Computers & Mathematics with Applications最新文献

Two-grid mixed finite element analysis of semi-linear second order hyperbolic problem

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-03 DOI: 10.1016/j.camwa.2025.03.035

Jiansong Zhang, Yanyu Liu

引用次数: 0

A new and efficient meshfree method to solve partial differential equations: Application to three-dimensional transient heat transfer problems

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-03 DOI: 10.1016/j.camwa.2025.03.034

Daud Ali Abdoh

{"title":"A new and efficient meshfree method to solve partial differential equations: Application to three-dimensional transient heat transfer problems","authors":"Daud Ali Abdoh","doi":"10.1016/j.camwa.2025.03.034","DOIUrl":"10.1016/j.camwa.2025.03.034","url":null,"abstract":"<div><div>The paper presents the average radial particle method (ARPM), a new mesh-free technique for solving partial differential equations (PDEs). Here, we use the ARPM to solve 3D transient heat transfer problems. ARPM numerically approximates spatial derivatives by discretizing the domain by particles such that each particle is only affected by its direct neighbors. One feature that makes ARPM different is using a representative neighboring particle whose average variable value, like temperature, is used to approximate first and second spatial derivatives. ARPM has several advantages over other numerical methods. It is highly efficient, with a time requirement of only 0.6 µs per particle per step. It makes conducting rapid simulations with half a million particles in one minute possible. It is also distinct from other methods because it does not suffer from boundary or surface effects. Besides, the ARPM application is straightforward and could be easily integrated into software packages. Additionally, ARPM has lower convergence requirements for both time and space. The method's effectiveness is validated through five problems with different configurations and boundary conditions, demonstrating its accuracy and efficiency.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 181-202"},"PeriodicalIF":2.9,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759533","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

MFPC-PIML: Physics-informed machine learning based on multiscale Fourier feature phase compensation

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-03 DOI: 10.1016/j.camwa.2025.03.026

Naixing Feng , Shuiqing Zeng , Xianpeng Wang , Jinfeng Zhu , Atef Z. Elsherbeni

{"title":"MFPC-PIML: Physics-informed machine learning based on multiscale Fourier feature phase compensation","authors":"Naixing Feng , Shuiqing Zeng , Xianpeng Wang , Jinfeng Zhu , Atef Z. Elsherbeni","doi":"10.1016/j.camwa.2025.03.026","DOIUrl":"10.1016/j.camwa.2025.03.026","url":null,"abstract":"<div><div>The paradigm of physics-driven forward electromagnetic computation holds significance for enhancing the accuracy of network approximations while reducing the dependence on large-scale datasets. However, challenges arise during the training process when dealing with objective functions characterized by high-frequency and multi-scale features. These challenges frequently occur as difficulties in effectively minimizing loss or encountering conflicts among competing objectives. To overcome these obstacles, we carried out analysis leveraging the Neural Tangent Kernel (NTK) as our theoretical framework for analysis. Through this, we propose a novel architectural solution: a Multi-scale Fourier Feature Phase Compensation (MFPC) technology, according to Gaussian kernel mapping. This architecture leverages a Gaussian kernel to enhance the spectral representation of coordinate data, expanding the frequency domain coverage of Fourier feature mapping. Additionally, by compensating for phase loss inherent in conventional Fourier mapping, our approach effectively mitigates training difficulties, accelerates convergence, and significantly improves the model's accuracy in capturing high-frequency components. Our research comprises a range of challenging examples, including the high-frequency Poisson equation and the isotropic layered medium scattering model. Through these examples, we demonstrate the proficiency of our proposed method in accurately solving high-frequency, multi-scale Partial Differential Equation (PDE) equations. This highlights its potential not only in forward modeling but also in solving evolution and inverse problems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 166-180"},"PeriodicalIF":2.9,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759532","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

Improved accuracy of an analytical approximation for option pricing under stochastic volatility models using deep learning techniques

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-02 DOI: 10.1016/j.camwa.2025.03.029

Donghyun Kim , Jeonggyu Huh , Ji-Hun Yoon

{"title":"Improved accuracy of an analytical approximation for option pricing under stochastic volatility models using deep learning techniques","authors":"Donghyun Kim , Jeonggyu Huh , Ji-Hun Yoon","doi":"10.1016/j.camwa.2025.03.029","DOIUrl":"10.1016/j.camwa.2025.03.029","url":null,"abstract":"<div><div>This paper addresses the challenge of pricing options under stochastic volatility (SV) models, where explicit formulae are often unavailable and parameter estimation requires extensive numerical simulations. Traditional approaches typically either rely on large volumes of historical (option) data (data-driven methods) or generate synthetic prices across wide parameter grids (model-driven methods). In both cases, the scale of data demands can be prohibitively high. We propose an alternative strategy that trains a neural network on the <em>residuals</em> between a fast but approximate pricing formula and numerically generated option prices, rather than learning the full pricing function directly. Focusing on these smaller, smoother residuals notably reduces the complexity of the learning task and lowers data requirements. We further demonstrate theoretically that the Rademacher complexity of the residual function class is significantly smaller, thereby improving generalization with fewer samples. Numerical experiments on fast mean-reverting SV models show that our residual-learning framework achieves accuracy comparable to baseline networks but uses only about one-tenth the training data. These findings highlight the potential of residual-based neural approaches to deliver efficient, accurate pricing and facilitate practical calibration of advanced SV models.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 150-165"},"PeriodicalIF":2.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143748609","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

Aubin–Nitsche-type estimates for space-time FOSLS for parabolic PDEs

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-01 DOI: 10.1016/j.camwa.2025.03.017

Thomas Führer , Gregor Gantner

引用次数: 0

Convergence analysis of variable-time-step BDF2/spectral approximations for optimal control problems governed by linear reaction-diffusion equations

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-01 DOI: 10.1016/j.camwa.2025.03.023

Tong Lyu, Xingyang Ye, Xiaoyue Liu

{"title":"Convergence analysis of variable-time-step BDF2/spectral approximations for optimal control problems governed by linear reaction-diffusion equations","authors":"Tong Lyu, Xingyang Ye, Xiaoyue Liu","doi":"10.1016/j.camwa.2025.03.023","DOIUrl":"10.1016/j.camwa.2025.03.023","url":null,"abstract":"<div><div>In this paper, we focus on the optimal control problem governed by a linear reaction-diffusion equation with constraints on the control variable. We construct an effective fully-discrete scheme to solve this problem by using the variable-time-step two-step backward differentiation formula (VSBDF2) in time combining with the Galerkin spectral methods in space. By using the recently developed techniques including the discrete orthogonal convolution (DOC) kernels, and the positive definiteness of BDF2 convolution kernels, we obtain an error estimate of order <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mi>p</mi></mrow></msup><mo>)</mo></math></span> under a mild restriction <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4.8645</mn></mrow></mfrac><mo>≤</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>≤</mo><mn>4.8645</mn></math></span> for the ratio of adjacent time steps <span><math><msub><mrow><mi>r</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>, where <span><math><mi>τ</mi><mo>,</mo><mi>N</mi><mo>,</mo><mi>p</mi></math></span> are the maximum time step size, polynomial degree, and regularity of the exact solution respectively. Several numerical examples are provided to validate the theoretical results and to demonstrate the efficiency of the proposed method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"189 ","pages":"Pages 48-69"},"PeriodicalIF":2.9,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738387","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 simulation of pollutant concentration patterns of a two-dimensional congestion traffic

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-01 DOI: 10.1016/j.camwa.2025.03.020

Anis Chaari , Waleed Mouhali , Mohammed Louaked , Nacer Sellila , Houari Mechkour

{"title":"Numerical simulation of pollutant concentration patterns of a two-dimensional congestion traffic","authors":"Anis Chaari , Waleed Mouhali , Mohammed Louaked , Nacer Sellila , Houari Mechkour","doi":"10.1016/j.camwa.2025.03.020","DOIUrl":"10.1016/j.camwa.2025.03.020","url":null,"abstract":"<div><div>An accurate calculation of the traffic density is a key factor in understanding the formation and evolution of the traffic-related emission concentration in urban areas. We have developed a two-dimensional numerical model to solve traffic flow/pollution coupled problem whose pollution source is generated by the density of vehicles. The numerical solution of this problem is calculated via an algorithm that combines the Characteristic method for temporal discretization with the Lagrange-Galerkin finite element method for spatial discretization. This algorithm is validated by varying certain physical parameters of the model (effective viscosity). We study the pollutant concentration diffusion impacted by the presence of an obstacle in a bifurcation topology traffic. We draw attention to the influence of the wind velocity as well as its direction on the pollutant concentration diffusion, in several situations. The temporal evolution of pollutant concentration at various relevant locations in the domain (before and after an obstacle) is studied for a single velocity and two wind directions. Different regimes have been observed for transport pollution depending on time and the wind direction.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"188 ","pages":"Pages 97-114"},"PeriodicalIF":2.9,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A kind of fast successive permutation iterative algorithms with the relaxation factor for nonlinear radiation diffusion problem

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-31 DOI: 10.1016/j.camwa.2025.03.033

Qiuyan Xu, Zhiyong Liu

引用次数: 0

A new error analysis of a linearized BDF2 Galerkin scheme for Schrödinger equation with cubic nonlinearity

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-31 DOI: 10.1016/j.camwa.2025.03.025

Huaijun Yang

引用次数: 0

Phase-field computation for 3D shell reconstruction with an energy-stable and uniquely solvable BDF2 method

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-31 DOI: 10.1016/j.camwa.2025.03.022

Dongting Cai, Boyi Fu, Renjun Gao, Xiangjie Kong, Junxiang Yang

{"title":"Phase-field computation for 3D shell reconstruction with an energy-stable and uniquely solvable BDF2 method","authors":"Dongting Cai, Boyi Fu, Renjun Gao, Xiangjie Kong, Junxiang Yang","doi":"10.1016/j.camwa.2025.03.022","DOIUrl":"10.1016/j.camwa.2025.03.022","url":null,"abstract":"<div><div>Three-dimensional (3D) reconstruction from points cloud is an important technique in computer vision and manufacturing industry. The 3D volume consists of a set of voxels which preserves the characteristics of scattered points. In this paper, a 3D shell (narrow volume) reconstruction algorithm based on the Allen–Cahn (AC) phase field model is proposed, aiming to efficiently and accurately generate 3D reconstruction models from point cloud data. The algorithm uses a linearized backward differentiation formula (BDF2) for time advancement and adopts the finite difference method to perform spatial discretization, unconditional energy stability and second-order time accuracy can be achieved. The present method is not only suitable for 3D reconstruction of unordered data but also has the effect of adaptive denoising and surface smoothing. In addition, theoretical derivation proves the fully discrete energy stability. In numerical experiments, the complex geometric models, such as Asian dragon, owl, and turtle, will be reconstructed to validate the energy stability. The temporal accuracy is validated by the numerical reconstructions of a Costa surface and an Amremo statue. Later, we reconstruct the Stanford dragon, teapot, and Thai statue to further investigate the capability of the proposed method. Finally, we implement a comparison study using a 3D happy Buddha. The numerical results show that the algorithm still has good numerical stability and reconstruction accuracy at large time steps, and can significantly preserve the detailed structure of the model. This research provides an innovative solution and theoretical support for scientific computing and engineering applications in the field of 3D reconstruction.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"189 ","pages":"Pages 1-23"},"PeriodicalIF":2.9,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738385","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