Computers & Mathematics with Applications最新文献

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Conformal mapping based Physics-informed neural networks for designing neutral inclusions 基于保角映射的物理信息神经网络设计中性包裹体

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-02-01 DOI: 10.1016/j.camwa.2026.01.026

Daehee Cho, Hyeonmin Yun, Jae Yong Lee, Mikyoung Lim

引用次数: 0

Stability and convergence of high-order WENO-OS scheme for the Allen-Cahn equation Allen-Cahn方程高阶WENO-OS格式的稳定性和收敛性

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-02-01 DOI: 10.1016/j.camwa.2026.01.030

Chun-Hua Zhang, Long Kuang, Wen-Ping Yuan, Xiang Wang

引用次数: 0

An enhanced MQRBF-FD method with parallel computing and multiscale modeling for efficient elastic wave propagation 基于并行计算和多尺度建模的改进MQRBF-FD弹性波高效传播方法

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-02-01 DOI: 10.1016/j.camwa.2026.01.029

Jian Sun, Wenshuai Wang

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 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

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

Lixian Zhao, Yeping Li

引用次数: 0

An optimal ADMM for the contact problem between membranes 膜间接触问题的最佳ADMM

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-31 DOI: 10.1016/j.camwa.2026.01.034

Shougui Zhang, Cairong Li, Yulu Duan

引用次数: 0

Solving the Monge-Ampère equation via Poisson series physics-informed neural networks and its convergence analysis 利用泊松系列物理信息神经网络求解monge - ampantere方程及其收敛性分析

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-30 DOI: 10.1016/j.camwa.2026.01.033

Ruibo Zhang , Fengjun Li , Jianqiang Liu

The Monge-Ampère equation is originated from geometric surface theory and is widely applied in optimal transport theory, image processing, optimization problem and so on. The numerical solution of the Monge-Ampère equation has recently attracted more and more attention. Physics-informed neural networks (PINNs), a new paradigm in numerical methods, introduce physical constraints during the training process so that the model not only can learn patterns in the data, but also satisfy the laws of physics. In our work, we try to solve the Monge-Ampère equation with Dirichlet boundary conditions by using the PINNs. To our knowledge, this is the first time that PINNs is applied to solve the Monge-Ampère equation. Unfortunately, the Monge-Ampère equation involves determinant calculation, which leads to calculation failure using the conventional PINNs. For this reason, inspired by the fixed-point method, we construct a Poisson series physics-informed neural networks (PS-PINNs) framework to solve this problem. The Monge-Ampère equation is transformed into a Poisson series using the fixed-point method, which avoids the direct computation of the determinant. As part of our analysis, we prove the convergence of loss function and neural networks in PS-PINNs. Moreover, we study the performance of PS-PINNs with source functions containing singularities and noise, as well as in asymmetric domains. It is worth noting that we can obtain better numerical results using a small number of sampling points and iterations. The data and code accompanying this paper are publicly available at https://github.com/RuiboZhangping/PSPINN.

monge - ampantere方程起源于几何曲面理论，广泛应用于最优输运理论、图像处理、优化问题等领域。monge - ampantere方程的数值解近年来受到越来越多的关注。物理信息神经网络（pinn）是数值方法中的一种新范式，它在训练过程中引入物理约束，使模型不仅能够学习数据中的模式，而且能够满足物理定律。在我们的工作中，我们尝试用pinn来求解具有Dirichlet边界条件的monge - amp方程。据我们所知，这是pin - ns第一次被应用于求解monge - ampante方程。不幸的是，monge - ampantere方程涉及行列式计算，这导致使用传统的pin n计算失败。因此，受不动点法的启发，我们构建了一个泊松系列物理信息神经网络（ps - pinn）框架来解决这个问题。采用不动点法将monge - ampantere方程转化为泊松级数，避免了行列式的直接计算。作为分析的一部分，我们证明了ps - pinn中损失函数和神经网络的收敛性。此外，我们还研究了源函数包含奇异点和噪声以及非对称域的ps - pin的性能。值得注意的是，我们可以使用少量的采样点和迭代获得更好的数值结果。本文附带的数据和代码可在https://github.com/RuiboZhangping/PSPINN上公开获取。

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引用次数: 0

A positive and asymptotic preserving scheme for the linear transport equation on 2D unstructured meshes 二维非结构网格上线性输运方程的正渐近保持格式

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-29 DOI: 10.1016/j.camwa.2026.01.023

Clément Lasuen

In this paper, we propose a finite volume scheme for the linear transport equation in two space dimensions. This scheme is based on a second order upwind flux where the velocity is modified so as to recover the correct diffusion limit. A partially implicit time discretization is used. This allows to have good properties while keeping the computational cost per iteration very low. The resulting scheme is asymptotic preserving, positive under a classical CFL condition, conservative and second order consistent in all the regimes. These properties are valid on general unstructured meshes and the computational cost is similar to an explicit scheme. Eventually, the extension of this scheme to 3D unstructured meshes is straightforward and its properties remain valid.

本文提出了二维线性输运方程的有限体积格式。该方案基于二阶迎风通量，其中速度被修改以恢复正确的扩散极限。采用部分隐式时间离散化。这允许在保持每次迭代的计算成本非常低的同时拥有良好的属性。所得到的格式是渐近保持的，在经典CFL条件下是正的，在所有情况下是保守的和二阶一致的。这些特性在一般的非结构化网格上是有效的，计算成本与显式方案相似。最终，将该方案扩展到三维非结构化网格是简单的，其性质仍然有效。

引用次数: 0

Uncertainty analysis framework of MPS and implementation in the simulation of MCCI phenomenon MPS的不确定性分析框架及其在MCCI现象模拟中的实现

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-28 DOI: 10.1016/j.camwa.2026.01.031

Xinkun Xiao , Qinghang Cai , Tianrui Li , Ronghua Chen , Guanghui Su

This study establishes the Moving Particle Semi-implicit Plus Uncertainty (MPSPU) framework to enable rigorous uncertainty quantification (UQ) for particle-based simulations in nuclear reactor safety analysis. Designed to extend the Best Estimate Plus Uncertainty (BEPU) methodology, MPSPU addresses the specific challenges of Lagrangian particle methods while maintaining compatibility with existing regulatory assessment protocols. The framework is validated using the SURC-4 experiment, which simulates the Molten Core–Concrete Interaction (MCCI) phenomenon. A critical advancement is the formulation of a time-dependent sensitivity analysis, which reveals that melt temperature is the dominant driver governing early-stage MCCI behavior. Furthermore, a comparative evaluation of surrogate models for MPS time-series data identifies Long Short-Term Memory (LSTM) networks as the optimal architecture, outperforming conventional polynomial and neural network approaches. To demonstrate the framework's practical utility, an end-to-end calculation example is presented, illustrating the complete workflow from raw simulation data to regulatory-grade risk metrics. This example explicitly quantifies the conditional failure probability of concrete ablation depth against safety limits, showcasing the framework's ability to support risk-informed decision-making. Ultimately, this work provides a systematic pathway for integrating particle methods into safety analysis.

本研究建立了移动粒子半隐式加不确定性（MPSPU）框架，为核反应堆安全分析中基于粒子的模拟提供严格的不确定性量化（UQ）。MPSPU旨在扩展最佳估计加不确定性（BEPU）方法，解决拉格朗日粒子方法的特定挑战，同时保持与现有监管评估协议的兼容性。使用SURC-4实验对该框架进行了验证，该实验模拟了熔融核-混凝土相互作用（MCCI）现象。一个关键的进步是制定了一个时间依赖的敏感性分析，这表明熔体温度是控制早期MCCI行为的主要驱动因素。此外，对MPS时间序列数据的替代模型进行了比较评估，发现长短期记忆（LSTM）网络是最优架构，优于传统的多项式和神经网络方法。为了展示该框架的实用性，本文给出了一个端到端计算示例，说明了从原始模拟数据到监管级风险指标的完整工作流程。这个例子明确地量化了混凝土消融深度相对于安全限制的条件失效概率，展示了框架支持风险知情决策的能力。最终，这项工作为将粒子方法整合到安全分析中提供了一个系统的途径。

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引用次数: 0

A novel evolutionary model using the Caputo time-fractional derivative and noise estimator for image denoising and contrast enhancement 一种基于卡普托时间分数阶导数和噪声估计的图像去噪和对比度增强的进化模型

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-24 DOI: 10.1016/j.camwa.2026.01.006

Anouar Ben-Loghfyry , Abderrahim Charkaoui , Anass Bouchriti , Nour Eddine Alaa

This paper proposes a novel fractional nonlinear parabolic model based on Caputo time-fractional derivative, designed to enhance the classical Perona-Malik model for image denoising and contrast improvement. A regularized diffusion mechanism is incorporated to control the diffusion rate and direction locally. The well-posedness of the model is analyzed, and two main existence results for weak solutions are established. The first, under a bounded reaction term, is proved using Schauder’s fixed-point theorem; the second, involving a nonlinear and weakly regular source term, ensures the existence of a weak SOLA solution via approximation techniques and new technical estimates. Numerical experiments on grayscale and MRI images validate the robustness and efficiency of the proposed model under various noise levels. The results show superior denoising and enhancement performance compared to state-of-the-art methods, preserving natural appearance and minimizing artifacts. This confirms the model’s potential for high-precision image restoration applications.

本文提出了一种基于Caputo时间-分数阶导数的分数阶非线性抛物模型，旨在对经典的Perona-Malik模型进行图像去噪和对比度改善。引入正则化扩散机制，局部控制扩散速率和扩散方向。分析了模型的适定性，建立了弱解的两个主要存在性结果。第一类，在有界反应项下，用Schauder不动点定理证明；第二，涉及一个非线性和弱正则源项，通过近似技术和新的技术估计确保弱SOLA解的存在。在灰度图像和MRI图像上的数值实验验证了该模型在不同噪声水平下的鲁棒性和有效性。结果显示，与最先进的方法相比，具有优越的去噪和增强性能，保留了自然外观并最大限度地减少了人工制品。这证实了该模型在高精度图像恢复应用中的潜力。

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引用次数: 0

Error estimates of the weak Galerkin mixed finite element method for parabolic interface problems 抛物界面问题的弱Galerkin混合有限元法误差估计

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2026-01-24 DOI: 10.1016/j.camwa.2026.01.024

Amit Kumar Pal , Jhuma Sen Gupta , Rajen Kumar Sinha

This paper aims to study a priori error analysis of the weak Galerkin mixed finite element method (WG-MFEM) for parabolic interface problems in a two-dimensional bounded convex polygonal domain. While discontinuous functions are employed for the approximation of spatial variable, an implicit backward Euler scheme is used for the time variable. Due to the presence of the discontinuous coefficient across the interface, the solution of parabolic interface problems possesses very low global regularity. Using the Stein extension operator and the H¹(div)-extension operator leads to the novel approximation results for the L² projection operators for both the scalar and the vector-valued functions, respectively. With the help of mixed elliptic projection operator and the new approximation properties combined with the standard energy argument, an almost optimal order a priori error bounds are derived for both the solution and the flux variables in the L^∞(L²) norm. Numerical outcomes for some test problems are reported to confirm the theoretical analysis.

本文研究了二维有界凸多边形区域中抛物界面问题的弱Galerkin混合有限元法的先验误差分析。空间变量采用不连续函数逼近，时间变量采用隐式后向欧拉格式逼近。由于界面上存在不连续系数，抛物型界面问题的解具有很低的全局正则性。使用Stein扩展算子和H1(div)-扩展算子分别可以得到标量函数和向量值函数的L2投影算子的新的近似结果。利用混合椭圆投影算子和新的近似性质，结合标准能量参数，导出了L∞(L2)范数上的解和通量变量的几乎最优阶先验误差界。文中还报道了一些试验问题的数值结果，以证实理论分析。

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引用次数: 0

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