Journal of Computational and Applied Mathematics最新文献

英文中文

Memory - and compute-optimized geometric multigrid GMGPolar for curvilinear coordinate representations – Applications to fusion plasma 曲线坐标表示的内存和计算优化几何多网格GMGPolar。在聚变等离子体中的应用

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-26 DOI: 10.1016/j.cam.2025.117308

Julian Litz , Philippe Leleux , Carola Kruse , Joscha Gedicke , Martin J. Kühn

Tokamak fusion reactors are actively studied as a means of realizing energy production from plasma fusion. However, due to the substantial cost and time required to construct fusion reactors and run physical experiments, numerical experiments are indispensable for understanding plasma physics inside tokamaks, supporting the design and engineering phase, and optimizing future reactor designs. Geometric multigrid methods are optimal solvers for many problems that arise from the discretization of partial differential equations. It has been shown that the multigrid solver GMGPolar solves the 2D gyrokinetic Poisson equation in linear complexity and with only small memory requirements compared to other state-of-the-art solvers. In this paper, we present a completely refactored and object-oriented version of GMGPolar which offers two different matrix-free implementations. Among other things, we leverage the Sherman-Morrison formula to solve cyclic tridiagonal systems from circular line solvers without additional fill-in and we apply reordering to optimize cache access of circular and radial smoothing operations. With the Give approach, memory requirements are further reduced and speedups of four to seven are obtained for usual test cases. For the Take approach, speedups of 16 to 18 can be attained. In an additionally experimental setup of using GMGPolar as a preconditioner for conjugate gradients, this speedup could even be increased to factors between 25 and 37.

托卡马克聚变反应堆作为一种实现等离子体聚变发电的手段正在积极研究中。然而，由于建造聚变反应堆和运行物理实验需要大量的成本和时间，数值实验对于理解托卡马克内部的等离子体物理，支持设计和工程阶段，以及优化未来的反应堆设计是必不可少的。几何多重网格法是许多由偏微分方程离散化引起的问题的最优解。研究表明，与其他最先进的求解器相比，多网格求解器GMGPolar解决了线性复杂性的二维陀螺动力学泊松方程，并且只需要很小的内存要求。在本文中，我们提出了一个完全重构和面向对象的GMGPolar版本，它提供了两种不同的无矩阵实现。除此之外，我们利用Sherman-Morrison公式从圆线求解器求解循环三对角线系统，而无需额外填充，我们应用重新排序来优化圆和径向平滑操作的缓存访问。使用Give方法，内存需求进一步降低，并且对于通常的测试用例可以获得4到7的加速。对于Take方法，可以达到16到18的加速。在使用GMGPolar作为共轭梯度的前置条件的另一个实验设置中，这种加速甚至可以增加到25到37倍之间。

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引用次数: 0

Adaptive FEM with explicit time integration for the wave equation 波动方程的显式时间积分自适应有限元法

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-26 DOI: 10.1016/j.cam.2025.117272

Marcus J. Grote , Omar Lakkis , Carina S. Santos

Starting from a recent a posteriori error estimator for the finite element solution of the wave equation with explicit time-stepping [Grote, Lakkis, Santos, 2024], we devise a space-time adaptive strategy which includes both time evolving meshes and local time-stepping [Diaz, Grote, 2009] to overcome any overly stringent CFL stability restriction on the time-step due to local mesh refinement. Moreover, at each time-step the adaptive algorithm monitors the accuracy thanks to the error indicators and recomputes the current step on a refined mesh until the desired tolerance is met; meanwhile, the mesh is coarsened in regions of smaller errors. Leapfrog based local time-stepping is applied in all regions of local mesh refinement to incorporate adaptivity into fully explicit time integration with mesh change while retaining efficiency. Numerical results illustrate the optimal rate of convergence of the a posteriori error estimators on time evolving meshes.

从最近的显式时间步进波动方程有限元解的后验误差估计器[Grote， Lakkis, Santos， 2024]开始，我们设计了一种时空自适应策略，其中包括时间演化网格和局部时间步进[Diaz， Grote, 2009]，以克服由于局部网格优化而对时间步长的任何过于严格的CFL稳定性限制。此外，在每个时间步长，自适应算法通过误差指标监测精度，并在细化网格上重新计算当前步长，直到满足所需的公差；同时，对误差较小的区域进行网格粗化处理。在局部网格细化的所有区域采用基于跨越式的局部时间步进，在保持效率的同时，将自适应融入到网格变化的完全显式时间积分中。数值结果表明，后验误差估计器在时间演化网格上具有最优的收敛速度。

引用次数: 0

Efficient construction of clothoidal splines using corotational beam splines 利用同向梁样条高效构建梭形样条

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-25 DOI: 10.1016/j.cam.2025.117318

Igor Orynyak, Yurii Kuznetsov, Danylo Tavrov

Corotational beam splines (CBS) further develop the ideas of beam splines theories that flourished towards the end of the 20th century. CBS adopt the idea of Fowler and Wilson, whereby the conventional explicit or parametric representation of the dependence between spline coordinates is replaced with an implicit formulation through the introduction of local coordinate systems associated with the segments between consecutive control points. In the context of the problem of interpolation, our principal refinement of the Fowler-Wilson scheme is the insertion of dummy points between the real ones, thereby ensuring that the angles between the local coordinate systems are small enough. This enables us to employ the usual structural mechanics hypothesis that the sine of a small angle is approximately equal to its tangent and to the angle itself. Constructed in this manner, the CBS consists of the segments of clothoid placed between the real points. The clothoid is widely regarded as a curve both aesthetic appeal and a broad practical utility. However, the construction of clothoidal splines in practice requires specific numerical methods, whereas our CBS framework offers an easy and efficient alternative. We study whether the CBS can replace the clothoid in its traditional applications, focusing on the task of constructing clothoidal splines between two points with prescribed tangents and curvatures. A further major contribution of the paper is the generalization of all beam spline techniques, including CBS, by allowing for an additional third boundary condition, achieved at the cost of relaxing third-derivative continuity at certain dummy points.

旋转束样条（CBS）进一步发展了20世纪末蓬勃发展的束样条理论。CBS采用了Fowler和Wilson的思想，即通过引入与连续控制点之间的线段相关的局部坐标系，将传统的样条坐标之间依赖关系的显式或参数化表示替换为隐式表述。在插值问题的背景下，我们对Fowler-Wilson方案的主要改进是在真实点之间插入假点，从而确保局部坐标系之间的角度足够小。这使我们能够采用通常的结构力学假设，即一个小角的正弦近似等于它的正切和这个角本身。以这种方式构造，CBS由放置在实点之间的仿线段组成。clodroid被广泛认为是一种具有美学吸引力和广泛实用价值的曲线。然而，在实践中，梭线样条的构造需要特定的数值方法，而我们的CBS框架提供了一个简单而有效的替代方法。在传统的应用中，我们研究了CBS是否可以取代cloclooid，重点研究了在具有指定切线和曲率的两点之间构造cloclooid样条的任务。本文的另一个主要贡献是通过允许额外的第三个边界条件来推广包括CBS在内的所有束样条技术，其代价是在某些虚拟点上放松三阶导数的连续性。

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引用次数: 0

A comparative study of two semi-analytical techniques for MHD viscous flow over a stretching sheet: Fusion of integral transform and homotopy perturbation method 拉伸薄板上MHD粘性流动的两种半解析方法的比较研究：积分变换融合和同伦摄动法

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-25 DOI: 10.1016/j.cam.2025.117323

Deepak Kumar

The investigation of magnetohydrodynamic (MHD) boundary layer flow over a stretching sheet is of significant interest due to its wide-ranging applications in engineering and industrial processes. This study presents a comparative analysis of two efficient semi-analytical approaches-the Shehu Transform and the Elzaki Transform-each integrated with the Homotopy Perturbation Method (HPM) to solve the governing nonlinear flow equations. The proposed hybrid schemes, Shehu–HPM and Elzaki–HPM, exhibit remarkable computational efficiency, simplicity of implementation, and accuracy in generating rapidly convergent series solutions without discretization or linearization errors. The consistency of both techniques is validated through dual-solution pathways, demonstrating excellent agreement and underscoring the necessity of parallel analytical verification in nonlinear flow computations. Graphical interpretations reveal that the dimensionless stream function

f

increases with an enhancement in the magnetic parameter

M

(ranging from 0.1 to 900) for fixed stretching parameter

β

and initial condition

α

. Furthermore, the solution maintains stability at smaller time scales before transitioning to a growth regime at larger time values. Overall, the findings affirm the robustness, reliability, and complementary nature of the Shehu–HPM and Elzaki–HPM formulations in modeling complex MHD flow phenomena.

由于磁流体动力学（MHD）边界层在工程和工业过程中的广泛应用，研究在拉伸板上的边界层流动具有重要的意义。本文比较分析了两种有效的半解析方法- Shehu变换和Elzaki变换-分别与同伦摄动法（HPM）相结合来求解控制非线性流动方程。所提出的混合方案Shehu-HPM和Elzaki-HPM具有显著的计算效率、实现简单和生成快速收敛的序列解的准确性，且没有离散化或线性化误差。通过双解路径验证了这两种技术的一致性，证明了良好的一致性，并强调了在非线性流动计算中并行分析验证的必要性。图形解释表明，在固定拉伸参数β和初始条件α下，无量纲流函数f随着磁参数M（范围从0.1到900）的增大而增大。此外，该解决方案在较小的时间尺度上保持稳定性，然后在较大的时间尺度上过渡到增长状态。总体而言，研究结果证实了Shehu-HPM和Elzaki-HPM公式在模拟复杂MHD流动现象方面的鲁棒性、可靠性和互补性。

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引用次数: 0

A posteriori error estimates of the weak Galerkin finite element method for time-dependent Poisson-Nernst-Planck equations 时变泊松-能-普朗克方程弱伽辽金有限元法的后验误差估计

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-25 DOI: 10.1016/j.cam.2025.117284

Wanwan Zhu , Guanghua Ji

Our research focused on the adaptive weak Galerkin finite element method to solve the time-dependent Poisson-Nernst-Planck (PNP) equations. Through the utilization of the Helmholtz decomposition and elliptic reconstruction operator, a comprehensive analysis of a posteriori error estimates was conducted. Both the upper and lower bound error estimators for the electrostatic potential and ion concentrations were formulated, taking into account both spatial and temporal residuals. A time-step adaptation strategy was developed to adjust the time step, followed by the development of a temporal and spatial adaptive algorithm for solving the time-dependent PNP equations using the constructed a posteriori error estimators. The validity of our methodology was confirmed through numerical simulations.

本文主要研究了求解时变泊松-能-普朗克（PNP）方程的自适应弱伽辽金有限元方法。利用亥姆霍兹分解和椭圆重构算子，对后验误差估计进行了综合分析。在考虑了空间和时间残差的情况下，给出了静电电位和离子浓度的上下限误差估计。提出了一种时间步长自适应策略来调整时间步长，然后利用构建的后验误差估计器开发了一种时空自适应算法来求解时间相关的PNP方程。通过数值模拟验证了本文方法的有效性。

引用次数: 0

Hesitant fuzzy time series forecasting: A novel approach to handle the hesitancy in the system 犹豫模糊时间序列预测：一种处理系统犹豫性的新方法

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-25 DOI: 10.1016/j.cam.2025.117322

Kamlesh Bisht , Sanjay Kumar , Manish Pant , Seema Negi

A fuzzy set lacks to determine the hesitancy of an element in terms of belongingness to a set, the same problem arises in forecasting time series data by the fuzzy set when there is the availability of multiple fuzzification methods to fuzzify the time series data to remove hesitancy in the system. In the present study, the HFS has been applied in time series forecasting and a HFTSF method is proposed by introducing essential concepts of weighted hesitant fuzzy Cartesian product, HFR, HFLRs, HFLGs and hesitant fuzzy defuzzification method. The basic steps followed in the mechanism of the proposed method are the construction of HFS by a partition of the UOD into intervals of equal and unequal length, distribution of weights based on the length of the interval, fuzzification of the data by using triangular membership function for equal and unequal intervals, construction of HFLRs and HFLGs, relation matrix obtained by weighted hesitant fuzzy Cartesian product, computation of hesitant fuzzy row vectors by max-min composition operation and finally hesitant defuzzification of the data. The proposed method is implemented over the enrollment data of the University of Alabama and the share price of SBI at Bombay stock exchange, India. Performance test, validity test, and statistical test are also examined on the forecasted value by the proposed method and well-known existing methods to examine the superiority of the proposed method. This article presents a novel prediction model that authentically captures methodological hesitancy which were absent in prior HFS based forecasting models due to reliant on aggregation operator that transform HFS into conventional fuzzy set. By directly formulating HFLRs through a weighted Cartesian product, our framework eliminates information loss. The model delivers a triple advantage: it maintain complete information integrity, guaranteeing interpretablity through a transparent calculus, and demonstrating superior accuracy and robustness against existing benchmarks in hesitant environment.

模糊集无法确定元素是否属于一个集合，当有多种模糊化方法可以模糊化时间序列数据以消除系统中的犹豫性时，用模糊集预测时间序列数据也会出现同样的问题。本研究将HFS应用于时间序列预测，并引入加权犹豫模糊笛卡尔积、HFR、HFLRs、HFLGs和犹豫模糊去模糊化等基本概念，提出了一种HFTSF方法。该方法的基本步骤是：将UOD划分为等长和不等长的区间来构造HFS，根据区间的长度分配权值，对等长和不等长的区间使用三角隶属函数对数据进行模糊化，构造hflr和hflg，通过加权犹豫模糊笛卡尔积得到关系矩阵，通过最大最小组合运算计算犹豫模糊行向量，最后对数据进行犹豫去模糊化。该方法以阿拉巴马大学的招生数据和印度孟买证券交易所的SBI股票价格为例进行了实现。并对所提方法的预测值进行了性能检验、效度检验和统计检验，以检验所提方法的优越性。本文提出了一种新的预测模型，该模型真实地捕捉了先前基于HFS的预测模型中由于依赖于将HFS转换为传统模糊集的聚合算子而缺乏的方法犹豫。通过通过加权笛卡尔积直接制定hflr，我们的框架消除了信息丢失。该模型提供了三重优势：它保持完整的信息完整性，通过透明的演算保证可解释性，并在犹豫环境中对现有基准显示出卓越的准确性和鲁棒性。

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引用次数: 0

Stabilizer-free weak galerkin methods for quad-Curl problems on polyhedral meshes without convexity assumptions 无凸性假设的多面体网格四旋度问题的无稳定器弱伽辽金方法

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-25 DOI: 10.1016/j.cam.2025.117279

Chunmei Wang , Shangyou Zhang

This paper introduces an efficient stabilizer-free weak Galerkin (WG) finite element method for solving the three-dimensional quad-curl problem. Leveraging bubble functions as a key analytical tool, the method extends the applicability of stabilizer-free WG approaches to non-convex elements in finite element partitions-a notable advancement over existing methods, which are restricted to convex elements. The proposed method maintains a simple, symmetric, and positive definite formulation. It achieves optimal error estimates for the exact solution in a discrete norm, as well as an optimal-order L² error estimate for k > 2 and a sub-optimal order for the lowest order case

k = 2

. Numerical experiments are presented to validate the method’s efficiency and accuracy.

介绍了求解三维四旋度问题的一种有效的无稳定器弱伽辽金（WG）有限元法。利用气泡函数作为关键的分析工具，该方法将无稳定器的WG方法扩展到有限元分区中的非凸单元的适用性-与现有方法相比，这是一个显着的进步，它仅限于凸单元。所提出的方法保持了一个简单、对称和正定的公式。它实现了离散范数精确解的最优误差估计，以及k >； 2的最优阶L2误差估计和最低阶k=2的次优阶。通过数值实验验证了该方法的有效性和准确性。

引用次数: 0

Numerical Hopf–Lax formulae for Hamilton–Jacobi equations on unstructured geometries 非结构几何上Hamilton-Jacobi方程的数值Hopf-Lax公式

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-24 DOI: 10.1016/j.cam.2025.117309

S. Cacace , R. Ferretti , G. Tatafiore

We consider a scheme of Semi-Lagrangian (SL) type for the numerical solution of Hamilton–Jacobi (HJ) equations on unstructured triangular grids. As it is well known, SL schemes are not well suited for unstructured grids, due to the cost of the point location phase; this drawback is augmented by the need for repeated minimization. In this work, we consider an existing, monotone version of the scheme, that works only on the basis of node values, and adapt the algorithm to the case of an unstructured grid, using the connectivity information. Then, applying a quadratic refinement to the numerical solution, we improve accuracy at the price of some extra computational cost. The scheme can be applied to both time-dependent and stationary HJ equations; in the latter case, we also study the construction of a fast policy iteration solver and of a parallel version. We perform a theoretical analysis of the two versions, and validate them with an extensive set of examples, both in the time-dependent and in the stationary case.

研究了半拉格朗日（SL）型的Hamilton-Jacobi （HJ）方程在非结构三角网格上的数值解。众所周知，由于点定位阶段的成本，SL方案不太适合非结构化电网；由于需要重复最小化，这一缺点更加突出。在这项工作中，我们考虑了该方案的现有单调版本，该方案仅基于节点值工作，并使用连通性信息使算法适应非结构化网格的情况。然后，对数值解进行二次细化，以一些额外的计算成本为代价提高精度。该格式既适用于时变HJ方程，也适用于平稳HJ方程；在后一种情况下，我们还研究了快速策略迭代求解器和并行版本的构造。我们对这两个版本进行了理论分析，并通过大量的例子验证了它们，无论是在时间相关的情况下还是在平稳的情况下。

引用次数: 0

Well -posedness of coupled Navier-Stokes and advection-diffusion equations for propagation of reaction fronts in viscous fluids 粘性流体中反应锋面传播的Navier-Stokes和平流-扩散耦合方程的适定性

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-24 DOI: 10.1016/j.cam.2025.117277

Mofdi El-Amrani , Anouar Obbadi , Mohammed Seaid , Driss Yakoubi

In this paper, we investigate a steady system used for modelling propagation of reaction fronts in viscous fluids subject to a generalized Arrhenius law. The model consists of the incompressible Navier-Stokes equations for the fluid flow and a set of advection-diffusion equations for the temperature and degree of conversion. The resulting system is strongly coupled and presents many additional nonlinearities as the physical parameters such as the viscosity, diffusion and source terms are assumed to depend on the temperature and/or degree of conversion. Using a fixed-point method we prove the existence and uniqueness of the weak solution for the considered problem. To solve the associated fixed-point problem we consider an iterative scheme and its convergence is also studied in the present study. Here, the proposed scheme uncouples the computation of velocity, temperature and degree of conversion using the fixed-point iteration and we theoretically establish its convergence towards the unique solution of the considered model. Numerical results obtained for two test examples are presented to verify the theoretical analysis and to assess the performance of the proposed algorithm. The obtained computational results for both examples support the theoretical expectations for a good numerical convergence with the developed estimates.

在本文中，我们研究了一个稳定系统，用于模拟反应锋面在粘滞流体中受广义Arrhenius定律约束的传播。该模型由流体流动的不可压缩Navier-Stokes方程和温度和转换度的平流-扩散方程组成。由此产生的系统是强耦合的，并且由于假定粘度、扩散和源项等物理参数依赖于温度和/或转换程度，因此呈现出许多额外的非线性。利用不动点法证明了所考虑问题弱解的存在唯一性。为了解决相关的不动点问题，我们考虑了一种迭代格式，并研究了它的收敛性。本文提出的方案利用不动点迭代解耦了速度、温度和转换度的计算，并从理论上证明了其收敛于所考虑模型的唯一解。给出了两个测试实例的数值结果，以验证理论分析和评估所提算法的性能。这两个算例的计算结果都支持了理论期望，与所开发的估计具有良好的数值收敛性。

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引用次数: 0

Applying fixed point approaches for solving non-autonomous integrodifferential evolution equations under mild conditions 应用不动点法求解温和条件下非自治积分微分演化方程

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-24 DOI: 10.1016/j.cam.2025.117295

Hasanen A. Hammad , Manal Elzain Mohamed Abdalla

The existence of solutions for non-autonomous integrodifferential evolution equations with nonlocal conditions is investigated in this article. Initially, existence results for mild solutions of the proposed equation are established through the leveraging of the theory of resolvent operators, fixed point theorems, and an estimation technique grounded in the measure of noncompactness. Finally, the applicability of the findings is illustrated by means of an example concerning a class of non-autonomous nonlocal partial integrodifferential equations.

研究了一类具有非局部条件的非自治积分微分演化方程解的存在性。首先，利用可解算子理论、不动点定理和基于非紧性测度的估计技术，建立了所提方程温和解的存在性结果。最后，通过一类非自治非局部偏积分微分方程的算例说明了所得结果的适用性。

引用次数: 0

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