Computers & Mathematics with Applications最新文献_第4页

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 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-04-01 Epub Date: 2026-02-01 DOI: 10.1016/j.camwa.2026.01.029

Jian Sun , Wenshuai Wang

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

Computers & Mathematics with Applications Pub Date : 2026-04-01 Epub Date: 2026-01-24 DOI: 10.1016/j.camwa.2026.01.024

Amit Kumar Pal , Jhuma Sen Gupta , Rajen Kumar Sinha

{"title":"Error estimates of the weak Galerkin mixed finite element method for parabolic interface problems","authors":"Amit Kumar Pal , Jhuma Sen Gupta , Rajen Kumar Sinha","doi":"10.1016/j.camwa.2026.01.024","DOIUrl":"10.1016/j.camwa.2026.01.024","url":null,"abstract":"<div><div>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 <strong><em>H</em></strong><sup>1</sup>(div)-extension operator leads to the novel approximation results for the <em>L</em><sup>2</sup> 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 <em>L</em><sup>∞</sup>(<em>L</em><sup>2</sup>) norm. Numerical outcomes for some test problems are reported to confirm the theoretical analysis.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"207 ","pages":"Pages 94-115"},"PeriodicalIF":2.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025840","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

Symmetric direct discontinuous Galerkin method for the biharmonic equation with non-homogeneous boundary condition 非齐次边界条件双调和方程的对称直接不连续Galerkin方法

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-04-01 Epub Date: 2026-01-19 DOI: 10.1016/j.camwa.2026.01.010

Hongying Huang , Huanhuan Wang , Lin Zhang

{"title":"Symmetric direct discontinuous Galerkin method for the biharmonic equation with non-homogeneous boundary condition","authors":"Hongying Huang , Huanhuan Wang , Lin Zhang","doi":"10.1016/j.camwa.2026.01.010","DOIUrl":"10.1016/j.camwa.2026.01.010","url":null,"abstract":"<div><div>The direct discontinuous Galerkin method is proposed and analyzed for the biharmonic equation with non-homogeneous boundary conditions. Numerical fluxes on all edges of arbitrary triangles are defined, which are concerned with four parameters (<em>β</em><sub>1</sub>, <em>β</em><sub>2</sub>, <em>β</em><sub>3</sub>, <em>β</em><sub>4</sub>), and then the weak variational form of the original problem is derived. The corresponding bilinear form is proved to be bounded and coercive for sufficiently large values of the parameters <em>β</em><sub>1</sub> and <em>β</em><sub>2</sub>. The well-posedness of the variational problem in finite element space <span><math><msubsup><mi>V</mi><mi>h</mi><mi>k</mi></msubsup></math></span> and optimal error estimates of the approximate solution under <em>L</em><sup>2</sup>-norm and energy norm are obtained. The accuracy and reliability of the proposed method were verified through numerical experiments. Although the theoretical analysis requires the solution <em>u</em> ∈ <em>H</em><sup>4</sup>, numerical results indicate that the method remains effective for solutions with low regularity.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"207 ","pages":"Pages 27-40"},"PeriodicalIF":2.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145996273","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

Lattice-Boltzmann-inspired finite-difference schemes for the convection-diffusion equation 对流扩散方程的格子-玻尔兹曼激励有限差分格式

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-04-01 Epub Date: 2026-02-24 DOI: 10.1016/j.camwa.2026.02.008

Xingchun Xu , Yurong He , Bing Dai , Jiaqi Zhu

引用次数: 0

EM propagation analysis of multilayered fully anisotropic media with an efficacious model equivalent approach 基于有效模型等效方法的多层全各向异性介质电磁传播分析

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-04-01 Epub Date: 2026-01-23 DOI: 10.1016/j.camwa.2026.01.022

Huan Wang , Naixing Feng , Chong-Zhi Han , Jinfeng Zhu , Lixia Yang , Atef Z. Elsherbeni

{"title":"EM propagation analysis of multilayered fully anisotropic media with an efficacious model equivalent approach","authors":"Huan Wang , Naixing Feng , Chong-Zhi Han , Jinfeng Zhu , Lixia Yang , Atef Z. Elsherbeni","doi":"10.1016/j.camwa.2026.01.022","DOIUrl":"10.1016/j.camwa.2026.01.022","url":null,"abstract":"<div><div>In this paper, the model equivalent approach is developed for full-wave analysis of electromagnetic propagation in multilayered fully anisotropic lossy media. In the process of geometric simulation, the 3D planar layered model is projected onto an axial stratified structure, effectively reducing spatial complexity. Then, the mesh free scheme is adopted for discretization, thus significantly decreasing the resource consumption. To accommodate generalized electromagnetic media, the governing equation for the electric field is formulated based on fully anisotropic media, characterized by full tensor parameters. The Galerkin method is employed to generate weak form partial differential equations (PDEs), then, the FEM is adopted to address the equations. To ensure accuracy in the FEM implementation, the divergence condition is imposed as a constraint on the PDEs, effectively eliminating spurious solutions from the computational domain. Finally, three numerical examples are presented to verify the effectiveness of the proposed method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"207 ","pages":"Pages 79-93"},"PeriodicalIF":2.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025839","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

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

Computers & Mathematics with Applications Pub Date : 2026-04-01 Epub Date: 2026-01-28 DOI: 10.1016/j.camwa.2026.01.031

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

{"title":"Uncertainty analysis framework of MPS and implementation in the simulation of MCCI phenomenon","authors":"Xinkun Xiao , Qinghang Cai , Tianrui Li , Ronghua Chen , Guanghui Su","doi":"10.1016/j.camwa.2026.01.031","DOIUrl":"10.1016/j.camwa.2026.01.031","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"207 ","pages":"Pages 116-136"},"PeriodicalIF":2.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072046","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

Unconditional uniform superconvergent error estimates of anisotropic nonconforming energy-dissipative SAV-CN FEM for fourth-order singular perturbation Bi-flux diffusion model 四阶奇异摄动双通量扩散模型各向异性非协调能量耗散SAV-CN有限元的无条件一致超收敛误差估计

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-04-01 Epub Date: 2026-01-20 DOI: 10.1016/j.camwa.2026.01.012

Dongyang Shi , Sihui Zhang

{"title":"Unconditional uniform superconvergent error estimates of anisotropic nonconforming energy-dissipative SAV-CN FEM for fourth-order singular perturbation Bi-flux diffusion model","authors":"Dongyang Shi , Sihui Zhang","doi":"10.1016/j.camwa.2026.01.012","DOIUrl":"10.1016/j.camwa.2026.01.012","url":null,"abstract":"<div><div>This investigation aims to delve into the unconditional uniform superconvergence behavior of the scalar auxiliary variable (SAV) Crank-Nicolson (CN) fully discrete scheme for the fourth-order singular perturbation Bi-flux diffusion equation with anisotropic constrained nonconforming rotated <span><math><msub><mi>Q</mi><mn>1</mn></msub></math></span> (<span><math><mrow><mi>C</mi><mi>N</mi><msubsup><mi>Q</mi><mrow><mn>1</mn></mrow><mrow><mi>r</mi><mi>o</mi><mi>t</mi></mrow></msubsup></mrow></math></span>) finite element method (FEM). Innovative high-accuracy estimates tailored specifically for the <span><math><mrow><mi>C</mi><mi>N</mi><msubsup><mi>Q</mi><mrow><mn>1</mn></mrow><mrow><mi>r</mi><mi>o</mi><mi>t</mi></mrow></msubsup></mrow></math></span> element on anisotropic meshes are established as the cornerstone for achieving superconvergent outcomes. Following this, a novel SAV-CN scheme is formulated, with the energy dissipation theoretically given to guarantee that the numerical solutions remain bounded in the broken <em>H</em><sup>1</sup>-norm. Then, by leveraging the aforementioned novel estimates and sidestepping the reliance on inverse inequalities, the unconditional uniform superclose result is rigorously derived, which transcends the constraints of the negative power of the perturbation parameter <span><math><mrow><mi>A</mi><mo>=</mo><msqrt><mrow><mi>β</mi><mo>(</mo><mn>1</mn><mo>−</mo><mi>β</mi><mo>)</mo><mi>R</mi></mrow></msqrt></mrow></math></span> and the limitations imposed by the ratio between the temporal step <em>τ</em> and spatial partition parameter <em>h</em>. Furthermore, an application of the economic interpolation post-processing technique enables the procurement of superconvergence estimates for the devised numerical schemes. Ultimately, the theoretical analysis is strengthened through the conduct of numerical experiments.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"207 ","pages":"Pages 41-59"},"PeriodicalIF":2.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145996272","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

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

Computers & Mathematics with Applications Pub Date : 2026-03-15 Epub Date: 2026-01-30 DOI: 10.1016/j.camwa.2026.01.033

Ruibo Zhang , Fengjun Li , Jianqiang Liu

{"title":"Solving the Monge-Ampère equation via Poisson series physics-informed neural networks and its convergence analysis","authors":"Ruibo Zhang , Fengjun Li , Jianqiang Liu","doi":"10.1016/j.camwa.2026.01.033","DOIUrl":"10.1016/j.camwa.2026.01.033","url":null,"abstract":"<div><div>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 <span><span>https://github.com/RuiboZhangping/PSPINN</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 316-333"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078330","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

Numerical solution of mixed-dimensional PDEs using a neural preconditioner 基于神经预调节器的混合维偏微分方程数值解

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-03-15 Epub Date: 2026-01-06 DOI: 10.1016/j.camwa.2025.12.013

Nunzio Dimola, Nicola Rares Franco, Paolo Zunino

{"title":"Numerical solution of mixed-dimensional PDEs using a neural preconditioner","authors":"Nunzio Dimola, Nicola Rares Franco, Paolo Zunino","doi":"10.1016/j.camwa.2025.12.013","DOIUrl":"10.1016/j.camwa.2025.12.013","url":null,"abstract":"<div><div>Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenges due to their inherent ill-conditioning. Moreover, the computational workload increases considerably when attempting to accurately capture the behavior of the system under significant variations or uncertainties in the low-dimensional structures such as fractures, fibers, or vascular networks, due to the inevitable necessity of running multiple simulations. In this work, we present a novel preconditioning strategy that leverages neural networks and unsupervised operator learning to design an efficient preconditioner specifically tailored to a class of 3D-1D mixed-dimensional PDEs. The proposed approach is capable of generalizing to varying shapes of the 1D manifold without retraining, making it robust to changes in the 1D graph topology. Moreover, thanks to convolutional neural networks, the neural preconditioner can adapt over a range of increasing mesh resolutions of the discrete problem, enabling us to train it on low resolution problems and deploy it on higher resolutions. Numerical experiments validate the effectiveness of the preconditioner in accelerating convergence in iterative solvers, demonstrating its appeal and limitations over traditional methods. This study lays the groundwork for applying neural network-based preconditioning techniques to a broader range of coupled multi-physics systems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 58-79"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940425","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

Linear relaxation schemes with asymptotically compatible energy law for time-fractional phase-field models 具有渐近相容能量律的时间分数相场模型线性松弛方案

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-03-15 Epub Date: 2026-01-16 DOI: 10.1016/j.camwa.2026.01.008

Hui Yu , Zhaoyang Wang , Ping Lin

{"title":"Linear relaxation schemes with asymptotically compatible energy law for time-fractional phase-field models","authors":"Hui Yu , Zhaoyang Wang , Ping Lin","doi":"10.1016/j.camwa.2026.01.008","DOIUrl":"10.1016/j.camwa.2026.01.008","url":null,"abstract":"<div><div>In this paper, we propose a variable time-step linear relaxation scheme for time-fractional phase-field equations with a free energy density in general polynomial form. The <span><math><mrow><mi>L</mi><msup><mn>1</mn><mo>+</mo></msup></mrow></math></span>-CN formula is used to discretize the fractional derivative, and an auxiliary variable is introduced to approximate the nonlinear term by directly solving algebraic equations rather than differential-algebraic equations as in the invariant energy quadratization (IEQ) and the scalar auxiliary variable (SAV) approaches. The developed semi-discrete scheme is second-order accurate in time, and the inconsistency between the auxiliary and the original variables does not deteriorate over time. Furthermore, we take the time-fractional volume-conserved Allen-Cahn equation, the time-fractional Cahn-Hilliard equation, and the time-fractional Swift-Hohenberg equation as examples to demonstrate that the constructed schemes are energy stable and that the discrete energy dissipation law is asymptotically compatible with the classical one when the fractional-order parameter <span><math><mrow><mi>α</mi><mo>→</mo><msup><mn>1</mn><mo>−</mo></msup></mrow></math></span>. Several numerical examples demonstrate the effectiveness of the proposed scheme. In particular, numerical results confirm that the auxiliary variable remains well aligned with the original variable, and the error between them does not continue to increase over time before the system reaches steady state.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 192-211"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979432","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