验证了当前的方法，并表明可以使用我们的方法解决非常大的时空块。

引用次数: 0

Low-cost adaptive characteristic finite element method for incompressible natural convection problems 不可压缩自然对流问题的低成本自适应特征有限元方法

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-01 Epub Date: 2025-12-26 DOI: 10.1016/j.camwa.2025.12.008

Bowen Ren , Jilian Wu , Ning Li , Leilei Wei

This paper firstly adopt a novel low-complexity finite element method for incompressible natural convection problems, which is based on the characteristic finite element method (CFEM) and achieves higher-order accuracy by introducing the time filter (TF) technique. The new method effectively addresses inherent limitations of the characteristic finite element method while retaining its essential advantages. By applying the TF to postprocess solutions obtained from the first-order characteristic finite element method (CFEM-1), we achieve a non-intrusive enhancement to existing code frameworks, boosting temporal accuracy by one order. Secondly, this paper constructs two error operators without increasing complexity, thus facilitating the construction of a new adaptive algorithm conveniently. Additionally, we consturct adaptive CFEM and adaptive CFEM plus TF. Subsequently, this paper proves the unconditional stability of the constant time stepsize CFEM plus TF. Lastly, numerical experiments presented to validate the theoretical analysis and substantiate the aforementioned propositions.

本文首先在特征有限元法（CFEM）的基础上，采用一种新的低复杂度有限元方法求解不可压缩自然对流问题，并通过引入时间滤波器（TF）技术实现了高阶精度。新方法有效地解决了特征有限元法固有的局限性，同时保留了特征有限元法的本质优势。通过将TF应用于从一阶特征有限元法（cfm -1）获得的后处理解，我们实现了对现有代码框架的非侵入性增强，将时间精度提高了一个阶。其次，本文在不增加复杂度的情况下构造了两个误差算子，方便了新的自适应算法的构造。此外，构造了自适应CFEM和自适应CFEM + TF。随后，证明了等时间步长CFEM + TF的无条件稳定性。最后，通过数值实验验证了理论分析，证实了上述结论。

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引用次数: 0

Numerical methods and analysis for magnetohydrodynamics slip flow and heat transfer of Jeffrey nanofluid with tempered fractional constitutive relationship 具有回火分数本构关系的Jeffrey纳米流体磁流体力学、滑移流动和传热的数值方法与分析

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-01 Epub Date: 2026-01-14 DOI: 10.1016/j.camwa.2025.12.030

Wenxin Zheng , Fawang Liu , Shujuan Lü , Ian Turner , Libo Feng

In this work, the magnetohydrodynamic (MHD) flow and heat transfer for a Jeffrey nanofluid flowing over a semi-infinite plate subjected to slip effects is considered. Firstly, the standard constitutive equation of a Jeffrey fluid is generalized to incorporate the tempered fractional derivative to describe the nonlocal but finite relaxation process, which leads to a novel tempered momentum equation. Combined with a tempered energy equation, the coupled momentum and energy system of a Jeffrey nanofluid is formulated. Secondly, the Legendre spectral method is employed to the tempered fractional coupled model, in which the modified shifted Grünwald superconvergence formula is proposed to discretize the tempered fractional derivative. To enhance computational efficiency, a fast algorithm is further developed, for which the stability and convergence analysis are rigorously established. Finally, some numerical examples are performed to confirm the efficiency of the proposed numerical schemes and to investigate the impacts of important model parameters on the variations of fluid movement and thermal transfer.

本文研究了杰弗里纳米流体在受滑移效应影响的半无限平板上的磁流体动力学流动和传热问题。首先，将Jeffrey流体的标准本构方程进行推广，引入回火分数阶导数来描述非局部有限松弛过程，得到了新的回火动量方程；结合调质能量方程，建立了Jeffrey纳米流体的动量-能量耦合系统。其次，将Legendre谱法应用于回火分数阶耦合模型，提出了修正位移grengwald超收敛公式对回火分数阶导数进行离散化；为了提高计算效率，进一步开发了一种快速算法，并严格建立了算法的稳定性和收敛性分析。最后，通过数值算例验证了所提数值格式的有效性，并探讨了重要模型参数对流体运动和传热变化的影响。

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引用次数: 0

Error analysis of the first-order and second-order fully discrete schemes for the Caginalp model Caginalp模型一阶和二阶完全离散格式的误差分析

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-01 Epub Date: 2026-02-01 DOI: 10.1016/j.camwa.2026.01.028

Lixian Zhao, Yeping Li

In this paper, we present first-order and second-order fully discrete finite element schemes for the Caginalp model with periodic boundary conditions. First, we derive the corresponding regularity estimates for the exact solution under different initial conditions, which are essential for subsequent numerical analysis. Next, based on these regularity results, we systematically analyze the energy stability of both schemes and rigorously derive error estimates, providing a theoretical justification for their advantages in terms of accuracy and stability. Finally, we perform numerical simulations to validate the theoretical results.

本文给出了具有周期边界条件的Caginalp模型的一阶和二阶完全离散有限元格式。首先，我们得到了不同初始条件下精确解的正则性估计，这对后续的数值分析至关重要。其次，基于这些规律性结果，我们系统地分析了两种方案的能量稳定性，并严格推导了误差估计，为它们在精度和稳定性方面的优势提供了理论依据。最后，通过数值模拟对理论结果进行验证。

引用次数: 0

Mathematical relationships and novel extensions of MLPG variants MLPG变体的数学关系和新扩展

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-03-01 Epub Date: 2026-01-10 DOI: 10.1016/j.camwa.2026.01.001

Elham Gholamipour , Ahmad Shirzadi , Hossein Hosseinzadeh , Vladimir Sladek , Jan Sladek

While various Meshless Local Petrov-Galerkin (MLPG) method variants exist, primarily distinguished by their choice of test functions in local subdomains, the mathematical relationships among these approaches remain unexplored. This paper establishes rigorous connections between existing MLPG formulations and proposes novel extensions based on an analysis of test function smoothness. It is shown that MLPG5, which employs Heaviside step test functions, corresponds to the mean value of MLPG2 (the collocation method), while MLPG4, using logarithmic test functions, is proven equivalent to the mean value of MLPG5 over the radius of local subdomains. Building on these insights, a systematic framework for generating new MLPG variants is introduced by leveraging the smoothness properties of test functions. All existing and newly proposed MLPG variants are demonstrated to have local weak forms equivalent to the original strong-form equations. This equivalence establishes the unique solvability of the methods, addressing long-standing questions regarding their consistency. Comprehensive numerical experiments validate the theoretical findings, confirming both the inter-variant relationships and the robustness of the newly extended MLPG variants.

虽然存在各种无网格局部Petrov-Galerkin （MLPG）方法变体，主要通过在局部子域中选择测试函数来区分，但这些方法之间的数学关系仍未被探索。本文建立了现有MLPG公式之间的严格联系，并在分析测试函数平滑性的基础上提出了新的扩展。结果表明，采用Heaviside步长测试函数的MLPG5与配置法的MLPG2均值相对应，而采用对数测试函数的MLPG4与局部子域半径上的MLPG5均值相对应。在这些见解的基础上，通过利用测试函数的平滑特性，引入了一个用于生成新的MLPG变体的系统框架。所有现有的和新提出的MLPG变体都证明具有与原始强形式方程等效的局部弱形式。这种等价建立了方法的唯一可解性，解决了关于其一致性的长期问题。综合数值实验验证了理论发现，证实了新扩展的MLPG变体之间的关系和鲁棒性。

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