Computers & Mathematics with Applications最新文献_第6页

A splitting-based KPIK method for eddy current optimal control problems in an all-at-once approach 涡流最优控制问题的一种基于分裂的KPIK方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-08 DOI: 10.1016/j.camwa.2025.03.038

Min-Li Zeng , Martin Stoll

引用次数: 0

A nonoverlapping domain decomposition method for extreme learning machines: Elliptic problems 极值学习机的非重叠区域分解方法：椭圆型问题

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-08 DOI: 10.1016/j.camwa.2025.04.001

Chang-Ock Lee , Youngkyu Lee , Byungeun Ryoo

{"title":"A nonoverlapping domain decomposition method for extreme learning machines: Elliptic problems","authors":"Chang-Ock Lee , Youngkyu Lee , Byungeun Ryoo","doi":"10.1016/j.camwa.2025.04.001","DOIUrl":"10.1016/j.camwa.2025.04.001","url":null,"abstract":"<div><div>Extreme learning machine (ELM) is a methodology for solving partial differential equations (PDEs) using a single hidden layer feed-forward neural network. It presets the weight/bias coefficients in the hidden layer with random values, which remain fixed throughout the computation, and uses a linear least squares method for training the parameters of the output layer of the neural network. It is known to be much faster than Physics informed neural networks. However, classical ELM is still computationally expensive when a high level of representation is desired in the solution as this requires solving a large least squares system. In this paper, we propose a nonoverlapping domain decomposition method (DDM) for ELMs that not only reduces the training time of ELMs, but is also suitable for parallel computation. We introduce local neural networks, which are valid only at corresponding subdomains, and an auxiliary variable at the interface. We construct a system on the variable and the parameters of local neural networks. A Schur complement system on the interface can be derived by eliminating the parameters of the output layer. The auxiliary variable is then directly obtained by solving the reduced system after which the parameters for each local neural network are solved in parallel. A method for initializing the hidden layer parameters suitable for high approximation quality in large systems is also proposed. Numerical results that verify the acceleration performance of the proposed method with respect to the number of subdomains are presented.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"189 ","pages":"Pages 109-128"},"PeriodicalIF":2.9,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143791396","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

Local Petrov-Galerkin meshfree method based on radial point interpolation for the numerical solution of 2D linear hyperbolic equations with variable coefficients 基于径向点插值的二维变系数线性双曲型方程的局部Petrov-Galerkin无网格法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-08 DOI: 10.1016/j.camwa.2025.03.031

Masoud Pendar, Kamal Shanazari

引用次数: 0

Superconvergence analysis of the decoupled and linearized mixed finite element methods for unsteady incompressible MHD equations 非定常不可压缩MHD方程解耦和线性化混合有限元法的超收敛分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-05 DOI: 10.1016/j.camwa.2025.03.032

Xiaochen Chu , Xiangyu Shi , Dongyang Shi

{"title":"Superconvergence analysis of the decoupled and linearized mixed finite element methods for unsteady incompressible MHD equations","authors":"Xiaochen Chu , Xiangyu Shi , Dongyang Shi","doi":"10.1016/j.camwa.2025.03.032","DOIUrl":"10.1016/j.camwa.2025.03.032","url":null,"abstract":"<div><div>The purpose of this article is to explore the superconvergence behavior of the first-order backward-Euler (BE) implicit/explicit fully discrete schemes for the unsteady incompressible MHD equations with low-order mixed finite element method (MFEM) by utilizing the scalar auxiliary variable (SAV) and zero-energy-contribution (ZEC) methods. Through dealing with linear terms in implicit format and nonlinear terms in explicit format, the original problem is decomposed into several subproblems, which effectively reduces the amount of calculation. Particularly, a new high-precision estimation is given, which acts as a requisite role in getting the expected results. Following this, combined with a simple, effective and economic interpolation post-processing approach, the superclose and superconvergence error estimates of the decoupled and linearized fully discrete finite element SAV-BE scheme are rigorously derived. And the derivation process is also applicable to the ZEC-BE scheme. Finally, the corresponding numerical simulations are carried out to confirm the accuracy and reliability of our theoretical findings.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"188 ","pages":"Pages 160-182"},"PeriodicalIF":2.9,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143777067","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

Asynchronous multimodal PINN pre-train framework based on TransVNet(MPP-TV) and its application in numerical solutions of the Cauchy problem for the Hamilton-Jacobi equation 基于TransVNet的异步多模态PINN预训练框架（MPP-TV）及其在Hamilton-Jacobi方程Cauchy问题数值解中的应用

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-05 DOI: 10.1016/j.camwa.2025.03.027

Tianhao Chen , Zeyu Li , Pengbo Xu , Haibiao Zheng

{"title":"Asynchronous multimodal PINN pre-train framework based on TransVNet(MPP-TV) and its application in numerical solutions of the Cauchy problem for the Hamilton-Jacobi equation","authors":"Tianhao Chen , Zeyu Li , Pengbo Xu , Haibiao Zheng","doi":"10.1016/j.camwa.2025.03.027","DOIUrl":"10.1016/j.camwa.2025.03.027","url":null,"abstract":"<div><div>The Hamilton-Jacobi(HJ) equation represents a class of highly nonlinear partial differential equations. Classical numerical techniques, such as finite element methods, face significant challenges when addressing the numerical solutions of such nonlinear HJ equations. However, recent advances in neural network-based approaches, particularly Physics-Informed Neural Networks (PINNs) and neural operator methods, have ushered in innovative paradigms for numerically solving HJ equations. In this work, we leverage the PINN approach, infused with the concept of neural operators. By encoding and extracting features from the discretized images of functions through TransVNet, which is a novel autoencoder architecture proposed in this paper, we seamlessly integrate Hamiltonian information into PINN training, thereby establishing a novel scientific computation framework. Additionally, we incorporate the vanishing viscosity method, introducing viscosity coefficients in our model, which equips our model to tackle potential singularities in nonlinear HJ equations. These attributes signify that our MPP-TV framework paves new avenues and insights for the generalized solutions of nonlinear HJ equations.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 203-230"},"PeriodicalIF":2.9,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143777485","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

Fourth order time-stepping VEM for the 2D acoustic wave equations 二维声波方程的四阶时间步进VEM

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-04 DOI: 10.1016/j.camwa.2025.03.030

Gouranga Pradhan, Bhupen Deka

引用次数: 0

A low-rank solver for conforming multipatch Isogeometric Analysis 符合多块等距分析的低秩求解器

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-04 DOI: 10.1016/j.camwa.2025.03.036

Monica Montardini , Giancarlo Sangalli , Mattia Tani

引用次数: 0

Explicit T-coercivity for the Stokes problem: A coercive finite element discretization Stokes问题的显式t -矫顽力：矫顽力有限元离散化

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-04 DOI: 10.1016/j.camwa.2025.03.028

Patrick Ciarlet Jr , Erell Jamelot

引用次数: 0

Two-grid mixed finite element analysis of semi-linear second order hyperbolic problem 半线性二阶双曲型问题的两网格混合有限元分析

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 一种新的高效的求解偏微分方程的无网格法：在三维瞬态传热问题中的应用

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